research article machine vision based automatic...

Research ArticleMachine Vision Based Automatic Detection Method ofIndicating Values of a Pointer Gauge

Jiannan Chi12 Lei Liu1 Jiwei Liu3 Zhaoxuan Jiang1 and Guosheng Zhang2

1School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China2Key Laboratory of Operation Safety Technology on Transport Vehicles Ministry of Transport Beijing 100088 China3School of Automation Shenyang Aerospace University Shenyang 110136 China

Correspondence should be addressed to Jiannan Chi ustbjncustbeducn

Received 4 November 2014 Revised 27 December 2014 Accepted 4 February 2015

Academic Editor Chih-Cheng Hung

Copyright copy 2015 Jiannan Chi et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study proposes an automatic reading approach for a pointer gauge based on computer vision Moreover the study aims tohighlight the defects of the current automatic-recognitionmethod of the pointer gauge and introduces a method that uses a coarse-to-fine scheme and has superior performance in the accuracy and stability of its reading identification First it uses the regiongrowing method to locate the dial region and its center Second it uses an improved central projection method to determine thecircular scale region under the polar coordinate system and detect the scale marks Then the border detection is implementedin the dial image and the Hough transform method is used to obtain the pointer direction by means of pointer contour fittingFinally the reading of the gauge is obtained by comparing the location of the pointer with the scale marksThe experimental resultsdemonstrate the effectiveness of the proposed approachThis approach is applicable for reading gauges whose scalemarks are eitherevenly or unevenly distributed

1 Introduction

With the rapid development of information technology thedigital meter has been widely applied But pointer gaugeis still very popular in various fields due to its simplestructure high reliability low price and easy operationHowever owing to the nondigital signal output of the pointergauge a computer cannot conduct the processing and remotetransmission of the data collected by the pointer gauge Thislimits its application Therefore the method of providing thepointer gauge with digital features such as automatic readingand transforming the collected value into the digital signalshould be urgently solved for wider application In particularin the process of calibration or metrological verification [1]the checkers need to read the output values of the standardand the indicating value of the calibrated gauge respectivelyand then make a comparison Random errors may occur inthis case due to the limited acuity of human observationFurthermore when an operator is far away from the gaugethe operator has to repeat the reading and manually recordthe indicating value This not only increases the operatorrsquos

burden but also lowers the efficiency of the gauge calibrationTo overcome the above limitations and to make the pointergauge more user-friendly new technologies are expected todigitalize its reading At present machine vision is widelyutilized to detect the gauge dial and pointer and then conducta reading

This study aims at the application of pressure gaugeverification and proposes a computer vision based automaticreading approach for a pointer gauge that adopts a coarse-to-fine scheme In this approach the dial region and itscenter of the pointer gauge are located by first using theregion growing method Then the circular scale region isdetermined by the adaptive threshold method under thepolar coordinate system In the circular region the scalemarks distribution diagram is produced using improvedcentral projection According to the scale marks distributiondiagram the main scale marks are located in the circularscale region of the dial In the following steps the Houghtransformation is used to detect the pointer in the dialregion and obtain its direction Finally the distance method

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 283629 19 pageshttpdxdoiorg1011552015283629

2 Mathematical Problems in Engineering

PC Image

Drive card Stepping

Other signal

CCD or

Stepping

High

standard

Tested

Worktable

Benchmarksignal

generator

collectors

capture card

motor driver

CMOS camera

motor

precision

gaugegauge

Figure 1 Hardware structure of the automatic recognition of the indicating value of the pointer gauge

Image Image

acquiring

Preprocessing gauge image

Pointerand scale

Automatic

reading

Gaugereadingoutput

Reading identification

preprocessing marks detection identification

Detection

of pointer

and scale

Figure 2 The image processing procedure of the automatic recognition of the indicating value of the pointer gauge

is adopted to obtain the indicating value of the gauge bycomparing the pointer direction with the position of the scalemarks

Since the indicating value is determined by comparing thepointer direction and the locations of the scale marks thisapproach is also suitable for gauges wherein the scale marksare unevenly distributed Therefore the proposed approachis in fact a general approach for gauge calibration

2 Related Work

21 Configuration of Hardware System Used in Gauge Ver-ification The hardware system used in gauge verificationgenerally comprises the following configuration [2ndash5] whichis shown in Figure 1 During the working process the highprecise gauge and the calibrated gauge are placed on theworktable A computer sends impulse signals to the motordriver Therefore the stepping motor is controlled to maketheworktablemove to allow for the adjustment of the locationof the gauge so that the gauges can be appropriately placedin the camerarsquos view while the standard signal source sendsreference signals to the calibrated pointer gauge and the highprecise gauge The indicating value of the high precise gaugeis treated as standard data Next computer vision is applied toautomatically recognize the values indicated by the calibratedand standard gauges Finally a comparison is made betweenthe two values and the verification result is reached

For some other pointer gauges the standard data pro-duced by the reference signal generator is directly inputted

into the computer by the other signal-acquisition equipmentThe verification result is achieved by comparing the standarddata with the indicating value of the calibrated gauge whichis extracted using computer vision

22 The Process of Automatic Reading of the Pointer GaugeBased on Computer Vision Figure 2 shows the procedure ofthe image processing used to recognize the pointer gaugevalue First to improve the image quality the gauge imagehas to be preprocessed by means of noise suppression andimage enhancement Next image processing and analyzingmethods are used to detect the pointer and scale marksAccording to the pointer direction and the location of scalemarks the value indicated by the pointer gauge can bedetected Finally the indicating value results are outputtedTherefore the automatic recognition methods of the gaugeindicating value mainly include three parts

(1) image preprocessing aimed to improve image qualityand suppress noise

(2) gauge pointer and scale marks detection based onimage processing and analyzing

(3) automatic recognition of the pointer gauge indicatingvalue

23 Related Work of the Pointer Gauge Indicating ValueDetection In the existing literature the pointer gaugeimage should be preprocessed to remove noise or enhance

Mathematical Problems in Engineering 3

the image especially for the images extracted from industrialfields Image preprocessing improves the image resolutionThus it is easier to detect the features relating to pointer andscale marks by means of image analyzing

