research article a natural image pointillism with...

Research ArticleA Natural Image Pointillism with Controlled Ellipse Dots

Dongxiang Chi

Institute of SDJU-PHICOMM Information Technology Shanghai Dianji University Shanghai 200240 China

Correspondence should be addressed to Dongxiang Chi chidongxiangaliyuncom

Received 8 July 2014 Accepted 1 December 2014 Published 24 December 2014

Academic Editor Deepu Rajan

Copyright copy 2014 Dongxiang Chi 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 paper presents an image-based artistic rendering algorithm for the automatic Pointillism style At first ellipse dot locations arerandomly generated based on a source image then dot orientations are precalculated with help of a direction map a saliency mapof the source image decides long and short radius of the ellipse dot At last the rendering runs layer-by-layer from large size dotsto small size dots so as to reserve the detailed parts of the image Although only ellipse dot shape is adopted the final Pointillismstyle performs well because of variable characteristics of the dot

1 Introduction

With rapid development of computer graphics it diversifiesitself gradually into two opposite branches photorealisticrendering and nonphotorealistic rendering (NPR) in the lasttwo decades In contrast to the traditional computer graphicswhich focuses on photorealism NPR is inspired by artisticstyles such as painting drawing technical illustration andanimated cartoons In one word NPR focuses on presentinga new world scene in an artistic view NPR has been appliedto movies and video games in the form of cartoon datavisualization and so forth

Unlike the photorealistic rendering which is engagedmainly by computer graphics scientists NPR attracts manyresearchers who love arts and science as a cross-disciplinaryresearch domainThe further NPR developed the closely theart and science are integrated One of the most importantbranch of NPR is ldquoimage-based artistic rendering (IBAR)rdquowhich deals with the two-dimensional content in pho-tographs and video with artistic stylization techniques [1]The aim of IBAR is to transfer aesthetic feeling and effectiveinformation to people instead of simply describing everydetails of an image It is like an artistic filter which turnsa natural image into an artistic work Too many detailsin the natural image often conceive the most importantthings A simplified image makes people grasp the primaryinformation as much as possible Similarly IBAR strengthensthe effective part of the image in a painting style instead ofoverlooking its details

According to [1] IBAR is roughly classified into strokebased rendering (SBR) region-based techniques example-based rendering image processing and filtering techniques(For convenience stroke point brush and dot will not bediscriminated with each other in the following parts of thispaper Different papers used different terminology for theirconveniences) As the most prevalent form of IBAR [1] SBRalgorithm renders a 2D image with atomic primitives tosimulate a particular style in a local or global manner Theprimitives involved in SBR are virtual painting brush [2 3]tiles [4] points (stippling Halftoning and hatching) [5ndash13]and even images [14ndash17] Some also simulated water-colorstyle [18] pencil and ink style [19 20] line drawing [21 22]and Pointillism [23ndash27]

As basic primitive dots are adopted in Pointillism stip-pling and so forth and could be extended in various ways Instippling it is important for dots to be placed in a denser orsparser ways to express dark or bright tones with only blackdotsWhen simulating Pointillism the dots colors are usuallyrestricted to about ten colors and similar strokes tomimic thestyle Classic painters like Georges Seurat and Paul Signac orcontemporary artists like Yayoi Kusama adopted dots asmainelements to transfer their artistic ideas

In fact dots here can be strong expressive elementswith different size color shape texture and arrangementIt has evolved into a new form in comparison to the classicPointillism and stippling In this paper not like the traditionalPointillism with juxtaposed dots and limited colors and

Hindawi Publishing CorporationAdvances in MultimediaVolume 2014 Article ID 567846 16 pageshttpdxdoiorg1011552014567846

2 Advances in Multimedia

(a) (b) (c) (d)

Figure 1 (a) Source image cat (b) saliency map (c) direction map details of the catrsquos nose (d) Pointillism of the source image with theproposed method119873 = 19000

stippling with black dots we focus on natural images (withcharacteristics of more colors and intensities) Pointillismwith multilayer dots overlapping with each other and wherecolors are based on the source image itself We transfer anatural image to Pointillism-like styleThe connotation of theterm ldquoPointillismrdquo here progresses further from the classicpainting style

The rest of this paper is organized as follows Section 2reviews some works related to this study Section 3 gives theproposed method and Section 4 the rendering results anddiscussion Section 5 concludes the paper and works in thefuture

The main contributions of this paper include the follow-ing

(a) a single dot shape with variable characteristics torender a Pointillism style image

(b) saliency map-guided dots to enhance the main bodyof the source image

(c) dot orientation with help of a direction map to followobject edges in the source image

(d) randomly generated dots positions to increase thevariance of the final Pointillism

(e) layer-by-layer strategy to keep the detailed informa-tion of the source image

(f) an equalized saliency map to adjust the long-short-axis ratios to further enhance the painting effect

Figure 1 shows the main points of the proposed method

2 Related Works

In recent years it has developed step by step frommimickingsimple painting techniques to painting style in NPR

Pointillism being a technique of painting with smalldistinct dots of pure color applied in patterns to form

an image is derived from neoimpressionism which wasdeveloped by Georges Seurat and Paul Signac in 1886 Someclassic works like ldquoA Sunday Afternoon on the Island of LaGrande Jatterdquo ldquoBathing at Asnieresrdquo by Georges Seurat ldquoTheWindmills at Overschierdquo by Paul Signac and so forth werecreated The practice of Pointillism is in sharp contrast tothe traditional methods of blending pigments on a palettePointillism is analogous to the four-color CMYK printingprocess used by some color printers and large presses thatplace dots of Cyan (blue) Magenta (red) Yellow and Key(black)

To simulate Seuratrsquos painting style C-K Yang and H-L Yang and so forth went through all accessible Seuratrsquospaintings and extracted some important features such as the22 primitive colors color juxtaposition point sizes and inparticular the effects of complementary colors and halos [23]They diffused points with poisson disks and kept different dotsizes and dot distances in background layer and second layerin an empiricalmanner Every parameter in this paper was setfaithfully according to Seuratrsquos Pointillism from dot color todot size and dot shapeThis imitation increases the similarityto Pointillism style to some extent while losing novelty of theproposedmethod And the adjustment of the four parametersis inconvenient for users Further there is not high levelunderstanding of an input imageThis increases the difficultyof automating the simulating process Comparing to [2] Wuet al also proposed theirmethod for Seuratrsquos Pointillism styleThey obtained a statistical color model through analyzing thecolor distributions of Seuratrsquos paintingsThen the model wascombinedwith amodifiedmulticlass blue noise sampling [12]to stylize an input image with characteristics of color com-position in Seuratrsquos paintings [28] They made a quantitativecomparison and a subjective user study to verify that theirresults are closer to Seuratrsquos painting style than the resultsof previous approaches [28] However the learning processwas too time-expensive besides segmentation sampling anddrawing processes of several hundred to thousand seconds

