3-d shape measurement endoscope using a single-lens system
TRANSCRIPT
Int J CARS (2013) 8:451–459DOI 10.1007/s11548-012-0794-2
ORIGINAL ARTICLE
3-D shape measurement endoscope using a single-lens system
Takaaki Takeshita · Minkyu Kim · Yoshikazu Nakajima
Received: 7 March 2012 / Accepted: 17 September 2012 / Published online: 16 October 2012© CARS 2012
AbstractPurpose A three-dimensional (3-D) shape measurementendoscopic technique is proposed to provide depth informa-tion, which is lacking in current endoscopes, in addition tothe conventional surface texture information. The integrationof surface texture and 3-D shapes offers effective analyticaldata and can be used to detect unusual tissues. We constructeda prototype endoscope to validate our method.Methods A 3-D measurement endoscope using shape fromfocus is proposed in this paper. It employs a focusing partto measure both texture and 3-D shapes of objects. Imagefocusing is achieved with a single-lens system.Results A prototype was made in consideration of properendoscope sizes. We validated the method by experimentingon artificial objects and a biological object with the prototype.First, the accuracy was evaluated using artificial objects. TheRMS errors were 0.87 mm for a plate and 0.64 mm for acylinder. Next, inner wall of pig stomach was measured invitro to evaluate the feasibility of the proposed method.Conclusion The proposed method was efficient for 3-D mea-surement with endoscopes in the experiments and is suitablefor downsizing because it is a single-lens system.
Keywords Endoscope · 3-D measurement · Shape fromfocus · Depth from focus · 3-D measurement endoscope
T. Takeshita (B) · M. Kim · Y. NakajimaSchool of Engineering, The University of Tokyo,Intelligent Modeling Laboratory Room # 602,Yayoi 2-11-16, Bunkyo, Tokyo 113-8656, Japane-mail: [email protected]
M. kime-mail: [email protected]
Y. Nakajimae-mail: [email protected]
Introduction
Endoscopes are widely used as common diagnostic toolssince they enable us to observe the inner parts of organsin a minimally invasive way. However, endoscopes gener-ally provide two-dimensional (2-D) images, which do notcontain depth information. Therefore, surgeons qualitativelyestimate 3-D shapes from 2-D images based on their experi-ences and knowledge.
The measurement of quantitative 3-D shapes by endo-scopes provides both texture and 3-D shape. Therefore, it hasmainly three merits. Firstly, it enables reliable, automatedscreening of polyps. Previously, several computer-basedscreening methods [1,2] have been proposed because theyhelp physicians to diagnose effectively and objectively. How-ever, most of them make use of either 3-D shape informa-tion from computed tomography (CT) [1] or 2-D endoscopicimages [2]. 3-D measurement endoscope has possibility toimprove screening accuracy and reliability since it providesthese two kinds of information. Secondly, it enables intuitiveunderstanding of diseased regions. Physicians can change thefield of view virtually and get a better understanding of posi-tional relationship between two points of interests. The mea-sured data could be useful during doctor–patient interaction.Lastly, it makes it easy to integrate 3-D shapes with preoper-ative data such as CT or magnetic resonance imaging (MRI).This fusion of endoscope images and preoperative data canbe used to guide endoscopes using preplanned paths [3].
There are several types of 3-D measurement endoscopesthat have been previously proposed. Most of all are classifiedinto 4 groups in terms of 3-D measurement method: shapefrom stereo [4], the laser scanning method [5,6], shape frommotion [7] and shape from shading [8]. Shape from stereois one of the most common 3-D measurement methods andis applied in many 3-D position sensor systems. However,
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Object Lens Image sensor
P
s’ s
QQ’
Camera
Fig. 1 A simple lens system model
this method uses two cameras and is thus not appropriate fordownsizing, which is necessary for uses with endoscopes.There is another method that avoids using two cameras.The ZaxialTM(iSee3D Inc., Canada) obtains stereoscopicimage pairs using a single-lens system. We think it couldbe a desirable technology for obtaining stereo image pairsand displaying 3-D shapes qualitatively. However, ambiguityoccurs in the stereo method when taking images with periodicpatterns [9] because correspondence computation betweenstereo images is needed to calculate disparity. Ambiguitycan occur when using endoscopes because, other than fold-ing, there are few features on the surface of organs comparedto the measurement of artificial objects. This may be prob-lematic for quantitative measurements. The laser scanningmethod is an active 3-D measurement method that enablesstable and accurate 3-D measurement. Similar to the stereomethod, it is not suitable for downsizing due to the laseremission mechanism that is required. Shape from motion isadvantageous when compared to the previous two methodsbecause it does not require additional mechanisms and canmeasure 3-D shapes with normal endoscopes. However, itrequires image sequence which contains motion for 3-D mea-surement and is thus inconvenient to use during surgeries.Shape from shading can also be easily integrated into normalendoscopes; nevertheless, this method increases error whenthere is texture on the surface of measured objects becauseit assumes no texture on the measured surface. Therefore, itis only appropriate to apply this technique to places wherethere is little surface texture, such as arthroscopic surgery.
