Optimized stereo matching in binocular three-dimensional measurement system using structured light Kun Liu, Changhe Zhou,* Shengbin Wei, Shaoqing Wang, Xin Fan, and Jianyong Ma Laboratory of Information Optics and Optoelectronics Techniques, Shanghai Institute of Optics and Fine Mechanics, University of Chinese Academy of Sciences, P.O. Box 800-211, Shanghai 201800, China *Corresponding author: [email protected] Received 14 May 2014; revised 6 August 2014; accepted 6 August 2014; posted 12 August 2014 (Doc. ID 212055); published 10 September 2014

In this paper, we develop an optimized stereo-matching method used in an active binocular threedimensional measurement system. A traditional dense stereo-matching algorithm is time consuming due to a long search range and the high complexity of a similarity evaluation. We project a binary fringe pattern in combination with a series of N binary band limited patterns. In order to prune the search range, we execute an initial matching before exhaustive matching and evaluate a similarity measure using logical comparison instead of a complicated floating-point operation. Finally, an accurate point cloud can be obtained by triangulation methods and subpixel interpolation. The experiment results verify the computational efficiency and matching accuracy of the method. © 2014 Optical Society of America OCIS codes: (110.6880) Three-dimensional image acquisition; (120.2830) Height measurements; (150.6910) Three-dimensional sensing; (330.1400) Vision - binocular and stereopsis. http://dx.doi.org/10.1364/AO.53.006083

1. Introduction

Noncontact and nondestructive three-dimensional (3D) digitalization of objects has attracted more and more attention and applications over the past decade. Examples of such applications include human-body-scanning, computer-aided medical procedures, 3D documentation of precious cultural relics, reverse engineering of existing mechanical devices, inspection and control of shape quality in industrial production systems, computer graphics and special effects, intelligent robot navigation, and movies and video games in the entertainment industry. A number of technologies have been developed for digitally acquiring the shape of 3D objects [1–10]. Noncontact active 3D scanners measure the surface through emitting light with its own light source. In contrast, passive scanners detect the 3D shape by the 1559-128X/14/266083-08$15.00/0 © 2014 Optical Society of America

features of the object itself. A time-of-flight 3D scanner is an active scanner that resolves distance based on the known speed of light [2]. The round-trip time determines the travel distance of the light, which is twice the distance between the scanner and each point on the surface. A triangulation-based 3D scanner that uses a laser dot or laser line to scan the object is also an active scanner [3]. Depending on how far away the laser strikes a surface, the laser dot or laser line appears at different places in the camera’s field of view. With respect to a time-of-flight scanner, the available range and depth variation of triangulation-based scanners are limited, but they have higher precision. A structured light-based 3D scanner projects one or more two-dimensional structured patterns onto the surface of an object in the scene and analyzes the information from the images of object [4–7]. The specially designed patterns can be projected using either a projector or other apposite light sources. A camera, offset slightly from the projector, looks at the object. The distance between the 10 September 2014 / Vol. 53, No. 26 / APPLIED OPTICS

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reference plane and points on the surface can be calculated. Instead of emitting any kind of radiation themselves, passive scanners rely on detecting reflected ambient radiation. For this reason, passive scanners cannot reconstruct objects’ lack of features, such as in human faces and white walls. There is a growing emphasis on accuracy and the speed of the measurement. Phase shifting is a wellknown fringe projection method for 3D measurement. A set of sinusoidal patterns whose phases are shifted a constant angle with respect to each other is projected onto the object surface. Lally et al. proposed a 3D shape-measurement algorithm based on a multiple reference method and shown to have RMS surface error less than 0.03 mm [8]. Wang and Zhang developed a 556 Hz system utilizing a three-frequency algorithm for simultaneously measuring multiple objects [9]. Gorthi et al. proposed a high-order instantaneous moments operator-based method for accurate and efficient phase estimation in digital holographic interferometry [10]. In this paper, we develop an optimized stereomatching method used in an active binocular 3D measurement system. The 3D measurement setup consists of two cameras and a portable projector. A binary fringe pattern (BFP) is projected on the object and divides the surface of the object into some vertical areas. Afterward, a series of N binarized bandlimited statistical patterns (BBLP) encodes the surface of the object. The optimized stereo-matching method that avoids a lot of unnecessary calculations is conducted to perform dense stereo matching. On one hand, the introduction of a binocular camera structure reduces the occlusion-caused unmeasurable area in a conventional single-camera structured light system. On the other hand, dynamic binary structured light projection greatly accelerated the dense stereo-matching process, which used to be a timeconsuming process. The 3D measurement system can meet the high-accuracy 3D measurement requirements for static objects at a cost of relatively short data-processing time. There are three sections in the rest of this paper. Section 2 briefly introduces the composition and main parameters of the system, as well as the 3D reconstruction algorithm we used. Section 3 describes the algorithm in detail and gives the experiment results. Finally, we give a conclusion in the last section. 2. 3D Reconstruction Scheme