Advances in Multimedia 3

Hertzmann and so forth painted an image with a series ofspline brush strokes Brush strokes are chosen tomatch colorsin a source image A painting is built up in a series of layersstarting with a rough sketch drawn with a large brush Thesketch is painted over with progressively smaller brushes butonly in areas where the sketch differs from the blurred sourceimage Thus visual emphasis in the painting correspondsroughly to the spatial energy present in the source image [2]

Paper [7] emulated a coarse to fine painting process cus-tomary to styles like impressionism by extending the conceptof layers [2] Instead of orienting each brush stroke largelybased on the local gradient estimates as suggested by [2 24]they oriented the brush strokes along the strongest gradientsEach brush strokersquos color is determined by averaging thecolor of the pixels underneath it in the source frame [7]Shiraishi and so forth [29] introduced a painterly stylewhich generated rectangular brush strokes approximating thelocal regions of the source image with suitable locationsorientations and sizes The resulting image is compositedwith smaller strokes at the details while its flat regions arepainted with larger ones

Sugita and Takahashi [25] presented a pointillistic Half-toningmethod for colorHalftoning on randomdots by utiliz-ing a spatial data structure of boundary sampling algorithmIn addition they implemented complementary color contrastand halo effect according to actual Seuratrsquos painting steps [25]But too many parameter settings prevent the method fromautomated implementation

In this paper the Pointillism style is expanded to a moregeneral manner which includes dots of different sizes colorsshapes and arrangement order With these effective expres-sive elements and very simple parameter settings we candeploy a different painting style extended from Pointillism

3 Proposed Method

The proposed algorithm is based on basic image featureimage color For a canvas image Ω and source image I Ω isrendered with ellipse dot Φi(PDC 119874) which sources fromsource image I

Ω = sum0119894 (PDC 119874) 119894 isin [1119873] (1)

119873 is the total number of dotsFor an ellipse dotΦi it is decided by Pi(119909 119910) the location

of the dot Di(119903119871 119903119878) the two axis radiuses of the ellipse dotCi(119903 119892 119887) the three color components of the dot and 119874

119894

orientation of the dotΩ and I are of the same size119883 times 119884When considering Pointillism style there are several

effective factors affecting the appearances of a paintingincluding size shape texture and color for any one dot andarrangement order for a group of dots

31 Shape Size Color and Location For a classic Pointillismthe shape size color and location of dots are very importantfactors affecting the final appearance of the painting Whensimulating a Pointillism style in a digital manner theseelements should not be neglected

311 Shape of Dots To simulate a classic Seuratrsquos Pointillismstrokes were usually derived from a single stroke pattern[25 29] or several stroke patterns [23] Others like curvedspline brush stroke [2] a transparent circle [30] an ellipsewith user-defined transverse and conjugate diameters [28]and an antialiased line with a circular brush [2 7 24] are allsimplified digital components of the Pointillism style

Considering the balance between painting style varianceand dot control an ellipse dot shape is selected in this paperbecause of its simplicity and two controllable orthogonalaxes long axisand short axis An ellipse dotrsquos shape is decidedby its long axis and short axis A small long-short-axis ratioleads to a circular ellipse and vice versa a large ratio makesa narrow ellipse Based on the color and gradient values ofthe source image the ellipse dots with different axis lengthsare placed in different locations of the canvas image Theseshape variances and placement strategy strengthen the edgesof the source image The long-short-axis ratio depends on anequalized saliency map The saliency map is an explicit two-dimensional map that expresses the saliency or conspicuityof objects in the visual environment [31] For a simulatedPointillism style there should be always something to beenhanced or strengthened in the source image Objects insidea source image can be described in a saliency map Thesaliency information affects the ellipse shape and size soas to enhance the saliency part See Section 33 for morediscussions

312 Size of Dots The dot size in this paper not only isadaptable to source image color but also is affected by gra-dient value of the source imageThismeans that the proposedmethod simulates the Pointillism style instead of faithfullyfollowing it In those areas with slow-changed colors andgradients large dots are rendered and areas with fast-changedcolors and gradients small dots are rendered In this paper theellipse dot size is defined as the long axis radius 119903

119871and short

axis radius 119903119878which depends on two saliency-related maps

119877119871Map and 119877

119878Map

119903119871= round (119877max minus 119877119871Map (119909 119910) times (119877max minus 119877min)) (2)

The short axis length 119903119878is empirically dependent on 119903

119871

and 119877119878Map

119903119878= round (119903

119871times (1 minus 120572 times 119877

119878Map (119909 119910))) (3)

The 119877119871Map and 119877

119878Map are normalized to range [0 1] They

are comprised of color and gradient information and decidethe long axis radius (dot size) and the short axis radiusrespectively See Section 33 for more discussions 120572 showshow much an ellipse is stretched or reduced It is empiricallyset as 095That means if a 119877

119878Map value of an ellipse location

is 1 the relationship between short radius and long radius ofthe ellipse is 119903

119878= round(005times119903

119871) 119903119878ranges in [005times119903

119871 119903119871]

313 Color ofDots Thedot colorCi is set by the average colorof the dot area 119888

119911

119862119894=1

119898sum

119898

119888119911 (4)


where 119898 is the pixel number of the zone the dot covers inthe source image For a RGB color image 119894 isin 1 2 3 Inthe canvas image a dot is rendered with an average color ofthe source image area covered by the dot According to (2)and (3) the more salient the area is the smaller the dot sizeis This means that those salient areas are substituted withsmall dots and the detailed areas are kept deliberately Andto some extent this method also keeps some characteristicsof the Pointillism style

314 Location of Dots For each dot location Pi(119909 119910) 119909 and119910 are randomly selected along the columns and rows of thesource image and every dot falls on the canvas image planeFor the image contents are not taken into account a dotlocation is selected without any guidance

315 Total Dot Number According to the proposed algo-rithm the total dot number is 119873 The larger the 119873 is thedenser the dots are So the dot number119873 affects the ultimatePointillism effect to some extent The 119873 is set empiricallyaccording to the size of the source image To diminish thehole-effect of the canvas image Ω in case of small 119873 Ω maybe predefined as a blurred source image or an average colorimage of the source image

32 Orientation and Edge Enhancement with Direction MapBesides the dot size color location and shape the dot orien-tation 119874