Shape from focus (SFF) [10,11] and shape from defo-cus (SFD) [12,13] are also 3-D measurement methods. Bothtechniques use image focus to calculate depth of an image.They are desirable approaches to endoscopic 3-D measure-ment for two reasons. Firstly, they only require the use ofa single-lens system for 3-D measurement; thus, they canbe easily downsized and integrated into existing endoscopicsystems. Secondly, unlike shape from stereo, ambiguousmeasurements do not occur when presented with images ofperiodic patterns. As for sensitivity, Schechner and Kiryati[9] proved that depth sensitivities of SFF and SFD are notinherently less than those of the stereo-based systems havingthe same physical dimensions (aperture size in SFF and SFD,
Table 1 Device specifications
Parameter Specification
Device size
Diameter φ15 mm
Length of the measurement part 150 mm
Lens
Focal length 6.7 mm
F number 2.0
Image sensor
Type 1/4 inch, CMOS
Active Pixels 1,280 (H) × 1,024 (V)
Moving step 20 µm
Measurable depth range 10–30 mm
distance between cameras in stereo). Therefore, the sensitivi-ties of SFF and SFD are fundamentally the same as the stereomethod when applied into endoscopes because the diameterof an endoscope is limited.
Comparing SFF and SFD, SFF measures depth by focus-ing on objects, and thus, it requires many images, while SFDrequires two images and measures depth by calculating theirrelative amount of blur. Since the number of images usedin SFD is less than SFF, SFD is more suitable for the mea-surement of moving objects. However, SFF is more reliablesince it uses many images. Reliability is important for endo-scopes because texture is minimal when detecting imagefocus of biological organ surface compared with artificialobject surface. Although the employment of illumination pat-tern projection was proposed to increase texture and accuracy[13,14], this increases the size of the equipment.
In SFF, focus can be achieved by three methods: chang-ing the lens position with respect to the image sensor andobject, changing the image sensor position with respect tothe lens and object or changing the relative object positionwith respect to the camera. These positional relationshipsare illustrated in Fig. 1. Nedzved et al. [15] proposed a 3-Dmeasurement endoscope using SFF. In their method, focuswas achieved by changing the object position with respect tocamera. The endoscope is moved physically to obtain mul-tiple images of the object without changing lens positionand image sensor position. A depth map is constructed byextracting the focus regions of these images. The merit ofthis method is that it does not use additional focusing mech-anisms to change focus. However, it is not suitable for precise3-D measurement because it assumes that the camera posi-tion and its movement are known. In fact, it is difficult toknow these parameters precisely because of the followingtwo reasons. Firstly, it is hard to control the tip of endoscopeprecisely, especially for flexible scopes. Even a slightly unex-pected movement of endoscope in the direction of optical axiscould produce depth error. Secondly, objects move during the
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Fig. 2 A prototype of the 3-D measurement endoscope: a the measurement part, b overall view of the device
0
5
10
15
20
25
30
35
0.5 1 1.5 2 2.5 3
Dep
th [m
m]
Image sensor position [mm]
Measured pointsFitted curve
Fig. 3 A graph of the relationship between the focused image sensorposition and the depth at the image center: The fitted curve is used tocalculate depths using image sensor positions
measurement; thus, the endoscope would have to move fastenough to offset the movements of the objects in order toobtain proper measurements. This speed may cause dam-ages to the internal organs. In this paper, we propose a 3-Dmeasurement endoscope using SFF with an active focusingmechanism. It enables accurate quantitative measurements.The feasibility of the proposed endoscopic technology wasevaluated using a prototype made in consideration of endo-scope sizes.