Figure 1 shows the schematic view of the optical setup for our 3D measurement system. This setup uses two 1.3 million pixel cameras (resolution  1280 × 960, CCD size  1∕300, pixel size  3.75 μm), which observe an object at a 0.5–0.8 m distance. The effective focal length of the lens is 8 mm and the length of base line is about 300 mm. In addition, there is a portable digital light procession projector with resolution of 800 × 600 placed between the two cameras. During measurement, a series of binary 6084

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Fig. 1. Schematic view of the active binocular 3D measurement system.

structured light patterns will be projected toward the object via the projector and captured by the cameras simultaneously. Similar to stereo vision of human eyes, dense stereo matching will be performed to search the homologous point, which is a pair of image points resulting from the same object point. A 3D point cloud can be obtained using the disparity between homologous points by triangulation methods. In this paper, a plaster head and a shell will be used to illustrate our scheme. Reconstructing 3D world coordinates from a twodimensional image plane, we need the corresponding parameters of cameras. The cameras are modeled as a traditional pinhole model and have been calibrated with a MATLAB toolbox before the measurement [11], so we know their intrinsic parameters (principal points, focal length, pixel size, and distortion coefficient) and extrinsic parameters (a 3 × 3 rotation matrix R and a 3 × 1 translation vector T). The rotation matrix and translation vector characterize the relative location of the right camera with respect to the left camera. Let P be a point on the target surface of coordinate vector XX L  x1 ; y1 ; z1  in the left camera coordinate system. Let XX R  x2 ; y2 ; z2  be the coordinate vector of P in the right camera coordinate system. Then XX L and XX R are related to each other through the following rigid motion transformation equation: XX L  XX R R  T:

(1)

Apart from the fact that rectifying the images results in a particularly simple structure for the epipolar line, it also results in a very simple reconstruction of depth [12,13]. As shown in Fig. 2, the rectified stereo configuration is displayed as viewed along the direction of the row axis of the images, i.e., the y axis of the camera coordinate system. By examining the similar triangles O1 O2 PW and P1 P2 PW , we can see that the depth of PW only depends on the disparity of P1 and P2 . Hence, the depth is given by z

fb fb  ; dW SP dP

(2)

Fig. 2. Rectified stereo configuration of a binocular 3D measurement system.

where b is the length of the base, f is the focal length, and dW is the disparity of P1 and P2 , i.e., the sum of the signed distances of points P1 and P2 to the principal points C1 and C2 . We will convert dW to world coordinates by scaling it with pixel size: dW  SP dP , SP is the size of the pixel. It is noted that SP especially represents the pixel size after rectification. As shown in Fig. 2, we can easily see that dP  cc1 − cc2   c2 − c1 , where c1 , c2 , cc1 , and cc2 denote the column coordinates of the points P1 , P2 , and the principal points, respectively. From Fig. 2 and Eq. (2), we can find that the lateral resolution is mainly caused by pixel size and focal length and longitudinal resolution depending on the angle between chief ray, pixel size, focal length, and length of base. In our setup, the lateral resolution is 0.3 mm and longitudinal resolution is about 0.8 mm. As we have mentioned, determination of disparity for each pixel is one of the most important steps of most binocular 3D measurement systems. However, surfaces of some objects, like a plaster or white wall, are too textureless to detect features, so matching methods based on passive scanning fail to find homologous points. Hence, some identifiable features should be added on the object by active scanning. So far, most stereomatching algorithms can be regarded as correlation-based template matching problems. Traditional template matching methods—sum of absolute intensity value differences, sum of squared intensity value differences, normalized cross correlation, or zero mean normalized cross correlation (ZNCC)—purely perform template matching in spatial domain, i.e., areal correlation technique. These methods give a rectangular correlation window around the current pixel in the left image and search the most similar window along the epipolar line in the right image. Chen and Chen proposed a 3D camera system that projects a random speckle pattern on the object and uses a spatial distance computation to find correspondence vectors [7]. However, with areal correlation technique, deformation caused by the different camera angle leads to many false matches and bad 3D reconstruction precision. On the other hand, some study found that reducing the size of correlation windows to one pixel in the spatial domain and extending the length of the correlation windows to N pixel