119894also plays an important role in the last appearance

of the painting style The dot orientation here is defined asthe orientation of the long axis Generally a group of ellipsedots with similar orientation along their long axis enhancean edge of a source image The edges in a source imageprovide important information to readers On enhancingedges [2 24] oriented each brush stroke largely based on theestimated local gradient Paper [7] oriented the brush strokesalong the strongest gradients however Paper [29] introduceda painterly style which is composite with smaller strokes atthe details while its flat regions are painted with larger onesto enhance the edges (details)

In this paper a directionmap is constructed to decide theorientation of every ellipse dotThe dot always places its longaxis along the orientation of the direction map of the sourceimage

According to Kang et al [21 32] for a given image I(x)in this paper the vector field of edge tangent flow that is adirection map t(x) is used as a guiding map of the ellipseorientations

The direction map is defined as an iterative process

t (x) = 1

119896∬Ω120583119890

0 (119909 119910) t (y) 119908119904(119909 119910)119908

119898(119909 119910)119908

119889(119909 119910) 119889y

(5)

whereΩ120583119890(119909 119910) denotes the kernel of radius 120583119890 at pixel x and

119896 is the vector normalizing term The tangent vector 119905(sdot) is

assumed to be 120587-periodic For the spatial weight function 119908119904

we use a box filter of radius 120583119890

119908119904(x y) = 1 if 1003817100381710038171003817x minus y1003817100381710038171003817 lt 120583119890

0 otherwise(6)

The magnitude weight function 119908119898

is defined to be amonotonically increasing function

119908119898=[119892 (y) minus 119892 (x) + 1]

2 (7)

This ensures the preservation of the dominant edge direc-tions

The direction weight function 119908119889is defined to promote

smoothing among similar orientations

119908119889(x y) = 1003816100381610038161003816119905 (x) sdot 119905 (y)

1003816100381610038161003816 (8)

where 119905(z) denotes the normalized tangent vector at z Thisweight function increases as the two vectors align closely

For tight alignment of vectors we temporarily reverse thedirection of 119905(y) using the sign function 0(x y) isin 1 minus1 incase that 120579 is bigger than 1205872

0 (x y) = 1 if 119905 (x) sdot 119905 (y) gt 0minus1 otherwise

(9)

The initial flow map denoted as 1199050(x) is obtained bytaking perpendicular vectors (in the counterclockwise sense)from the initial gradient map 1198920(x) of the input image I1199050(x) is then normalized before use The initial gradient

map 1198920(x) is computed by employing a Sobel operator

The input image may be optionally Gaussian-blurred beforegradient computation Figure 2(b) shows direction map with2 iterations The map preserves edge directions well aroundimportant features while keeping them smooth elsewhereFor any dot position x(119909 119910) and a direction map t theorientation 119874

119894of the dot Φi is 119905(x) We note from the maps

that the edges of the source images are kept and enhancedSome ldquoweakrdquo flows are adjusted to follow the strong flows

33 Arrangement Layer-by-Layer according to Saliency MapWith the attributes of the dot shape size color locationand orientation a Pointillism style image is ready to berendered To keep the detailed areas uncovered a layer-by-layer-strategy is adopted According to the dot size smallsize dots are painted after the large size dots That is to saylarger dots are always below smaller dots For the smallerdots always show the detailed information in salient regionsand large dots cover nonsalient regions this layer-by-layer-strategy makes the detailed parts stand out of the sourceimage Also readers pay more attention to those salient areasthan to those nonsalient areas So a saliency map here canbe constructed to decide dot size Usually the salient areasare those areas where there exist color contrasts intensitychanges or edgesThese salient areas provide finer details andimportant contents which attract the readersrsquo attention morethan the other areas do


(a) (b)

(c) (d)

Figure 2 One source image its direction map saliency map and Pointillism ((a) (b) (c) and (d))

A saliency map is a salient metric of an image A highsalient value attracts readersrsquo attention more than a smallsalient value does The saliency map helps the proposedrendering Pointillism to enhance the salient parts To dealwith a source image where no a priori knowledge availableItti et al introduced their bottom-up visual attention model[31] inspired by the behavior and the neuronal architecture ofthe early primate visual system In their method multiscaleimage feature maps of color intensity and orientation areextracted and local spatial contrast is estimated for eachfeature at each location providing a separate conspicuitymap for each feature These maps are combined to a singletopographical saliency map that guides the attention focusin a bottom-up manner In this paper a modified saliencymap by [33] is applied to the source image The map iscomprised of intensity color and edge information of fivepyramid images of the source image

At first intensity image 119868 is obtained through 119903 119892 and 119887components of the source image 119868 is calculated as 119868 = (119903+119892+119887)3Those pixels with intensity less than 10of itsmaximumover the entire image have zero 119903 119892 and 119887 values becausehue variations are not perceivable at very low luminance (andhence not salient) 119877 119866 119861 and 119884 are formed in this way119877 = 119903 minus (119892 + 119887)2 119866 = 119892 minus (119903 + 119887)2 119861 = 119887 minus (119892 + 119903)2 119884 =(119903+119892)2minus|119903minus119892|2minus119887 if (119903+119892)2minus|119903minus119892|2minus119887 gt 0 else119884 = 0Five groups of Gaussian pyramid level 119868(120590) 119877(120590)119866(120590) 119861(120590)and 119884(120590) are generated from 119868 119877 119866 119861 and 119884 respectivelywhere 120590 is Gaussian pyramid level index 120590 isin [1 2 3 4 5]

Then according to a contrast-based saliency map [34] thecenter-neighborhood distances of 119868 119877 119866 119861 and 119884 whichinclude the luminant and chromatic saliency information arecalculated within a 3 times 3 window by Euclidean distance Asfor orientations a different approach of four line detectionmasks R0 R45 R90 and R135 [35] is proposed to filter theintensity image 119868 to simplify the calculation of Itti-KochrsquosGabor filters Each level of intensity image is filtered by fourdirection masks contrast saliency maps are calculated andcombined to be an orientation saliency map 119874(120590) At lastall saliency maps are resized to the original image size (level0) and combined together to be a saliency map To enhancethe high salient region and restrain the low salient region thesaliency map is square power transformed

119878 = [119868(120590) + 119877(120590) + 119866(120590) + 119861(120590) + 119884(120590) + 119874(120590)]

6

2

(10)

Experiments prove the proposed method to be efficientand effective in several aspects At first the luminancechrominance and orientation factors are taken into accountto find the salient region secondly the simplified orientationcalculation does not decrease the oriental salience thirdlythe power transformation makes the salient region moresignificant without changing the smooth tone of the saliencymap Figure 2(c) shows the saliency maps of source imagesEvery salient area like color differences gradient changesand intensity variances gives support to the saliency map