Method
In this section, we will briefly discuss the principles aroundSFF. SFF is a 3-D measurement method using focus infor-mation. It provides a 3-D shape and an all-in-focus image.As mentioned above, focus is achieved by changing the lensposition, changing the image sensor position or changing therelative object position. Among them, changing either thelens position or the image sensor position is applied to ourmethod. In this section, we will focus on the method thatchanges the position of the image sensor for simplicity. Asimple lens system is depicted in Fig. 1. Diffused reflectionfrom point P passes through the lens and makes an image of
Fig. 4 An optical probe that provides the 3-D positions of objects thatit is directed at. It consists of a needle and an OPTOTRAK marker
point P at point Q. When point Q is on the image sensor, afocused image of point P is obtained.
Since the relationship between the focused image sen-sor (pixel) position and a focused position on the object isgenerally a one-to-one relationship, the depth (the distancebetween the lens and a measured object) can be calculatedusing the image sensor position when the measured object isfocused. A depth map is calculated as follows. Firstly, imagesare taken by changing image sensor position. Next, degrees-of-focus of corresponding pixels across all obtained imagesare compared. The image sensor position at the pixel with thebest focus, which is called “focused image sensor position,”is calculated. This is repeated for all pixels. Finally, a depthmap is converted from the focused image sensor positions.
The acquired images generally contain blur and are thusnot so useful for direct clinical applications since SFFrequires the use of the lens system with a shallow depth offield (DOF) to detect focus precisely. However, an all-in-focus image can be made by collecting focused pixels fromacquired blurred images.
Focus measure
Various focus measurement methods have been proposedpreviously [10,11,16]. In this section, we introduce a simple
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Fig. 5 Experimental setups of the accuracy evaluation. Arrangementof both experiment is the same with the exception of the usage of plateand cylinder: a A textured plate is placed in front of the prototype. It isinclined about at 45◦. b A textured cylinder whose diameter is 20 mmis placed
focus detection methods using high-pass filtering [16]. Thismethod was applied in our experiments. Let s be the positionof the image sensor on the optical axis as shown in Fig. 1, letg (s, x, y) be the image intensity function where x and y arespatial coordinates, and let d (x, y) be the distance from thelens to the measured object. The purpose of SFF is to com-pute d(x, y) from g (si , x, y), for i = 0, 1, 2, . . . , M − 1where M is the number of acquired images. Let f (x, y) beg (s, x, y) without blur. By using the point spread function(PSF) h (s, x, y) , g (s, x, y) is expressed by
g (s, x, y) = h (s, x, y) ∗ f (x, y) (1)
where * denotes the 2-D convolution along x and y. The PSFis camera specific. The pillbox function [13] or the Gaussianfunction [10] has often been used for imaging devices witha circular aperture. Here, the Gaussian function is used forsimplicity. It is given by
h (s, x, y) = 1
2πσ(s, x, y)2 e− x2+y2
2σ(s,x,y)2 (2)
where σ is proportional to the amount of blur. Assuming thatσ is locally constant, we substitute Eq. (2) into Eq. (1) andtake the Fourier transform of both hand sides to obtain
G (s, u, v) = e− u2+v22 σ(s)2
F (u, v). (3)
In Eq. (3), u and v denote the spatial frequencies. F and Gdenote the Fourier transform of f and g, respectively. Asobvious from Eq. (3), high-frequency component G(s, x, y)
decreases when the amount of blur σ increases. This meansthat the degree of focus can be compared by using the high-frequency power |G(s, u, v)|2. As the computational cost ofFourier transform is high, the high-pass-filtering method isoften used to estimate the power of high-frequency com-ponent. This computation can be separated into two steps.Firstly, high-pass filter is applied to the image g(s, x, y) toremove low-frequency components. In this paper, the Lapla-cian of Gaussian (LoG) was used as the high-pass filter. It isgiven by
LoG(x, y) =(
x2 + y2 − 2σ 2l
σ 4l
)e− x2+y2
2σ2l . (4)
Let the resulting high-pass-filtered image be g′(s, x, y).Using LoG (x, y) and g(s, x, y), g′ (s, x, y) is expressed by
g′ (s, x, y) = LoG (x, y) ∗ g(s, x, y). (5)
In this paper, the degree of focus is evaluated by
fm (s, x, y)
=y+N∫
Y=y−N
x+N∫X=x−N
e− (X−x)2+(Y−y)2
2σ2w .g′ (s, X, Y )2 dXdY
(6)
where Gaussian window is used for the pixels closer to (x, y)
to get more weights. In this paper, Eq. (6) is used to comparedegree of focus.