in the temporal domain solves this problem [14,15]. This is the so-called temporal correlation technique (TCT). Davis et al. comprised the performance of spatial and temporal matching in the measurement of static objects and got a conclusion that temporal matching produces much better results than spatial matching [14]. Based on this conclusion and our measurement needs for static objects, TCT will be used here. To encode the surface of the object, a series of N statistical patterns will be projected to the target objects via the portable projector. Wiegmann et al. introduced bandlimited random patterns (BLP), which avoids the negative influence of binary pixelized patterns in 3D reconstruction [16]. Grosse et al. further pointed out that the quality of the reconstruction was further improved by using BBLPs. Benefiting from better contrast, the BBLP delivers the most point matches as well as the lowest noise level. For more information about random patterns and laser speckles used in 3D measurement, Refs. [7,15–18] are given for details. Figure 3(b) shows an example of a BBLP. Each BBLP projected onto the surface, as shown in Fig. 3(d), will be captured synchronously by two cameras. After capture is finished, there are N pairs of stereo images. Then, rectification will be performed using a MATLAB toolbox [11] to ensure that the epipolar line for a point is simply the line that has the same row coordinate as the point, i.e., the epipolar lines are horizontal. After the rectified images are obtained, a series of operations that contains extraction of the region of interest (ROI), SAB, initial matching, exhaustive matching, and so forth will be performed in order to reconstruct the 3D surface. 3. Experiment and Analysis

In this section, we will discuss the reconstruction procedure from extraction of the ROI to output of point cloud in detail. A. Extraction of the Region of Interest

After the rectified images are obtained, morphological operations will be done to extract the ROI. ROI is the area where the target objects are located, and all subsequent operations will be carried out within ROI. We select an intensity threshold for image segmentation that selects pixels whose intensity value is greater than the threshold value in the temporal average value image. At first, we read rectified stereo image pairs in turn and calculate the temporal average intensity of each pixel. For a pixel sequence, temporal average intensity can be calculated as follows: I AVE x; y 

PN

t1

Ix; y; t : N

(3)

Figure 4(a) shows the temporal average image of the left side calculated using Eq. (3). It is obvious that target objects reflect light leads so they are 10 September 2014 / Vol. 53, No. 26 / APPLIED OPTICS

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Fig. 3. (a) Binary fringe pattern. (b) Binarized bandlimited statistical pattern. (c) Rectified binary fringe pattern of object. (d) Rectified binarized bandlimited statistical pattern of object.

brighter than the background. Based on this understanding, pixels whose intensity value is less than a threshold will be returned to zero, and the other pixels will be returned to one. In other words, the temporal average images are binarized. To remove noise and small gaps in binarized temporal average images, we build a disk-shaped structural element

and simply perform a closing. In image processing, opening removes small objects, while closing removes small gaps. Figure 4(b) shows the ROI extracted from temporal average image. B. Self-Adapting Binarization

In order to eliminate the harmful impact caused by uneven brightness, defocus, or texture of the object itself and simplify the calculation process, a selfadapting binarization (SAB) is used in our method. Different from the local window binarization used in [7], we use the temporal average intensity of the pixel sequence as the threshold for binarization process of the pixel sequence itself, i.e., self-adaptive. Experiments have proved that SAB helps us test some objects with complex surface texture, such as a vase. For one pixel Ix; y; t in stereo-image pairs, the binarization value I BW x; y; t can be defined as follows:  I BW x; y; t 

1 0

Ix; y; t > I AVE x; y : Ix; y; t ≤ I AVE x; y

(4)

Figure 5 shows a binarization image of left side. C.