(a)

(b)

(c)

(c1) (c6)

(c7)(c2)

(c8)(c3)

(c9)(c4)

(c10)(c5)

Figure 3 Dot-placement strategy and rendering process from large dots to small dots from nonsalient areas to salient areas one by onelayer-by-layer (a) Source image (b) saliency image (c) final Pointillism with 10000 dots (c1)sim(c10) rendering process from 100 dots to 1000dots 2000 dots until 9000 dots taking the saliency image as canvas image so as to check the placement strategy In real rendering processthe blurred source image is taken as a canvas image

In this paper a coarse to fine strategy is proposed that thedots are rendered from large dots to small dots Further thedot size (long axis length) is decided by the saliency map inan inverse proportional manner as (2) shows 119877

119871Map here is

derived from the normalized saliency map 119878

119877119871Mapx =

1

119899sum

Ω120583119904

119878 (11)

The 119877119871Map value of a dot position x is mean value of a block

zone Ω with block size 120583119904 in the normalized saliency map 119878For the dot size is relative to the saliency of the source imagesmaller dots mean larger salient values of the source imageand are thus on the top of larger dots which are relative tothe smaller salient values Figure 3 shows the dot-placement-strategy from large dots in the nonsalient areas to small dotsin salient areas one by one layer-by-layer


0

200

400

600

800

1000

1200

1400Histogram of equalized radius map

0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200

1400Histogram of radius map

0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)

Figure 4 Comparisons of two Pointillisms with equalizedunequalized 119877119878Map119873 = 40000

34 Equalized Standard Deviation Saliency Map to Decide theShort Axis of an Ellipse Once we have decided the long axislength of the ellipse dot the short axis length and orientationare the last two things to be taken into account To enhancethe edges of the painting image the long axis of the ellipsehas to follow its orientation (Section 32) At the same timethe short axis should also be variable based on the saliencymap As we have discussed before the ellipse dots help toenhance the edges of the source image Compared to anellipse with small long-short-axis ratio (near to 1) the ellipsewith large ratio (larger than 1) stretches itself to a long ellipseto follow the edgesThis shape deformation achieves a furtherenhancement as the orientation doesThe shape deformationdepends on saliency variance with block zoneΩwithin blocksize 120583119904 A high variance value means there exsited a sharpedge while a low variance value means slow-changed edgesSo the standard deviation map 119877

119878Map0x is defined as

119877119878Map0x = STD

Ω120583119904(119878) (12)

The 119877119878Map0 value of a dot position x is a standard

deviation value of zone Ω120583119904in the normalized saliency map

Aswe can see from the histogramof the block zones deviationwithin saliencymap (Figure 4(b)) the deviation values do notdistribute in a balanced wayThus the high and low deviationvalues are not distributed evenly This makes these dots tobe either stretched too much or not stretched That is to saythese unbalanced deviation values lead to stretched dots orcircular dots and there are not ldquomidlevelrdquo dots Nearly all dotstend to be too circular to describe edges in most areas inour experiments because of too many low deviation values(Figure 4(d))

Apparently the unbalanced deviation map has to bebalanced In this paper it is equalized with a LOGSIGfunction that is to make the distribution contour fit aLOGSIG function

119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)

The target function is

LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)

Figure 5 Two portrait imagesrsquo Pointillisms119873 = 40000 (a) and119873 = 39000 (b) ((a1) (b1)) Source image with size 1024times1024 and 768times1024((a2) (a3)) with maximalminimal dot size 10311 and 515 ((b2) (b3)) with maximalminimal dot size 779 and 395

The bin is empirically set and up-rounded to be an integernumber

bin = lceil 119873

1000rceil (15)

119873 is the total dot numberAs (13) shows the new 119877

119878Map value of a dot position

x is an equalized standard deviation value of zone Ω120583119904

inthe normalized saliency map Figure 4(a) shows its equalizedhistogram of Figure 4(b) which are histograms of 119877

119878Map

This equalization generates 119877119878Map which decides short-axis-

length of the ellipse dot The Pointillism (Figure 4(c)) with

equalized119877119878Map is renderedwith ellipseswith different long-

short-axis ratios while the long-short-axis ratios of ellipsesin the Pointillism (Figure 4(d)) with unequalized 119877

119878Map are

nearly similar to each other Apparently the equalization tothe 119877

119878Map works The equalized 119877

119878Map makes the dotsrsquo

short axis radii distribute so flatly that dots with differentlong-short-axis ratios render the Pointillism more clearlycompared to the unequalized version

Besides several main parameters discussed above someother parameters are set empirically in Table 1

With these settings the proposedmethod is implementedwithMATLABWewill show the aforementioned and several


Table 1 Pointillism settings

Parameters SettingsTotal dot number 119873 = 119883 times 11988420 constrained from 10000 to 40000Minimal dot size (pixels) 119877min = 119877max10 minimal to 3Maximal dot size (pixels) 119877max = 119890 timesmin(119883 119884) maximal to 99

119890005sim01 119890 controls the maximal dot size according to the sourceimage size

Block radius (pixels) for direction map 120583119890 = 4Block size (pixels) when deciding dot size with saliency values 120583119904 = 2 times 119877min + 1 constrained from 9 to 21

(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)

Figure 6 Flower and bird imagesrsquo Pointillism 119873 = 21000 (a) and 119873 = 39000 (b) ((a1) (b1)) Source image with size 1024 times 425 and1024 times 777 ((a2) (a3)) with maximalminimal dot size 437 and 213 ((b2) (b3)) with maximalminimal dot size 799 and 395

other natural source images and their Pointillism in the nextsection

4 Results and Discussion

41 Pointillism Style Pointillism results of source imagesfrom Figure 1(a) are shown in Figure 1(d) Figure 2(d)shows the results of the aforementioned source images ofFigure 2(a) Figures 5 6 and 7 show several other naturalimages like portraits flowers and birds and their Pointillismwith different dot-size settings

Several factors including dot size saliency map anddirection map should be taken into account when consider-ing the whole generative process

(1) Dot size a rough observation could disclose that thedot size especially minimal dot size is a primary settingaffecting the style The smaller the minimal dot size is the

clearer the Pointillism image is That is of course because asmaller size dot zone contains average color information ina small zone while a larger dot zone contains average colorinformation in a large zone If the minimal dot size shrinksto one pixel the target image becomes the source imageitself So it should be noted that there is a balance betweenthe minimal dot size and the Pointillism style As we havedeclared in Section 312 the long axis radius is defined asdot size At the same time the short axis radius also playsimportant roles in generating the style Distributions of shortand long radii of dots size corresponding to different dotnumber (in Figure 9) are shown in Figure 10 On one handthe flat distribution of the short radius benefits from theequalized 119877