Calculation of depth map
Focused image sensor position, which is the image sensorposition when object is in focus, is calculated as
s f (x, y) = arg maxs
fm (s, x, y). (7)
Using the relationship between focused image sensor posi-tion s f (x, y) and depth d(x, y) calibrated previously, depthd(x, y) can be easily calculated from s f (x, y). The concretemethod to estimate the relationship is described in “Cali-bration”. In fact, as image position s is a discrete variable,s f (x, y) is obtained by fitting a curve such as the Gaussianfunction to (si , fm (si , x, y)), for i =0, 1, 2, . . . , M −1 [10].
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Fig. 6 Measured 3-D shapes of artificial objects. All-in-focus images are mapped on the surfaces. a–c Three views of the plate. d–f Three viewsof the cylinder
Fig. 7 Computed error maps of artificial objects. The error was theabsolute value of the difference between the measured depth map andthe ground truths that measured by OPTOTRAK. The color represents
the amount of the error. Red indicates large error and blue indicatessmall error: a error map of a plate, b error map of a cylinder
The all-in-focus image is obtained by
g f (x, y) = g(s f (x, y) , x, y
). (8)
This image is mapped on the surface of the measured 3-Dshape.
Table 2 Estimated error
RMS error (mm) Maximum error (mm)
Plate 0.87 1.9Cylinder 0.64 2.3
Implementation
A prototype was made in consideration of sizes of actualendoscopes. Endoscope diameter was an important variablebecause the aperture size affects the sensitivity in SFF asmentioned in section “Introduction”. In this section, we dis-cuss the implementation and the development method ofthe prototype. The focus technique used by this prototypeis achieved by moving its image sensor.
Parameter settings of the prototype
Three factors need to be considered when setting the cam-era parameters. First is DOF. As SFF needs accurate focus
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Fig. 8 Experimental setup for the measurement of pig stomach
detection, DOF should be set in consideration of the requireddepth resolution. Let c be the diameter of the circle of con-fusion, let f be the focal length, and let F be the F number.DOF T is expressed by
T ≈ 2 f 2d2 Fc
f 4 − F2c2d2 . (9)
Ray [17]. Second is the range of the workspace becauseSFF needs to focus on measured objects in SFF. Therefore,the depth of the workspace determines the range of s. Thirdis the interval at which image sensor moves. Too small stepsize is useless because the image sensor cannot detect suchsmall difference limited by DOF.
Considering the above points, we fabricated the proto-type to resemble a gastroscope using parameters shown inTable 1. Parameters were set for DOF, with T being less than1.0 mm so that 2 mm polyps could be detected. The prototypewe developed is shown in Fig. 2. Focusing is performed bymoving the image sensor position with the wire in Fig. 2b.The wire is moved by a stepper motor. A photo interrupter ismounted on the measurement part to offset the origin of theimage sensor position. This offset is performed every time
at the beginning of a measurement because the image sensorposition changes as the wire bends. A spring is also placedhere to sustain the tension of the wire. Spatial resolution ofthe image to the real space is given as 1 pixel equaling toroughly 8.6–14.4 µm.
Calibration
Here, we introduce how to get the relationship betweenfocused image sensor position s f (x, y) and depth d(x, y).First, a calibration board with checkerboard pattern is setin front of the prototype. The focused image sensor positions f (x, y) at every pixel is calculated as shown in “Focus mea-sure”. The depth map is calculated by an optical 3-D positionsensor. Thus, a pair of s f (x, y) and d(x, y) is obtained. Sim-ilarly, changing the position of the calibration board, the pairof s f (x, y) and d(x, y) is measured several times. Finally, acurve is fitted to the pairs at every pixel. The measured pointsand fitted curve at the center pixel of the image are shown inFig. 3. The image sensor is moved with a step size of 20 µm,which results in a change in focus depth of about 0.1–0.6 mmwith the prototype. This change in focus depth is positivelycorrelated to the focus depth; a large focus depth correspondsto a large change in focus depth.