Image preprocessing of the pointer gauge mainly com-prises two parts First image preprocessing is used to filterout interference and noise that result from the change ofenvironment For example in [6] the homomorphic filteringmethod was adopted to process the gauge image that hasa large area of glare and reflection Second image prepro-cessing is used to correct an image distortion caused bycamera imaging or different shooting angles For instance[7] discussed how to reduce the reading error when thegauge dial was uneven with the camera lens surface Thepapers [8 9] proposed an intelligent method of gauge valuereading to avoid the influence of imaging distortion thismethod was able to correct the angle between the pointer andthe zero-scale marks and the angle between the zero-scalemarks and the other longer scale marks It also adopted theNewton interpolation method to approximate the functionalrelationships between the pointer angle and its indicatingvalue

After image preprocessing image segmentation shouldbe implemented to obtain a binarization image wherein thethreshold-segmentation method is always applied [10ndash13] Inthe following step image thinning needs to be conducted inthe binarization image to achieve a one-pixel-wide pointerimageThen straight-line fitting is used to detect the pointerSo the key point of the automatic recognition of the gaugeindicating value is the detection of the pointer and scalemarks In the existing literature several methods for pointerdetection such as subtractionmethod the templatematchingmethod the Hough transform method and the central pro-jectionmethodwere proposed In the subtractionmethod [414 15] two gauge images with roughly the same backgroundswere taken by camera while the pointer pointed toward adifferent scaleWhen one image was subtracted from anotherone there were only two pointers left in the difference imageNext the difference image was segmented to detect thepointer Finally the gaugersquos indicating value could be obtainedby calculating the position of the pointer and scale marksThe subtraction method was easily implemented by meansof image subtraction However the different image not onlyreserves the pointer target but also leaves out a lot of noise dueto the influence of illuminationTherefore in many cases thesubtraction method does not produce reliable results

In the template feature method [16] the features thatrepresent the pointer and its direction such as shape areaand gray distribution formed amultiple parameters templateused to match the pointer in the gauge image for pointerdetection Since the template comprises multiple cues of thepointer and its direction the template feature method couldavoid the influence of an uneven illumination and otherenvironmental changing factors However the process of atemplate match is too complicated to accurately detect thepointer

The Hough transform method has often been used inpointer detection In [17 18] after edge detection and imagethinning in the gauge image the Hough transform method

or its improved version was applied to detect the pointer byfitting the pointer edge The Hough transform method couldachieve good results for the pointer gauge that has manywords and symbols on the dial In [19 20] a novel pointerdetection method called central projection was describedThemain idea of the central projection method was to searchfor the pointer location bymeans of calculating the projectionfrom the feature points to the known central point Everyprojection value corresponded to the angle of the straightline that connected the projection and central points Theremust be an angle that corresponds to the largest numberof projection points and represents the pointer Hence thecentral projection method was always used to determine thelocation of the gauge pointer

The least squares method [21] was also a straight-linefitting method just like the Hough transformmethod whichwas used to detect the pointer Compared with the Houghtransform method the least squares method required fewercalculations

After the pointer was detected angle and distance meth-ods [22]were always used to determine the indicating value ofthe point gauge The angle method recognized the indicatingvalue by calculating the deflection angle between the detectedpointer and the zero-scale mark according to the formula119872 times 120573120572 Here 119872 was the range 120572 was the premeasuredangle between the maximum- and zero-scale mark and 120573

was the angle between the current pointer and zero-scalemarkThe distancemethod [23] obtained the indicating valueby calculating the distance between the pointer and nearestscale mark In this method each scale reticule was locatedand labeled with the corresponding scale number in a two-dimensional coordinate system If the distance between thepointer and each reticule is as follows

119889119894=

1003816100381610038161003816119860119909119894 + 119861119910119894 + 1198621003816100381610038161003816

radic1198602 + 1198612 (1)

then the indicating value of the pointer is

119878119899= 119878119871+

1198891

1198891+ 1198890

times (119878119867minus 119878119871) (2)

Here (119909119894 119910119894) is the coordinate of the points in the scale marks

119889119894is the distance between the point and the line 119860119909 + 119861119910 +

119862 = 0 119878119899represents the indicating value of the pointer 119878

119867

and 119878119871are the values of the scale marks which are located

on both sides of the pointer and 1198891and 119889

0are the distance

between the pointer and the nearest scale marks on bothsides respectively The angle method is simpler than thedistance method but it is unsuitable for the pointer gauge inwhich the scale is uneven

3 Overview of Our Work

As mentioned above the current methods for gauge readingrecognition are limited in terms of their practical applicationmainly due to two deficiencies (1)Theexistingmethods wereall implemented in the global gauge images Therefore thepointer and scale marks segmentation cannot be accurately


conducted when there is some interference or where thereis some complex writing on the gauge dial (2) In manystudies the scale marks are not precisely detected Hence theindicating value of the pointer gauge with an uneven scalecannot be recognized

This study aims to overcome the shortcomings of theexisting methods As its contextual application it also aimsto improve the calibration of the pressure gauge and developan automatic recognition method of pointer gauge readingsbased on machine vision This method implements a schemethat takes detection from coarse to fine in terms of thepointer and scale marks detection First the pointer gaugersquosdial region is located in a global image Then the dialrsquosannular scale region is located In the following steps thescale marks are detected in the annular scale region and thepointer is detected in the dial region Finally based on theresults of the detection of the pointer and scale marks theimproved distance method is used to recognize the gaugersquosvalue Since the improved distance method is implementedfrom the coarse region to the fine target it has a strongability for suppressing interference Since the indicating valueis obtained from the pointer and scale marks detection themethod is also suitable for reading the gauge whose scalemarks are unevenly distributed

31 Machine Vision Based Pressure Gauge Verification SystemMetrological departments usually calibrate pressure gaugeswith piston manometers In this case the standard pressureoutput of piston manometers given by manually addedweights is passed on to the tested pressure gauge Then thequalification of the pressure gauge is determined throughreading analysis and comparison of the indicating value Ingeneral verification personnel manually handle this processthrough observation by recording and analyzing the indicat-ing value of the gauge panel Many problems still exist withthis verification method They include (1) low accuracy andrepeatability in human visual observations and (2) poor workefficiency due to the large workload of verification personnelHence development of an automatic verification methodfor the pressure pointer gauge will boost the advancementof the technology used in their production and verificationcapabilities The system composition for pointer pressuregauge verification is shown in Figure 3 We can see thatimages of pointer gauges are obtained through a camera andprocessed and analyzed by computer wherein the indicatingvalues of the standard pressure gauge and the test gaugeare detected and recognized The final results of the gaugereading will be displayed on amonitor to operators and reacha verification conclusion based on the analyses of the abovereadingsThe detection software also has suchmultifunctionsas the storage of historical data graphical display and imageswitching to realize the automatic verification of pointergauges