119878Map On the other hand the unbalanced long

radius distribution keep the target image covered as much aspossible if the number of dots is fixed (further discussion inlater part)


(a) (b)

(c)

(d)

Figure 7 ((a) (c)) Pointillism without direction map and with saliency map to decide the dot size ((b) (d)) Pointillism without directionmap and with equalized standard deviation map of the saliency map to decide the dot size All other settings are as same as those in Figures2(d) and 6(a3)

(2) Direction map further a close research shows thatthe detailed parts in the source image are kept deliberatelywith help of the direction map For example the hairs inFigure 2(d) seemed to be rendered in a random directionComparison of its source image in Figure 2(a) shows thatevery hair on the eaglersquos head has its own direction Thedetailed random hairs in the Pointillism in fact originatefrom the source image that is the direction informationis kept in the generated Pointillism Comparisons betweensource images of Figures 6(a1) and 6(b1) and target imagesof Figures 6(a3) and 6(b3) also give similar conclusion Fluffson the flower and fine feather in birdrsquos neck keep the detailedinformation while generating Pointillism

Several target images without the help of direction mapare shown in Figure 7 It shows two different conditions atfirst Figures 7(a) and 7(c) give Pointillism whose dot size isdecided by a saliency map secondly Figures 7(b) and 7(d)show Pointillism whose dot size is decided by an equalizedstandard deviationmap of the saliencymap All other settingsare the same as those in Figures 2(d) and 6(a3) With thesaliency map deciding the dot size the generated targetimages show Pointillism style withmany similar size dots (forFigures 7(a) and 7(c)) or non-similar-size dots (for Figures7(b) and 7(d)) Those non-similar-size dots come from anequalized standard deviation map of the saliency map whilethe similar-size dots from the saliency map itself Compared


(a) (b)

(c)

(d)

Figure 8 ((a) (c)) Pointillism without direction map and with edge map to decide the dot size ((b) (d)) Pointillism without direction mapand with equalized standard deviation map of the edge map to decide the dot size All other settings are as same as those in Figures 2(d) and6(a3)

to those target images in Figures 2(d) and 6(a3) these targetimages without the guidance of directionmap could not keepclear edges For example in Figure 7(a) the head of the eagleshows ghost edges because of the similar-size dots aroundthe head and every dot does not rotate itself to enhance theedge of the head without the direction map In Figure 7(b)however the edge of the eagle head is clearer than that inFigure 7(a) because of the equalized standard deviation mapAll dots have a flat distribution So the edge of the headis rendered with smaller dots which keep the detailed headedges compared to Figure 7(a) A further observation aroundthe edge of the eagle head and its eye in Figure 7(b) indicatesthat there are many holes around these edges compared toFigure 2(d)

(3) Saliency map a saliency map is comprised of severalfactors like gradients color differences and edge informa-tion So it is reasonable for a saliency map to decide the dotsize of a source image

Several target images without the help of direction mapand saliencymap are shown in Figure 8 It shows twodifferentconditions at first Figures 8(a) and 8(c) give Pointillismwhose dot size is decided by an edge map (source imagefiltered by vertical and horizontal Sobel operators) secondlyFigures 8(b) and 8(d) show Pointillism whose dot size isdecided by an equalized standard deviation map of the edgemap All other settings are the same as those in Figures2(d) and 6(a3) Compared to target images in Figures 2(d)1(d) and 6(a3) they are not acceptable at all considering the


Figure 9 Pointillism results with different dot number settings from left to right top to down 500 1000 5000 10000 20000 30000 and40000 dots The maximal and minimal dot size are 51 and 5 respectively

prominent dots holes and blurred edges Even if comparedto target images in Figure 7 those target images also giveeven poor results For example in Figure 8(a) only edge-map-guided dot size makes the target image show a rough look ofthe source image while in Figure 8(b) an equalized standarddeviation map of the edge map makes the target image lookwell with a flat-dot-size distribution But the holes and ghostedges around the target image could not be ignored

(4) Number of dots each dot occupies its own zoneand overlapped with each other if there are enough dotsWe compare different dot number settings in Figure 9 Themaximal dot size and minimal dot size are set to 51 and5 Intuitively enough dots cover the whole target image InFigure 9 we can see that it is enough for only 5000 dots tocover most part of the target image The coverage increasesrapidly from 500 dots to 5000 dots Increasing dot numberfrom 10000 to 40000 does not give a considerable coverageincrease however There are minor holes in the target imageeven with 40000 dots In the proposed method this problemis avoided by taking a blurred source image as the canvasimage (see Section 315)

42 Comparisons As we had mentioned in the former partwe expand the Pointillism style to a more general manner

That is to say the proposed method has something incommon with a typical Pointillism For example similar dotshape is adopted as rendering element and dot color is takenfrom the averaged source image color The proposed methodldquoborrowsrdquo ideas from the process of simulating Pointillismand tries to expand to a new field The aim of the proposedmethod is to expand the Pointillism instead of simulatingthe style Figure 11 demonstrates the comparisons of theproposed method and Wursquos method [28] We adopt similardot size as shown in Wursquos results However these two resultshave different aim and show different style Wursquos style is moreclose to Seuratrsquos Pointillism in dot size andplacement strategywhile ours consisted of different dot size and shape and layer-by-layer placement strategy It is not easy for the proposedmethod to be judged or compared with other simulatedresults

43 Computational Complexity Computational complexityis a key characteristic in assessing a method The computa-tional complexity of the proposedmethodmainly depends oncalculations of the direction map the saliency map and thedot placement process which respond to119874(119883sdot119884sdot(2120583119890 minus 1)2)119874(119883 sdot 119884) and 119874(119873 sdot 119883 sdot 119884) The proposed method runs


6 8 10 12 14 16 18 20 22 24 260

50100150200250300350Long radius distribution dot number 500

0100200300400500600700800

Long radius distribution dot number 1000

8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100

120Short radius distribution dot number 500

140160180

Short radius distribution dot number 1000

0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)

Figure 10 Dot radius distributions (left column long radius right column short radius) from 500 1000 5000 and 10000 to 40000 dots inFigure 9


(a)

(b)

(c)