Experimental results
For validation of the proposed method, the prototype wastested in the following two experiments. Firstly, the accuracywas evaluated by measuring artificial objects whose shapesare already known. Next, the inner wall of pig stomach wasmeasured in vitro to evaluate the feasibility of our methodfor the use of endoscope. Images were taken at 101 imagesensor positions to measure one 3-D shape. The depth mapswere computed by a DELL PRECISION T7400 with Intel(R)Xeon(R) CPU X5460 3.16 GHz and 3.25 RAM.
Fig. 9 a–f Sample images taken by the prototype in the measurement of pig stomach. g–l Measured depth maps of pig stomach (a–f). The colorrepresents the depth from the prototype to measured objects. Red indicates near distance and blue indicates far distance
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Fig. 10 Two views of the estimated shape of pig stomach. All-in-focusimage is mapped on the shape
Accuracy evaluation
The depth maps of a plate and a cylinder were measured withthe prototype to evaluate the accuracy. For the evaluation, themeasured depth maps were compared with the ones that wereobtained by an optical 3-D position sensor (OPTOTRAK,Northern Digital Inc.), which served as the ground truths.The ground truth of the depth map was obtained followingthe procedures described below.
For simplicity, we show only the case of the plate. Thesame approach can be applied in the case of the cylinder.Three OPTOTRAK markers were used. Each marker pro-vides spatial coordinates with respect to a world coordinatesystem. One marker is attached to the endoscope and anotheris attached to the plate. Let these markers be denoted by Te
and To, respectively. The third marker Tp is attached to aneedle as shown in Fig. 4. Since the relative position of thetip of the needle with respect to Tp has been already known,
this needle provides the 3-D position of its tip. We call thisdevice an optical probe, which can be used to measure thelocation of objects it points at. By using two markers andthe probe, the position of the surface is obtained as follows.First, many sample points on the plate surface are obtainedin the coordinate system of To using the probe. Next, sincethe shape of the object being measured is already known, aplane is fitted to the sample points. Then, the position of theplate is expressed in the coordinate system of the endoscopemarker Te. Furthermore, the camera parameters of the endo-scope are obtained by camera calibration [18]. Finally, theground truth of depth map is calculated using the position ofthe fitted surface and the camera parameters.
As SFF requires surface texture of measured objects,checkerboard patterns were attached on the surfaces of themeasured objects. The experimental setups are shown inFig. 5. The measured plate was placed inclined to the pro-totype at about 45◦. The diameter of the measured cylinderwas 20 mm. The distances from the tip of the prototype to themeasured objects were in the range between 10 and 30 mm.
The measured 3-D shapes are shown in Fig. 6a–c for theplate and Fig. 6d–f for the cylinder. All-in-focus images aremapped on the surfaces. The estimated errors are shown inFig. 7 and Table 2. Figure 7 shows the absolute differencebetween the measured depth and the ground truth measuredby OPTOTRAK. The maximum error was 2.3 mm at thelower left of the error map in the cylinder measurement asshown in Fig. 7b. The RMS errors of measured depth were0.87 mm for the plate and 0.64 mm for the cylinder. The timefor taking images for one measurement was 27 s. The com-putational time was about 57 s.
Measurement of biological organ
It is important to check the feasibility by measuring biolog-ical organ because focus detection uses the texture of mea-sured objects. Thus, pig stomach was used in this experiment.Six samples of the inner wall of pig stomach were placed infront of the prototype and measured. The experimental setupis shown in Fig. 8. Sample images taken by the prototypeare shown in Fig. 9a–f. The range of the distance from thetip of the prototype to the measured object was the sameas the experiment in “Accuracy evaluation”. Time averag-ing (10 images) was performed over the images used for thecomputation to increase the signal-to-noise ratio (SNR).