32 Introduction of OurWork In this study a new automaticrecognition method of the pointer gauge that indicates valueis proposed Figure 4 shows a block diagram of this method

In general the computer vision based automatic recog-nition method of indicating value comprises two parts One

Piston gaugeCalibrated gauge

Standard gauge

Display PC

Camera

Image capture card

Figure 3 Schematic of a machine vision based pressure gaugeverification system

part is the detection of the indicating value of the pointergauge This mainly includes the scale detection and thepointer detection which refer to the location of the dialregion and the dial center the determination of the annularscale region in the dial the scale detection and the pointerdetection The other is the automatic recognition of thereading Namely it makes the final judgment of the gaugereading according to the detected direction of the pointer andthe distribution of the scale marks As seen in Figure 4 theautomatic recognition of the indicating value proposed inthis paper falls into five steps

(1) The dial region and its center location first in theentire image the dial region can be determined bysemi-interaction (using the mouse to drop downthe box in the image) The pixel point with thebiggest gray value is searched out in the dial regionand taken as the seed point of the region growingmethod used to produce the circular region in thedial In the process of the region growing methodthe similarity threshold value between the pixel pointsis automatically determined Finally according to theresults of the region growing method the radius andcenter of the circular dial are obtained

(2) Determination of the scale region in the dial theimage coordinate is first converted into the polarcoordinate with the dial center as its origin whichis used to express the coordinate of each pixel in theimage Then by comparing the pixel sum of the lowgray value with that of the high gray value in theannular region the annular scale region in the dial isdetermined And finally it is copied into a new imageas the annular scale region

(3) The scale marks are detected using the central pro-jection method In the newly generated annular scaleregion image first the scale mark segmentation isconducted by theOSTUmethod to form the binariza-tion scale imageThen the angle of each line that linksthe black pixel with the circle center is calculatedand the number of each angle is obtained The angleswith large numbers (connecting line) in a narrowangle range correspond to the thick scalemarks (mainscales) on the dial Thus the angles of the scale marksin the scope of 0∘ndash360∘ are obtained


Scale detection by central projection method

Segment the image in annular scaleregion by OSTU to obtain the

binarization scale image

Traverse the black pixel points in theimage link each black point to the

circle center and then calculate the angleof the connecting line to get that of

each coarse scale mark

Detection of gauge pointer by Houghtransform

Utilize the Canny operator to performborder detection on the dial image

Use the adaptive threshold value toperform the Hough transform on dial

border image and fit the gauge pointercontour

Calculate the pointer direction within

The indicating value reading

Calculate the indicating valueaccording to the pointer direction and

the dial scale distribution

Dial region and center location

Search the pixel point with maximumgray in the dial region as the seed

Conduct region growing from the seedpoint and adaptively determine thesimilarity principle between the pixels

Obtain the center and radius ofcircular dial region by region growing

Determination of annular scale region in the dial

Convert the image into the polarcoordinates with the dial center as its

origin center

Determine the annular scale region bycomparison between the pixel sum oflow gray value and that of high gray

value

Copy the circular scale regionestablished into a new image

the scope of 0ndash Obtain the scale in the scope of 0ndash360degrees

360 degrees

Figure 4 The flow chart of the pointer gauge indicating value recognition

(4) Pointer detection first the Canny operator is usedto implement the border detection Then the Houghtransform method is used to fit the detected edgeand obtain the pointer contour Finally the pointerdirection is obtained according to the center positionand the pointer contour

(5) The indicating value is calculated according to thepointer direction and the dial scale distribution

4 Indicating Value Recognition Approach ofPointer Gauge

41 Pointer Gauge Indicating Value Detection As mentionedabove the detection of the indicating value is achievedthrough the scale and pointer detection As for the scaledetection first the gauge center and dial region should belocated followed by the extraction of the annular scale region


(a) Typical pointer gauge (b) The results of the dial region growing method

Figure 5 The diagram of the dial region growing results

and the scale mark detection Finally the detection of thepointer direction is performed

411 Dial Region and Its Center Location As for the detectionof the indicating value first the gauge pointer and its directionshould be detected to determine its rotation center In generalthe gaugersquos dial center is the pointerrsquos rotation center Hencefirst the dial center should be detected In this study thecircular dial region is detected for determining the dial centerAs is shown in Figure 5(a) typically there are the labelswords and scale marks in the circular dial Therefore it isdifficult to confirm the circular region of the dial by suchsegment methods as the border and threshold values Inview of the above this paper introduces the adaptive-region-growing method to locate the gaugersquos circular region andfurther to obtain its dial center The specific steps are asfollows

(1) The placement of the seed [24] since the dial isusually white the region with a high gray level orthe pixel point with the highest gray level in thegauge is certainly located at the part where the dialis Therefore the latter is selected as the seed point ofthe region growing

(2) Subject to the similarity of the pixel gray level theexpansion of the dial region is conducted from theseed point However it is hard to fix an appropriatesimilarity threshold value of the gray level betweenpixels As is shown in Figure 5(b) the circular dialregion cannot be completely produced with a smallthreshold value while an oversized dial region will begenerated with a large threshold value

This study proposes an adaptive method to determinethe similarity threshold value of the gray level the concreteprocess is as follows

(A) A small similarity threshold value 119879 of the graylevel is empirically chosen and then the dial regiongrowing method is conducted from the seed point

(B) The ratio of the circumscribed rectanglersquos length andwidth of the newly generated dial region is calculatedto detect whether it is in the 095ndash105 range

(C) If the ratio of the length and width fails to meetthe conditions in (B) the similarity threshold valuewould be increased with a certain step length (119878)and the first step (A) would continue to conductthe region growing from the seed point Howeverif it meets the conditions in (B) the growing regionwill be the circular dial region the center of thecircumscribed rectangle will be the circle center andthe smaller value between the length and width willbe the diameter of the circular region (Figure 6)

412 Polar Coordinate Based Scale Region Location

(1) Image in Polar Coordinates In general in light of thecircular permutation the pointer gauge scale marks aredistributed around the center Therefore to correctly andexpediently show where the scale marks in the image arethe polar coordinate system is utilized to position the pixelsin the image In this study a conversion from the imagecoordinates into the polar coordinates is performed Thismeans that the pixel coordinates expressed by the rectangularimage coordinate system are converted into those expressedby polar coordinates The polar coordinates defined in thisstudy are shown in Figure 7 the circle center being its origin

(2) Detection of the Scale Region in the Dial The procedurefor scale region detection based on the adaptive thresholdmethod is as follows