Figure 11 Comparisons between our method and Wursquos method The source images are in the first row the second row and third row areWursquos results and our results The maximal and minimal dot sizes of our method are 13 and 5 respectively which are similar to Wursquos dot size

onMATLAB platformwithout optimization underMicrosoftWindow-XP Professional 2002 operating system and IntelDuo CPU P8700 253GHz 289GB Memory A typicalrunning time of the above three processes is 3270 seconds 63seconds and 212 seconds for 1024times1024 image of Figure 5(a1)with 40000 dots The running time for 512 times 512 imagewith 12000 dots is 137 seconds 15 seconds and 44 secondsrespectively In general the image size119883 119884 and block radius120583119890 are primary factors affecting the computation time

5 Conclusion and Future Work

Generally the proposed method gives a plausible Pointillismof natural images like portraits flowers and birds and soforth This kind of Pointillism is not as same as the classicpointillism in that all dots in the proposed method arerendered in a random way and overlapped with each otherlayer-by-layer from large dots to small dots so as to keep thedetails of the source image The proposed method not onlyreserves the classic Pointillism style but also increases thevariances of the style with different settings in a digital wayby simply controlling the ellipse parameters including the dotsize (long axis length) long-short-axis ratios and directionof the ellipse All these settings are adjusted according to thedirectionmap and saliencymap of the source image Further

the equalized standard deviation saliency map smoothensthe dot size distribution which describes the Pointillism ina vivid way In most cases the parameters are preset and thewhole process is automated

Portraits flowers and birds are all rendered carefully dotsby dots one after anotherThedetailed parts of the Pointillismare clear enough and at the same time keep the Pointillismstyle

Currently there is not an objective method to evaluatethe aesthetics of an art work It is even difficult to determinewhether it is an art work or meaningless scribbles in anobjective way Further everyone has hisher own point ofviews because of different culture backgrounds and personalexperiences and so forth In the future we will focus onevaluation method of digital art works like Pointillism

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research is supported by Shanghai Dianji UniversityLeading Academic Discipline Project (Grant no 10XKF01)


Source images are courtesy of CubaGallery (Figure 5(a1))LaurentMallea (Figure 5(b1)) and digisnapper (Figures 6(a1)and 6(b1)) in httpswwwflickrcom and all other anony-mous contributors The author also thanks the anonymousreviewers for their careful and valuable comments andsuggestions

References

[1] J E Kyprianidis J Collomosse T Wang and T IsenbergldquoState of the ldquoArtrdquo a taxonomy of artistic stylization techniquesfor images and videordquo IEEE Transactions on Visualization andComputer Graphics vol 19 no 5 pp 866ndash885 2013

[2] A Hertzmann ldquoPainterly rendering with curved brush strokesof multiple sizesrdquo in Proceedings of the 25th Annual Conferenceon Computer Graphics and Interactive Techniques (SIGGRAPHrsquo98) pp 453ndash460 ACM 1998

[3] C G Healey L Tateosian J T Enns and M Remple ldquoPercep-tually based brush strokes for nonphotorealistic visualizationrdquoACM Transactions on Graphics vol 23 no 1 pp 64ndash96 2004

[4] K Dalal AW Klein Y Liu and K Smith ldquoA spectral approachto NPR packingrdquo in Proceedings of the 4th International Sym-posium on Non-Photorealistic Animation and Rendering (NPARrsquo06) pp 71ndash78 Annecy France June 2006

[5] O Deussen S Hiller C Van Overveld and T StrothotteldquoFloating points a method for computing stipple drawingsrdquoComputer Graphics Forum vol 19 no 3 pp 41ndash50 2000

[6] A Secord ldquoWeighted Voronoi stipplingrdquo in Proceedings of the2nd International Symposium on Non-Photorealistic Animationand Rendering (NPAR rsquo02) pp 37ndash43 2002

[7] J Hays and M Essa ldquoImage and video based painterly anima-tionrdquo in Proceedings of the 3rd International Symposium onNon-Photorealistic Animation and Rendering (NPAR rsquo04) pp 113ndash120 June 2004

[8] S Y Kim R Maciejewski T Isenberg et al ldquoStippling byexamplerdquo in Proceedings of the 7th International Symposium onNon-Photorealistic Animation and Rendering (NPAR rsquo09) pp41ndash50 ACM New York NY USA August 2009

[9] D Martın G Arroyo M V Luzon and T Isenberg ldquoExample-based stippling using a scale-dependent grayscale processrdquoin Proceedings of the 8th International Symposium on Non-Photorealistic Animation and Rendering (NPAR 10) pp 51ndash61Annecy France June 2010

[10] D Martın G Arroyo M V Luzon and T Isenberg ldquoScale-dependent and example-based grayscale stipplingrdquo Computersamp Graphics vol 35 no 1 pp 160ndash174 2011

[11] D Kim M Son Y Lee H Kang and S Lee ldquoFeature-guidedimage stipplingrdquo Computer Graphics Forum vol 27 no 4 pp1209ndash1216 2008

[12] J Kopf C O Daniel O Deussen and D Lischinski ldquoRecursiveWang tiles for real-time blue noiserdquo ACM Transactions onGraphics vol 25 no 3 pp 509ndash518 2006

[13] DVanderhaeghe P Barla JThollot and F X Sillion ldquoDynamicpoint distribution for stroke-based renderingrdquo in Proceedings ofthe Eurographics Symposium on Rendering pp 139ndash146 2007

[14] D Chi M Li Y Zhao G Xu W Liu and J Hu ldquoImage-basedmosaics an variable construction methodrdquo in Proceedings ofthe 5th International Symposium on Computational IntelligenceandDesign (ISCID rsquo12) pp 370ndash375 Hangzhou China October2012

[15] D Chi Y Zhao M Li G Xu W Liu and J Hu ldquoAnaesthetic mosaic image construction in a controllable mannerrdquoin Proceedings of the 5th International Congress on Image andSignal Processing (CISP rsquo12) pp 750ndash755 IEEE ChongqingChina October 2012

[16] S Battiato G Di Blasi G M Farinella and G Gallo ldquoDigitalmosaic frameworksmdashan overviewrdquo Computer Graphics Forumvol 26 no 4 pp 794ndash812 2007

[17] D Pavic U Ceumern and L Kobbelt ldquoGIzMOs Genuineimage mosaics with adaptive tilingrdquo Computer Graphics Forumvol 28 no 8 pp 2244ndash2254 2009

[18] T Luft and O Deussen ldquoReal-time watercolor illustrationsof plants using a blurred depth testrdquo in Proceedings of theInternational Symposium on Non-Photorealistic Animation andRendering (NPAR rsquo06) pp 11ndash20 2006