The ground truth of the pig stomach was not obtainedby OPTOTRAK because of two reasons. First, the shape ofthe pig stomach is so soft that sampling by pointing with theprobe is difficult because the shape could deform. Second, theexact shape of the pig stomach is not known. Thus the groundtruth and the error of the measurement are not provided. Weevaluate the result qualitatively.
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The results of measured depth maps are shown inFig. 9g–l. The measured depth maps were fairly good as awhole since folds and inclinations of the surface were mea-sured. However, there were some error regions such as at theupper right corner in Fig. 9i. Estimated texture-mapped 3-Dshape of the sample shown in Fig. 9a is shown in Fig. 10.The time for taking images for one measurement was 162 sincluding time averaging.
Discussion
In the accuracy evaluation experiments, the maximum errorwas 2.3 mm. It occurred at the lower left part of the depthmap of the cylinder measurement shown in Fig. 7b. At thisposition, the inclination of the object (cylinder) surface withrespect to the image plane was large. Also, there was imageshift caused by focusing because the image sensor movedas images are taken. For example, in Fig. 1, when the imagesensor is placed at s, the image of point P is at point Q.By changing the image sensor position, the image of P is atpoint Q’. Thus, there is image shift from point Q to point Q’.Moreover, focus measurement uses spatial filter and depthchange in the filter kernel also increased the error. We thinkthat the large inclination and the image shift resulted in arelatively large error. To improve the accuracy, employmentof tele-centric optics [13] or compensation of zoom distortion[19] is required.
The results of pig stomach measurement showed someerror regions, especially in Fig. 9i, l. In SFF, texture is usedto measure degree of focus. However, texture quality waspoorer on the surface of the pig stomach when compared tothat of the artificial objects since checkerboard patterns wereattached on the surface to enhance the contrast while there isno additional texture on the surface of pig stomach. To over-come this point, we think there are three methods: improv-ing focus measuring method for noisy images, employingillumination that enhances the texture, and introducing high-sensitivity image sensor.
The diameter of the prototype was 15 mm. It is a littlelarger than existing normal gastroscopes, whose diameter isfrom 5 to 11 mm. However, the diameter of the lens itself was6 mm. Thus, we believe that miniaturization can be achievedduring fabrication. As for the length of the measurement part,the largest unit is the CMOS image sensor controller as shownin Fig. 2a, which is 52 mm in the direction of the opticalaxis. By using a smaller image sensor system or separatingthe controller from the measurement part, the length can beshorter.
Due to its shallow DOF, acquired images are not suit-able for inspection. As we showed, SFF provides all-in-focusimage, which we think can be used for inspection. For takingimages faster, we think it is effective to change the optical
settings of the lens in order to be used as a general endoscope.This can be done by increasing the DOF, such as changingthe aperture size or the focal length.
For practical uses, the time of taking images should beshorter because SFF assumes that measured objects do notmove while images are taken. There are three main methodsto reduce the image acquisition time. Firstly, time averagingwas used to increase SNR to measure the pig stomach. Thisprocess was used to increase the signal-to-noise ratio (SNR).More robust focus detection method or enhancing of texturecould reduce or eliminate the time-averaging process. Thesecond method is to introduce faster image sensor. The imagesensor used in the prototype takes images about 5 frames persecond (fps) for obtaining the image resolution of 1,280 ×1,024 pixels, and it could be replaced by higher one. Thelast method is the optimization of the parameters used for ameasurement. Especially, we think that the optimization ofthe image resolution and the number of images used for ameasurement could decrease the image acquisition time.
Conclusion
A 3-D measurement endoscope using SFF was proposed. Itemploys a focusing mechanism to measure texture and 3-Dshape without moving the endoscope itself. A prototype wasmade in consideration of actual endoscope sizes. The methodwas validated by experimenting on artificial objects and a bio-logical object using the prototype. Firstly, the accuracy wasevaluated measuring artificial objects. The RMS errors were0.87 mm for a plate and 0.64 mm for a cylinder. Next, innerwall of pig stomach was measured in vitro to qualitativelyevaluate feasibility of the proposed method. Although therewere some error regions, the shape was well reconstructed asa whole. The proposed method enables 3-D measurementswith a single-lens system and was efficient for 3-D measure-ment in the experiments.
Conflict of interest This research is conducted at the University ofTokyo and has no known conflicts of interests with any organizations
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