(A) The circular dial radius detected in Section 411 istaken as the initial radius 119877 its decreasing step lengthbeing 119887 and the initial 119899 = 1 In the gauge dial thegray value difference between the scale marks anddial background is generally rather large Thereforethe adaptive threshold value method can be adoptedto segment the scale In the polar coordinate theannular binarization image is gained by employing


(a) (b)

(c) (d)

Figure 6 The region growing results under different pixel similarity threshold values

90∘

60∘

210∘

150∘

120∘

180∘

240∘

270∘300∘

330∘

30∘

0∘

Figure 7 Schematic of the polar coordinate

the OSTU method [25] to perform the binarizationsegmentation in the annular region

(B) The ratio between the number of black andwhite pixelpoints in the annular binarization region between theradius 119877 and 119877minus119899lowast119887 is calculated and denoted by 119903

1

After reducing the inner radius according to the steplength 119887 the ratio between the number of black and

white pixel points in the region between 119877minus(119899+1)lowast119887and 119877 is computed and denoted by 119903

2

(C) If 1199031is obviously different from 119903

2 the inner radius

and the outer radius of the scale region would be 119877 minus(119899 + 1) lowast 119887 and 119877 respectively

(D) If 1199031is approximated to 119903

2 the annulus between 119877 minus

(119899 + 1) lowast 119887 and 119877 would still be in the circular scaleregion At thismoment let 119899 = 119899+1 the ratio betweenthe number of black and white pixel points in theannulus between 119877 minus (119899 + 1) lowast 119887 and 119877 is computedand is still denoted by 119903

2 Then go to (B) (Figure 8)

After obtaining the annular scale region in the abovepolar coordinate the scale region is selected on the basis ofangle and radius and copied into a new image called the scalemark region image119872 (Figure 9)

413 Scale Mark Detection Based on the Improved CentralProjection Method In the newly generated image119872 whichis the annular scale region the OSTU method is adopted tosegment the scale marks to form the binarized scale imageIn this image the pixel value of the scale mark is 0 (black)and those in other places are 255 (white) Each black pixelpoint and the circle center are linked and the slope 119870 ofthe connecting line is calculated according to the formula119896 = tan120572 wherein 120572 is the angle between the 119909-axis and


(a) (b)

(c)

Figure 8 Schematic of scale mark region detection

(a) (b)

Figure 9 The scale mark region diagram and its binarized image


x

y

0

(a) Schematic of the image coordinate system

x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4

(b) The rectangular coordinate system

Figure 10 Schematic of the image coordinate system and the rectangular coordinate system

the connecting line between the black pixel point and thecircular center Due to the origin of the image coordinatebeing in the top left corner and the119910-axis running downwardit is inconvenient to denote the central angle within thescope of 0∘ndash360∘ Therefore in this study the rectangularcoordinate system with the image center as its origin isintroduced to express the angle between the black pixelpoint on the scale mark and the circle center instead of theimage coordinate system As is shown in Figure 10 the anglesbetween the black pixel point and the circle center are in the0∘ndash360∘ range

After calculating the number for angle 120572 the angle witha large number (connecting lines) in a small angle range isthat of the thick scale mark (main scale) on the dialThe stepsto detect the scale mark by central projection are detailed asfollows

(1) The black pixel point and the image central pointthat is the circle center (119909

0 1199100) in the new image are linked

to determine the slope 119896 which is converted to an angleaccording to the following formula

120572 = arctan (119896) lowast 180

120587 (3)

(2) As shown in Figure 10 the image coordinate systemis transformed to a rectangular one The angle 120572 followingformula (4) is converted into an angle in the rectangularcoordinate

120579 = minus120572 119894 lt 119903 119895 gt 119903 the first quadrant

120579 = 180 minus 120572 119894 lt 119903 119895 lt 119903 the second quadrant

120579 = 180 minus 120572 119894 gt 119903 119895 lt 119903 the third quadrant

120579 = 360 minus 120572 119894 gt 119903 119895 gt 119903 the forth quadrant

(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940

Figure 11 The angle histogram

(3) An angle histogram is generated by recording theoccurrence frequency of each angle Figure 11 shows the anglehistogram

(4) The angle with the most occurrence times in thehistogram is selected and denoted by max all the angleswhose occurrence times are more thanmax 2 are foundTheoccurrence times of the angles are denoted by 119891(120579) Here 120579represents the angles that occur more than max 2

(5) For every angle 120579 we calculate the weighted averagevalue anglemean(119898) according the following to formula

anglemean (119898)

=119891 (120579 + 1) lowast (120579 + 1) + 119891 (120579) lowast (120579) + 119891 (120579 minus 1) lowast (120579 minus 1)

119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)

Here119898 is the sign of the angle


12057221205721

1205720

1205723

Thick scale marksy

x

Figure 12 The location of the thick scale marks

(6) Calculate specific value 119875 according to the followingformula

119875 =anglemean (119898)

anglemean (119898 + 1) (6)

If 119875 is within the 09ndash11 range anglemean(119898) is the angleof the thick scale mark All the angles sorted out successivelyare taken as 120572

0 1205721 1205722 which correspond to the thick

scale marks Therefore the thick scale marks are located onFigure 12

414 Improved Hough Transform-Based Pointer DetectionThe edge detection is implemented in the pointer gaugeimage using the Canny operator to obtain the edge imageof the gauge Then the Hough transform method is adoptedto fit the straight line in the image to obtain all the straightlines among which the pointer border is included Finallyonly the pointer border can be determined by excluding theother straight edges

(1) The Hough transform method is adopted to fit thestraight line and find all the straight lines in the image Inaddition each straight line described in the image coordinatesystem by 119910 = 119896119909 + 119887 is calculated

(2)The distance 119889 from the circle center (1199090 1199100) to the

straight line is calculated according to the following formula

119889 =

10038161003816100381610038161199100 minus 119896 lowast 1199090 minus 1198871003816100381610038161003816

radic1 + 1198962 (7)

Based on prior knowledge we know that the distancefrom the circle center to the straight line of the pointer ismuch less than the diameter of the dial all the straight lines

Figure 13 Schematic of pointer fitting and its direction

conforming to 119889 lt 211990310 are picked out Here 119903 is thediameter of the dial

(3) The angle of each straight line in (1) is calculatedaccording to formula (8) and stored into an array angle[]

120593 =arctan (119896) lowast 180

120587 (8)

(4) As the angles of the pointer direction are acute onesgenerally in the range of 2∘ sim 10