[19] H Lee S Kwon and S Y Lee ldquoReal-time pencil renderingrdquoin Proceedings of the 4th International Symposium on Non-Photorealistic Animation and Rendering (NPAR rsquo06) pp 37ndash45Annecy France June 2006

[20] L Coconu O Deussen and H C Hege ldquoReal-time pen-and-ink illustration of landscapesrdquo in Proceedings of the 4thInternational Symposium on Non-Photorealistic Animation andRendering (NPAR rsquo06) pp 27ndash35 2006

[21] H Kang S Lee and C K Chui ldquoCoherent line drawingrdquoin Proceedings of the 5th International Symposium on Non-Photorealistic Animation and Rendering (NPAR rsquo07) pp 43ndash50August 2007

[22] M P Salisbury M T Wong J F Hughes and D H SalesinldquoOrientable textures for image-based pen-and-ink illustrationrdquoin Proceedings of the Conference on Computer Graphics (SIG-GRAPH rsquo97) pp 401ndash406 August 1997

[23] C-K Yang and H-L Yang ldquoRealization of Seuratrsquos pointillismvia non-photorealistic renderingrdquoTheVisual Computer vol 24no 5 pp 303ndash322 2008

[24] P Litwinowicz ldquoProcessing images and video for an impres-sionist effectrdquo in Proceedings of the 24th Annual Conference onComputerGraphics and Interactive Techniques (SIGGRAPH rsquo97)pp 407ndash414 August 1997

[25] J Sugita and T Takahashi ldquoAmethod for generating pointillismbased on seuratrsquos color theoryrdquo ITE Transactions on MediaTechnology and Applications vol 1 no 4 pp 317ndash327 2013

[26] D Chi M Li Y Zhao W Liu and J Hu ldquoMulti-layerpointillismrdquo in Proceedings of the 6th International Congress onImage and Signal Processing (CISP rsquo13) pp 1056ndash1060 IEEEHangzhou China December 2013

[27] S Seo S Ryoo and K Yoon ldquoArtistic image generationfor emerging multimedia services by impressionist mannerrdquoTransactions on Embedded Computing Systems vol 12 article22 2013

[28] Y-C Wu Y-T Tsai W-C Lin and W-H Li ldquoGeneratingpointillism paintings based on Seuratrsquos color compositionrdquoComputer Graphics Forum vol 32 no 4 pp 153ndash162 2013

[29] M Shiraishi and Y Yamaguchi ldquoAn algorithm for automaticpainterly rendering based on local source image approxi-mationrdquo in Proceedings 1st International Symposium on NonPhotorealistic Animation and Rendering pp 53ndash58 June 2000

[30] R Bosch andAHerman ldquoPointillism via linear programmingrdquoThe UMAP Journal vol 26 no 4 pp 405ndash412 2005

[31] L Itti C Koch and E Niebur ldquoAmodel of saliency-based visualattention for rapid scene analysisrdquo IEEE Transactions on PatternAnalysis and Machine Intelligence vol 20 no 11 pp 1254ndash12591998


[32] H Kang S Lee and C K Chui ldquoFlow-based image abstrac-tionrdquo IEEE Transactions on Visualization and Computer Graph-ics vol 15 no 1 pp 62ndash76 2009

[33] D Chi ldquoSelf-organizing map-based color image segmentationwith k-means clustering and saliencymaprdquo ISRN Signal Process-ing vol 2011 Article ID 393891 18 pages 2011

[34] Y-F Ma and H-J Zhang ldquoContrast-based image attentionanalysis by using fuzzy growingrdquo in Proceedings of the 11th ACMInternational Conference on Multimedia (MM rsquo03) pp 374ndash381Berkeley Calif USA November 2003

[35] R C Gonzalez and R E Woods Digital Image ProcessingPearson Education 3rd edition 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



(a) (b) (c) (d)

Figure 1 (a) Source image cat (b) saliency map (c) direction map details of the catrsquos nose (d) Pointillism of the source image with theproposed method119873 = 19000

stippling with black dots we focus on natural images (withcharacteristics of more colors and intensities) Pointillismwith multilayer dots overlapping with each other and wherecolors are based on the source image itself We transfer anatural image to Pointillism-like styleThe connotation of theterm ldquoPointillismrdquo here progresses further from the classicpainting style

The rest of this paper is organized as follows Section 2reviews some works related to this study Section 3 gives theproposed method and Section 4 the rendering results anddiscussion Section 5 concludes the paper and works in thefuture

The main contributions of this paper include the follow-ing

(a) a single dot shape with variable characteristics torender a Pointillism style image

(b) saliency map-guided dots to enhance the main bodyof the source image

(c) dot orientation with help of a direction map to followobject edges in the source image

(d) randomly generated dots positions to increase thevariance of the final Pointillism

(e) layer-by-layer strategy to keep the detailed informa-tion of the source image

(f) an equalized saliency map to adjust the long-short-axis ratios to further enhance the painting effect

Figure 1 shows the main points of the proposed method

2 Related Works

In recent years it has developed step by step frommimickingsimple painting techniques to painting style in NPR

Pointillism being a technique of painting with smalldistinct dots of pure color applied in patterns to form

an image is derived from neoimpressionism which wasdeveloped by Georges Seurat and Paul Signac in 1886 Someclassic works like ldquoA Sunday Afternoon on the Island of LaGrande Jatterdquo ldquoBathing at Asnieresrdquo by Georges Seurat ldquoTheWindmills at Overschierdquo by Paul Signac and so forth werecreated The practice of Pointillism is in sharp contrast tothe traditional methods of blending pigments on a palettePointillism is analogous to the four-color CMYK printingprocess used by some color printers and large presses thatplace dots of Cyan (blue) Magenta (red) Yellow and Key(black)

To simulate Seuratrsquos painting style C-K Yang and H-L Yang and so forth went through all accessible Seuratrsquospaintings and extracted some important features such as the22 primitive colors color juxtaposition point sizes and inparticular the effects of complementary colors and halos [23]They diffused points with poisson disks and kept different dotsizes and dot distances in background layer and second layerin an empiricalmanner Every parameter in this paper was setfaithfully according to Seuratrsquos Pointillism from dot color todot size and dot shapeThis imitation increases the similarityto Pointillism style to some extent while losing novelty of theproposedmethod And the adjustment of the four parametersis inconvenient for users Further there is not high levelunderstanding of an input imageThis increases the difficultyof automating the simulating process Comparing to [2] Wuet al also proposed theirmethod for Seuratrsquos Pointillism styleThey obtained a statistical color model through analyzing thecolor distributions of Seuratrsquos paintingsThen the model wascombinedwith amodifiedmulticlass blue noise sampling [12]to stylize an input image with characteristics of color com-position in Seuratrsquos paintings [28] They made a quantitativecomparison and a subjective user study to verify that theirresults are closer to Seuratrsquos painting style than the resultsof previous approaches [28] However the learning processwas too time-expensive besides segmentation sampling anddrawing processes of several hundred to thousand seconds