∘ the angle Δ120593 is calculatedsubject to the following formula

Δ120593 =1003816100381610038161003816angle [119899] minus angle [119899 + 1]1003816100381610038161003816 (9)

If it is in the situation where 2 lt Δ120593 lt 10 the straight lineshould be selected as one side of the pointer Therefore bothlines where the two sides of the pointer lie can be found

(5) According to the straight lines of the two sides thepointer direction can be determined

42 The Pointer Gauge Indicating Value Recognition As isshown in Figure 11 the intersection point 119866 of the twostraight lines of the pointer border is calculated and thenlinked to the circle center 119874(119909

0 1199100) The angle of the

line 119874119866 is calculated In accordance with the position ofthe intersection point 119866 the angle 120573 in the rectangularcoordinate system is computed according to formula (1)(Figure 13)

According to the angle 120573 the readings 1198630 1198631 119863

119899

corresponding to each thick scale mark are obtained Basedon the angle that corresponds to the thick scale markand its number 119899 which is detected in Section 414 thepointer reading can be determined according to formula (10)


Table 1 Experimental samples

Sample name Image resolution Sample character The purpose of sample selectionThe pressure gauge with manylabels and a lot of writing on thedial

1000750A lot of writing on the dial which mayinfluence the location of the dial centerand the pointer segmentation

Verify the robustness of thealgorithm and the capability ofresisting interference

Flow gauge with the unevenscale 500500 Uneven distribution of the scale marks Verify the universality of the

algorithm

The scale within the adjacent thick scale marks is divided bylinear interpolation

119878indicating value

=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572

119899are the angles that correspond to the

thick scale marks

5 Experimental Results and Analysis

To verify the effectiveness of the proposed approach a seriesof experiments are conducted to test its performance

51 Experiment Design The experiments include two partsFirst the images of the different kinds of pointer gauges areselected to conduct the simulation experiments and verifythe effectiveness and applicability of the approach Thenthe pressure gauge calibration system which is composedof a float gauge high precise pressure gauge test pressuregauge camera and computer is established to verify theactual performance of this approach in the pointer gaugecalibration

52 Part One of the Experiments Reading Identification ofthe Various Pointer Gauges

521 Samples Selection As can be seen in Table 1 two groupsof representative samples are selected for the experimentThey include the pressure gauge with a lot of writing on thedial and the flow gauge with an uneven scale

522 Experimental Results and Analysis In this part ofthe experiment we adopt the proposed approach to theautomatic recognition of the indicating value of the abovementioned two types of gauges To verify the effectivenessof the proposed approach Figures 14 and 15 illustrate theexperimental results of each step

Figure 14(a) is the original pointer gauge image FromFigure 14(a) we can see that the pointer and scale marks

cannot be directly detected by segmentation methods sincethere is a lot of writing on the dial Therefore the proposedapproach applies an idea that conducts a coarse-to-finesearch The dial and scale regions are located first since theyare more easily detected than the pointer and scale marks Asshown in Figures 14(c) and 14(d) the dial region is locatedusing the adaptive-region-growing method and the scaleregion is detected under the polar coordinate system Thenin both regions the pointer and scale marks are accuratelydetected As shown in Figures 14(e) and 14(f) the improvedHough transform method is adopted to detect the pointerand the improved central projectionmethod is used to detectthe scale marks The location of the thick scale marks isdetermined according to the angle histogram generated fromthe central projection of the scale marks Their indicatingvalues are given according to the location of the thick scalemarks The scale values within any two adjacent thick marksare determined by linear division According to the directionof the pointer and the location of the scale marks the anglemethod which is adopted in the adjacent thick scale marksis used to indicate the pointer gauge value

The proposed approach detects the pointer direction andthe scale marks location respectively In Figures 15(e) and15(f) it can be seen that the location of the scale marks isprecisely obtained by the angle histogram and the pointer isdetected in the dial region Based on the location of the scalemarks and the pointer direction the distance between thepointer and the adjacent scale marks can be calculated usingthe distance method then the pointer indicating value canbe estimatedTherefore whether or not the distribution of thescale is even the proposed approach is able to precisely detectthe gaugersquos indicating value while the most current existingmethods cannot

53 Part Two of the Experiments The Recognition of the FloatPointer Gauge Indicating Value

531 The System and Procedure of Experiments To verifythe performance of the practical application of the proposedapproach in practical application the float gauge is used as thepressure gauge verification system The type of float gauge isY-047 The main technical parameters of the float gauge aredescribed as follows The range of output pressure is 001ndash025MPa the accuracy class is plusmn005 the rated pressureis 05MPa and the standard weights are from 001MPato 25MPa A high-precision gauge is used as the standardpressure gauge whose accuracy class is 15 The test gaugeis a gauge with general accuracy A visual detection systemis established in front of the float gauge An optical lens


(a) The original gauge image (b) The dial region of the manual interception

(c) Detection results of dial center and dial region (d) Detection results of scale region

1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210

(e) Angle histogram for scale marks detection (f) Results of the pointer and scale marksdetection

Figure 14 The detection results of the pointer gauge with a lot of writing on the dial

whose focal length can be adjustable from 10 to 20mm anda 500-megapixel HD CMOS camera with a 60 fps framerate are applied as image sensors The system is equippedwith a coaxial light source which is placed on the cameralens The hardware configuration of the computer used inthis experiment is Inter Pentium(R) Dual CPU E2200 and

22GHz The programming environment is VS2010 Theverification system of the pointer gauge that is based oncomputer vision is shown in Figure 16 The camera used inthe experiments takes images of the high-precision standardgauge and the test gauge The proposed approach is adoptedto detect the indicating value of both standard and test gauges


(a) Original gauge image (b) Dial region by manual interception


1205721 1205722 12057231205720


Figure 15 The detection results of the pointer gauge with an uneven scale

According to the gauge calibration regulations the exper-iment procedure is as follows First a positive stroke isconducted Here the float gaugersquos output is increased bygradually loading the weights while the gaugersquos indicatingvalue is increased At each indicating value test point thecamera takes images of both the standard pointer and testgauges The proposed approach is to use the images torecognize the indicating values Then a negative stroke isconducted of which the process is that the float gauge outputis reduced from the highest test point by gradually unloadingthe weights while the gaugersquos indicating value is accordinglyreduced An image of each test point is taken to recognize theindicating values

532 Experimental Results and Analysis The experimentalresults are shown in Figures 17 and 18 The gaugersquos upperlimit is 025MPa the lower limit is 0MPa Whatever theexperiment is in the positive or negative stroke the floatgauge output intervals are 0025MPa The detection resultsfor the indicating values of the standard and test gauges areshown in Tables 2 and 3 respectively

As can be seen from the experimental results the pro-posed approach is applicable to the pressure gauge ver-ification The indicating values of the test and standardgauges can be obtained by the proposed approach instead ofbeing obtained through manual observation The test gaugecalibration is completed by comparing the indicating value


(a) (b)

Figure 16 The experimental system of gauge test

Figure 17 The standard gauge results

Figure 18 The test gauge results

of the test gauge with that of the standard gauge From theexperimental results in Tables 2 3 and 4 comparing thevisual data with the manual reading we can see that thedetection results of the indicating value based on computervision are more accurate valid and have more significantdigits and a faster detection speed

54 Experimental Conclusion From the above experimentalresults we can draw the following conclusions

(1) The indicating value of the pointer gauge can beeffectively detected using themethod proposed in this

paper the approach can be used for pressure gaugeverification

(2) The approach proposes a stable frame about thereading identification of the pointer gauge Frombig region to small target the approach first locatesthe scale and the pointer region Then it preciselysegments the pointer and scale marks in the targetarea Finally the indicating value of the gauge isobtained based on the direction of the pointer andthe distribution of the scale marks This frameworkis a general recognition method of a pointer gaugebased on computer vision and has good interferenceimmunity However to achieve more satisfactoryresults in its practical application each step has to beimproved For example in the process of locating ofthe dial region based on the region growing methodmany factors need to be considered to determinewhether the use of this method should be terminated

(3) In its practical application the image preprocessingmethod should be used along with the proposedmethod so as to obtain more satisfactory resultsespecially for some industrial field applications

6 Conclusion

This study proposes a pointer gauge automatic readingapproach based on computer vision The approach aims atovercoming the defects in the current pointer gauge auto-matic reading approach and the application of pressure gaugeverification According to the framework of the proposedapproach which is conducted from big-region segmentationto small-target detection first the target region in the dialis located Then the pointer and scale marks are detected inthis region Finally the indicating gauge value is obtained Assuch the proposed approach has good interference immunityand is applicable for both gauges with and without evenlydistributed scale marks The approach can be widely appliedto the reading identification of different types of pointergauges

The proposed method is robust and precise enough to beused in pointer gauge verificationHowever in some practical


Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233


applications especially in the industrial field it should beused by combining it with image preprocessing methodsso as to achieve better effects The improved approach canalso be used for the pointer gauge whose dial is noncircularTherefore in the future we will conduct the following studiesto complete the digitization work on the pointer gauge so asto develop a general indicating value readingmethod (1)Theimage preprocessing methods will be developed to eliminatethe influence of stray or reflective light or to correct the imagedistortion caused by changes in the relative position betweenthe camera and gauge (2) A general automatic readingmethod will be developed for different types of pointergauges which can be used in various hardware systems andhave a unified standard output format

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work is supported by Beijing Key Discipline Develop-ment Program (no XK100080537) the Beijing Natural Sci-ence Foundation (4122050) andOpening Project of Key Lab-oratory of Operation Safety Technology on Transport Vehi-cle Ministry of Transport China

References

[1] L Yanwen G Jinfeng Z Hongwei and R Hui ldquoDetection sys-tem of meter pointer based on computer visionrdquo in Proceedingsof the International Conference on Electronic and MechanicalEngineering and Information Technology (EMEIT rsquo11) pp 908ndash911 August 2011

[2] Z Jun F Haiping and K Ming ldquoAutomatic calibration ofdial gauges based on computer visionrdquo Infrared and LaserEngineering vol 37 pp 333ndash336 2008

[3] MKGellaboina G Swaminathan andVVenkoparao ldquoAnalogdial gauge reader for handheld devicesrdquo in Proceedings of theIEEE 8th Conference on Industrial Electronics and Applications(ICIEA rsquo13) pp 1147ndash1150 June 2013

[4] F C Alegria and A C Serra ldquoAutomatic calibration of analogand digital measuring instruments using computer visionrdquoIEEE Transactions on Instrumentation and Measurement vol49 no 1 pp 94ndash99 2000

[5] B Sun C Zhang Z Liu B Qian and H P Zhang ldquoStudy ofFPGA-based visual detection for pointer dialrdquo in Proceedings ofthe 26th Chinese Control and Decision Conference (CCDC 14)pp 1467ndash1472 Changsha China May-June 2014

[6] G Gui-fa W Ren-huang and W Huan ldquoA pretreatment ofimage based on reformative homomorphic filteringrdquo Journal ofGuangdong University of Technology vol 26 no 3 pp 57ndash592009

[7] D-C Luo S-C Wang H-G Zeng Z-Z Li and X-M LuldquoDesign of recognition system of analog measuring instru-mentsrdquo Laser amp Infrared vol 37 no 4 pp 377ndash380 2007

[8] H Wen Z Teng S Yang and S Liu ldquoIntelligent readingmethod for analog meter based on computer visionrdquo Chinese

Journal of Scientific Instrument vol 28 no 7 pp 1234ndash12392007

[9] W Qi T Xiling D Cheng H Yao and F Yanjun ldquoAutomaticalignment system based on center point recognition of analogmeasuring instruments dialrdquo in Proceedings of the 39th AnnualConference of the IEEE Industrial Electronics Society (IECONrsquo13) pp 5532ndash5536 IEEE Vienna Austria November 2013

[10] F-J Sun T-J An J-Q Fan C-P Yang and Z Xu ldquoStudy on therecognition of pointer position of electric power transformertemperature meterrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 27 no 7 pp 470ndash475 2007

[11] Z LeThe research of indication recognition for dial instrumentsbased on image processing [MS thesis] North China ElectricPower University Beijing China 2013

[12] S-H Lu Study on automatic test system for high precision pointerinstrumeng based on machine vision [Dissertation for the MasterDegree in Engineering] Harbin Institute of Technology 2013

[13] Q Wang Y Fang W Wang M Wu R Wang and Y FangldquoResearch on automatic reading recognition of index instru-ments based on computer visionrdquo in Proceedings of the 3rdInternational Conference on Computer Science and NetworkTechnology (ICCSNT rsquo13) pp 10ndash13 October 2013

[14] Z Shutao Direct reading instrument calibration method basedon computer vision [PhD thesis] North China Electric PowerUniversity Beijing China 2006

[15] S W Wang and Y W Dai ldquoAutomatic recognizing of multi-pointerrsquo water meter using image processingrdquo Chinese Journalof Scientific Instrument vol 26 no 11 pp 1178ndash1120 2005