3 Proposed Method


Ω = sum0119894 (PDC 119874) 119894 isin [1119873] (1)



119894







119871and short


119877119871Map and 119877

119878Map



119871

and 119877119878Map

119903119878= round (119903


119878Map (119909 119910))) (3)

The 119877119871Map and 119877





119878= round(005times119903

119871) 119903119878ranges in [005times119903

119871 119903119871]


119911

119862119894=1

119898sum

119898

119888119911 (4)











t (x) = 1

119896∬Ω120583119890

0 (119909 119910) t (y) 119908119904(119909 119910)119908

119898(119909 119910)119908

119889(119909 119910) 119889y

(5)





119908119904(x y) = 1 if 1003817100381710038171003817x minus y1003817100381710038171003817 lt 120583119890

0 otherwise(6)



119908119898=[119892 (y) minus 119892 (x) + 1]

2 (7)




119908119889(x y) = 1003816100381610038161003816119905 (x) sdot 119905 (y)

1003816100381610038161003816 (8)




(9)








(a) (b)

(c) (d)





119878 = [119868(120590) + 119877(120590) + 119866(120590) + 119861(120590) + 119884(120590) + 119874(120590)]

6

2

(10)



(a)

(b)

(c)

(c1) (c6)

(c7)(c2)

(c8)(c3)

(c9)(c4)

(c10)(c5)



119871Map here is


119877119871Mapx =

1

119899sum

Ω120583119904

119878 (11)




0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)




119877119878Map0x = STD

Ω120583119904(119878) (12)





119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)


LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














3 Proposed Method


Ω = sum0119894 (PDC 119874) 119894 isin [1119873] (1)



119894







119871and short


119877119871Map and 119877

119878Map



119871

and 119877119878Map

119903119878= round (119903


119878Map (119909 119910))) (3)

The 119877119871Map and 119877





119878= round(005times119903

119871) 119903119878ranges in [005times119903

119871 119903119871]


119911

119862119894=1

119898sum

119898

119888119911 (4)











t (x) = 1

119896∬Ω120583119890

0 (119909 119910) t (y) 119908119904(119909 119910)119908

119898(119909 119910)119908

119889(119909 119910) 119889y

(5)





119908119904(x y) = 1 if 1003817100381710038171003817x minus y1003817100381710038171003817 lt 120583119890

0 otherwise(6)



119908119898=[119892 (y) minus 119892 (x) + 1]

2 (7)




119908119889(x y) = 1003816100381610038161003816119905 (x) sdot 119905 (y)

1003816100381610038161003816 (8)




(9)








(a) (b)

(c) (d)





119878 = [119868(120590) + 119877(120590) + 119866(120590) + 119861(120590) + 119884(120590) + 119874(120590)]

6

2

(10)



(a)

(b)

(c)

(c1) (c6)

(c7)(c2)

(c8)(c3)

(c9)(c4)

(c10)(c5)



119871Map here is


119877119871Mapx =

1

119899sum

Ω120583119904

119878 (11)




0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)




119877119878Map0x = STD

Ω120583119904(119878) (12)





119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)


LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















t (x) = 1

119896∬Ω120583119890

0 (119909 119910) t (y) 119908119904(119909 119910)119908

119898(119909 119910)119908

119889(119909 119910) 119889y

(5)





119908119904(x y) = 1 if 1003817100381710038171003817x minus y1003817100381710038171003817 lt 120583119890

0 otherwise(6)



119908119898=[119892 (y) minus 119892 (x) + 1]

2 (7)




119908119889(x y) = 1003816100381610038161003816119905 (x) sdot 119905 (y)

1003816100381610038161003816 (8)




(9)








(a) (b)

(c) (d)





119878 = [119868(120590) + 119877(120590) + 119866(120590) + 119861(120590) + 119884(120590) + 119874(120590)]

6

2

(10)



(a)

(b)

(c)

(c1) (c6)

(c7)(c2)

(c8)(c3)

(c9)(c4)

(c10)(c5)



119871Map here is


119877119871Mapx =

1

119899sum

Ω120583119904

119878 (11)




0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)




119877119878Map0x = STD

Ω120583119904(119878) (12)





119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)


LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)





119878 = [119868(120590) + 119877(120590) + 119866(120590) + 119861(120590) + 119884(120590) + 119874(120590)]

6

2

(10)



(a)

(b)

(c)

(c1) (c6)

(c7)(c2)

(c8)(c3)

(c9)(c4)

(c10)(c5)



119871Map here is


119877119871Mapx =

1

119899sum

Ω120583119904

119878 (11)




0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)




119877119878Map0x = STD

Ω120583119904(119878) (12)





119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)


LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)

(c)

(c1) (c6)

(c7)(c2)

(c8)(c3)

(c9)(c4)

(c10)(c5)



119871Map here is


119877119871Mapx =

1

119899sum

Ω120583119904

119878 (11)




0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)




119877119878Map0x = STD

Ω120583119904(119878) (12)





119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)


LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(a)

0

200

400

600

800

1000

1200


0 01 02 03 04 05 06 07 08 09 1

0

01

02

03

04

05

06

07

08

09

1

(b)

(c) (d)




119877119878Map0x = STD

Ω120583119904(119878) (12)





119877119878Mapx = HISTEQ (119877

119878Map0x LOGSIG (119899)) (13)


LOGSIG (119899) = 1

(1 + 119890minus119899) 119899 = 0 bin (14)


(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)



bin = lceil 119873

1000rceil (15)





119878Map





119878Map are












(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(a1)

(a2)

(a3)

(a)

(b1)

(b2)

(b3)

(b)











(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c)

(d)





(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c)

(d)













6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















6 8 10 12 14 16 18 20 22 24 260


0100200300400500600700800


8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 260

500100015002000250030003500



0

1

2

3


6 8 10 12 14 16 18 20 22 24 26

6 8 10 12 14 16 18 20 22 24 26

times104

05

15

25

(a)

0 5 10 15 20 250

20

40

60

80

100


140160180


0 5 10 15 20 250

20406080

100120


0 5 10 15 20 250

100

200

300

400

500

600

700

0 5 10 15 20 25

0 5 10 15 20 25

0

500

1000


0

1000

2000

3000

4000

5000


(b)



(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)

(c)










Acknowledgments




References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a natural image pointillism with...

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