[16] F-J Sun T-J An J-Q Fan C-P Yang and Z Xu ldquoStudy on therecognition of pointer position of electric power transformertemperature meterrdquo Proceeding of the CSEE vol 27 no 7 pp70ndash78 2007

[17] B Hemming and H Lehto ldquoCalculation of uncertainty ofmeasurement in machine vision case a system for the cal-ibration of dial indicatorsrdquo in Proceedings of the 18th IEEEInstrumentation and Measurement Technology Conference pp665ndash670 Budapest Hungary May 2001

[18] B Chen and L Jin ldquoA new meter dial indicator detectionmethod based on center point projectionrdquo Application Researchof Computers vol 22 no 1 pp 246ndash248 2005

[19] J Zetao W Shi and L Kewei ldquoAn effective method onnon-contact measurement for gauges with pointerrdquo ComputerApplication and Software vol 26 no 4 pp 281ndash285 2009

[20] J-C Yin J Lou and H-T Zhao ldquoVision system and itsapplication in the auto door latch assembly linerdquo Techniques ofAutomation and Applications no 1 pp 79ndash82 2010

[21] H Zhou H-E Xu and C-G Geng ldquoAutomatic checking ofpointer automotive dashboard based on HIS model and Houghtransformationrdquo Journal of Zhejiang University (EngineeringScience) vol 44 no 6 pp 1108ndash1113 2010

[22] J Han E Li B Tao and M Lv ldquoReading recognition methodof analog measuring instruments based on improved houghtransformrdquo in Proceedings of the IEEE 10th International Con-ference on Electronic Measurement and Instruments (ICEMI rsquo11)pp 337ndash340 August 2011

[23] C Li L Yang Z Liu and K Li ldquoA new automatic seeded regiongrowing algorithmrdquo in Proceedings of the 6th InternationalCongress on Image and Signal Processing (CISP 13) vol 1 pp543ndash549 Hangzhou China December 2013

[24] SHengqiang andWChangji ldquoAnewalgorithmbased on super-green features for ostursquos method using image segmentationrdquo in


Proceedings of the World Automation Congress (WAC rsquo12) pp1ndash4 June 2012

[25] J Xu X Sun D Zhang and K Fu ldquoAutomatic detection ofinshore ships in high-resolution remote sensingimages usingrobust invariant generalized hough transformrdquo IEEEGeoscienceand Remote Sensing Letters vol 11 no 12 pp 2070ndash2074 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


PC Image

Drive card Stepping

Other signal

CCD or

Stepping

High

standard

Tested

Worktable

Benchmarksignal

generator

collectors

capture card

motor driver

CMOS camera

motor

precision

gaugegauge

Figure 1 Hardware structure of the automatic recognition of the indicating value of the pointer gauge

Image Image

acquiring

Preprocessing gauge image

Pointerand scale

Automatic

reading

Gaugereadingoutput

Reading identification

preprocessing marks detection identification

Detection

of pointer

and scale

Figure 2 The image processing procedure of the automatic recognition of the indicating value of the pointer gauge

is adopted to obtain the indicating value of the gauge bycomparing the pointer direction with the position of the scalemarks

Since the indicating value is determined by comparing thepointer direction and the locations of the scale marks thisapproach is also suitable for gauges wherein the scale marksare unevenly distributed Therefore the proposed approachis in fact a general approach for gauge calibration

2 Related Work

21 Configuration of Hardware System Used in Gauge Ver-ification The hardware system used in gauge verificationgenerally comprises the following configuration [2ndash5] whichis shown in Figure 1 During the working process the highprecise gauge and the calibrated gauge are placed on theworktable A computer sends impulse signals to the motordriver Therefore the stepping motor is controlled to maketheworktablemove to allow for the adjustment of the locationof the gauge so that the gauges can be appropriately placedin the camerarsquos view while the standard signal source sendsreference signals to the calibrated pointer gauge and the highprecise gauge The indicating value of the high precise gaugeis treated as standard data Next computer vision is applied toautomatically recognize the values indicated by the calibratedand standard gauges Finally a comparison is made betweenthe two values and the verification result is reached

For some other pointer gauges the standard data pro-duced by the reference signal generator is directly inputted

into the computer by the other signal-acquisition equipmentThe verification result is achieved by comparing the standarddata with the indicating value of the calibrated gauge whichis extracted using computer vision

22 The Process of Automatic Reading of the Pointer GaugeBased on Computer Vision Figure 2 shows the procedure ofthe image processing used to recognize the pointer gaugevalue First to improve the image quality the gauge imagehas to be preprocessed by means of noise suppression andimage enhancement Next image processing and analyzingmethods are used to detect the pointer and scale marksAccording to the pointer direction and the location of scalemarks the value indicated by the pointer gauge can bedetected Finally the indicating value results are outputtedTherefore the automatic recognition methods of the gaugeindicating value mainly include three parts

(1) image preprocessing aimed to improve image qualityand suppress noise

(2) gauge pointer and scale marks detection based onimage processing and analyzing

(3) automatic recognition of the pointer gauge indicatingvalue

23 Related Work of the Pointer Gauge Indicating ValueDetection In the existing literature the pointer gaugeimage should be preprocessed to remove noise or enhance











119889119894=

1003816100381610038161003816119860119909119894 + 119861119910119894 + 1198621003816100381610038161003816

radic1198602 + 1198612 (1)


119878119899= 119878119871+

1198891

1198891+ 1198890

times (119878119867minus 119878119871) (2)




119867



0are the distance











Standard gauge

Display PC

Camera

Image capture card



























origin center


value



360 degrees






















(a) (b)

(c) (d)


90∘

60∘

210∘

150∘

120∘

180∘

240∘

270∘300∘

330∘

30∘

0∘




1



2


2 the inner radius









(a) (b)

(c)


(a) (b)



x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















119889119894=

1003816100381610038161003816119860119909119894 + 119861119910119894 + 1198621003816100381610038161003816

radic1198602 + 1198612 (1)


119878119899= 119878119871+

1198891

1198891+ 1198890

times (119878119867minus 119878119871) (2)




119867



0are the distance











Standard gauge

Display PC

Camera

Image capture card



























origin center


value



360 degrees






















(a) (b)

(c) (d)


90∘

60∘

210∘

150∘

120∘

180∘

240∘

270∘300∘

330∘

30∘

0∘




1



2


2 the inner radius









(a) (b)

(c)


(a) (b)



x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Standard gauge

Display PC

Camera

Image capture card



























origin center


value



360 degrees






















(a) (b)

(c) (d)


90∘

60∘

210∘

150∘

120∘

180∘

240∘

270∘300∘

330∘

30∘

0∘




1



2


2 the inner radius









(a) (b)

(c)


(a) (b)



x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






























origin center


value



360 degrees






















(a) (b)

(c) (d)


90∘

60∘

210∘

150∘

120∘

180∘

240∘

270∘300∘

330∘

30∘

0∘




1



2


2 the inner radius









(a) (b)

(c)


(a) (b)



x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























(a) (b)

(c) (d)


90∘

60∘

210∘

150∘

120∘

180∘

240∘

270∘300∘

330∘

30∘

0∘




1



2


2 the inner radius









(a) (b)

(c)


(a) (b)



x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)

(c)


(a) (b)



x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










x

y

0


x

y

1

1

2

2

3

3

4

4

minus1

minus1

minus2

minus2

0minus3

minus3

minus4

minus4








120572 = arctan (119896) lowast 180

120587 (3)






(4)

Occ

urre

nce t

imes

Angle (deg)1205791 1205792 1205793 12057940





anglemean (119898)


119891 (120579 + 1) + 119891 (120579) + 119891 (120579 minus 1)

(5)



12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










12057221205721

1205720

1205723

Thick scale marksy

x



119875 =anglemean (119898)

anglemean (119898 + 1) (6)








119889 =


radic1 + 1198962 (7)





120593 =arctan (119896) lowast 180

120587 (8)










119899








algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















algorithm



=

10038161003816100381610038161003816100381610038161003816

1205720minus 120573

1205720minus 1205721

10038161003816100381610038161003816100381610038161003816

(1198631minus 1198630) 120572

0lt 120573 lt 120572

1

10038161003816100381610038161003816100381610038161003816

1205721minus 120573

1205721minus 1205722

10038161003816100381610038161003816100381610038161003816

(1198632minus 1198631) + 1198631 120572

1lt 120573 le 120572

2

10038161003816100381610038161003816100381610038161003816

120572119899minus1

minus 120573

120572119899minus1

minus 120572119899

10038161003816100381610038161003816100381610038161003816

(119863119899minus 119863119899minus1

) + 119863119899minus1

120572119899minus1

lt 120573 le 120572119899

(10)

Here 1205720 1205721 1205722 120572


thick scale marks















1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1205721 1205722 1205723 12057241205720 1205725 1205726 1205727 1205728 1205729 12057210








1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1205721 1205722 12057231205720







(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)










6 Conclusion




Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table2Th

estand

ardgauged

etectio

nresults

Thep

ressureo

fcheckp

oint

(MPa)

Theind

icatingvalueo

fstand

ardgauge

Thec

itederror

(absolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0024343

0024

000

0657

0001

0025610

0025

000

0610

0026024

0050

004

8727

0049

0001273

0001

0049761

005

000

0240

0051010

0075

0074386

0075

000

0614

00075876

0076

000

0876

0001

025035

0100

01004

080099

000

0408

0001

0100147

01

000

0147

0016006

0125

0125060

0125

000

0060

00125482

0126

000

0482

0001

0024019

0150

0149762

015

000

0238

001506

470151

000

0647

0001

0095026

0175

0174613

0175

000

0387

00174720

0176

000

0280

0001

0155011

0200

0198316

02

0001684

00201540

0201

0001540

0001

0674062

0225

0225053

0224

000

0053

0001

0225149

0225

000

0149

0002006

0250

0249344

0249

000

0656

0001

0249344

0249

000

0660

0001

026026


Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table3Th

etestgauge

detectionresults

Thep

ressure

output

ofthe

checkp

oint

(MPa)

Theind

icatingvalueo

ftestedgauge

Thec

itederrors

(thea

bsolutee

rrorrange)

Positives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Negatives

troke

Error1

(visu

aldetection-weights

value)

Error2

(manual

reading-weights

value)

Visual

detection

Manual

reading

Visual

detection

Manual

reading

00

00

00

00

00

0025

0025650

0026

000

0650

0001

0027084

0028

0002084

0003

026083

0050

0050200

0051

000

0200

0001

0051623

0052

0001623

0002

008065

0075

0075470

0076

000

0470

0001

0077778

0078

0002778

0003

019111

0100

0100100

0101

000

0100

0001

0101095

0102

0001095

0002

004

044

0125

01260

000126

0001000

0001

0126106

0127

000110

60002

04044

0150

0150900

0152

000

0900

0002

0151486

0153

0001486

0003

036059

0175

0177626

0173

0002626

0002

0177678

0179

0002678

000

410

510

70200

0202263

0203

0002263

0003

0202445

0204

0002445

000

40900978

0225

0226146

0227

000114

60002

0226223

0228

0001223

0003

046

049

0250

0249057

0252

000

0940

0002

0249057

0252

000

0940

0002

038038


Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

0075

0074387

0075470

0001080

145644

0075

0076

0001

1333

001225

0100

01004

080100100

000

0308

030675

0099

0101

0002

202

002051

0125

0125060

01260

00000

0940

075164

0125

0126

0001

08

000706

0150

0149762

0150900

000114

0075987

015

0152

0002

1333

001219

0175

0174613

0177626

0003010

172553

0175

0173

0002

11429

00144

00200

0198316

0202263

0003950

199026

02

0203

0003

15001105

0225

0225053

0226146

0001090

048566

0224

0227

0003

1339

001230

0250

0249344

0249057

000

0287

011510

0249

0252

0003

1205

001233





Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table4Com

paris

onsb

etweenmanualreading

andvisualdetection

Thep

ressureo

utpu

tof

thec

heckpo

int

(MPa)

Theind

icatingvalueo

fvisu

aldetection

Theind

icatingvalueo

fmanualreading

Com

paris

on(error

1minuserror2

)Po

sitives

troke

Error1

1205751minus1205752(M

Pa)

Relativ

eerror

1(1205751minus1205752)1205751(

)Po

sitives

troke

Error2

1205901minus1205902(M

Pa)

Relativ

eerror

2(1205901minus1205902)1205901(

)Standard

gauge

1205751(M

Pa)

Teste

dgauge

1205752(M

Pa)

Standard

gauge

1205901(M

Pa)

Teste

dgauge

1205902(M

Pa)

00

00

00

00

00

0025

0024343

0025650

0001310

53700

00024

0026

0002

8333

008202

0050

004

8727

0050200

0001473

302296

0049

0051

0002

4082

003533

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Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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