Fig. 4. (a) Temporal average image of left side. (b) ROI extracted from temporal average image. 6086

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Initial Matching

To obtain a sufficient number of point clouds, dense stereo-matching algorithms calculate, or at least attempt to calculate, a disparity for each pixel. Most of the stereo-matching algorithms calculate disparities by evaluating similarity measure. Since it tolerates uniform brightness variations as well, ZNCC-based template matching is one of the most popular

Fig. 5. Binarization image of left side.

similarity measure algorithms. For the TCT-based stereo-matching problem, it is given by TCTx; y; d PN I L x; y; t − M L  · LR x  d; y; t − M R  :  t1 SL x; y; t · SR x  d; y; t

(5)

The numerator of Eq. (5) represents the correlation cross correlation between the two temporal intensity value vectors, and binocular correlation aligns horizontal epipolar lines so that there is no vertical disparity. Furthermore, M i and Si denote the mean intensity value and the standard deviation of the temporal intensity vector in the left and right images, i.e., M

N 1X Iu; v; t; N t1

v u N u1 X Iu; v; t − M2 : St N t1

(6)

(7)

We should note that −1 ≤ TCT ≤ 1. While the two temporal intensity value vectors match perfectly only if TCT  1, large absolute values of the TCT generally indicate that the temporal vector closely corresponds to each other. Two pixels are considered to be homologous when the TCT exceeds the threshold and reaches a maximum. However, Eq. (5) contains complicated floating-point number operations such as square, multiply, plus, and subtract; its computation turns out to be the bottleneck in the evaluation of the TCT. Moreover, the operation of searching the homologous pixels in ROI, evaluating the TCT function value within a width search range, and determining the homologous pixel pairs is very time consuming. Other than the complexity of the calculation itself, another factor that causes dense stereo matching to be time consuming is that for each pixel in the left, a ROI matching algorithm needs to evaluate the similarity measure at all possible positions to find the homologous one. For example, if we want to find the homologous pixel of P, a pixel in the left ROI, we would have to evaluate the similarity measure

along the entire epipolar line in the right image. Fortunately, this is not the case. Since the disparity is inversely related to the depth of a point, we typically know in which range of distances the points we are interested in occur. Therefore, we can restrict the disparity search range to a much smaller interval than the entire epipolar line. We have d ∈ dmin ; dmax , where dmin and dmax can be estimated from the minimum and maximum expected distance in the images. Hence, the length of the disparity search range is given by L  dmin − dmax  1. After we have evaluated the similarity measure for the disparity search range for a pixel to be matched, we attempt to use the disparity with the maximum similarity measure as the match for the current pixel. However, this typically leads to many false matches, since some pixel may not have a good match in the right image. For example, the current pixel is occluded because of the perspective effects. With the above search strategy, the matching process has a complexity of OWHLN. W and H denote the size of the image. This complexity is too expensive for real-time application. Fortunately, it can be shown that with a clever implementation, the above similarity measures can be computed simply. To derive a faster search strategy, we note that the runtime complexity of the TCT mainly depends on the length of search range and the complexity of the matching methods. In this section, we mainly discuss the method to reduce the search range. Therefore, to prune the search range, we project a BFP onto the object. As shown in Fig. 3(a), BFP is composed of a series of vertical black and white stripes. It is obvious that the homologous pixels must be located within the corresponding fringes in the stereo-image pairs. In other words, we can find corresponding fringes before homologous pixels. These operations provide huge convenience to search homologous pixels. First, by establishing the ROI, we reduce the search area from a whole image to a relatively small area. Second, a disparity search range will be cut greatly by projecting BFP. For a pixel in the left image, we just need to search the homologous one along the epipolar line in a narrow range designated by the corresponding fringe in the right image instead of searching all possible pixels. We call this process initial matching. Third, instead of complex floatingpoint arithmetic, we use simple logic operations to evaluate the similarity measure. The above optimization strategies derive a faster search strategy in dense stereo matching. Figure 3(a) gives an example of a BFP: The size of the pattern is 800 600 pixels, and the width of each fringe is 30 pixels. Figure 3(c) shows the captured BFP image. There are two rectangles embedded in each fringe, and the area of those rectangles increases from up to down. Different areas and locations help us identify them easily. Rectangles embedded in neighboring fringe maintain a certain horizontal distance, like 10 pixels. In a pair of rectified BFP stereo images, a rectangle in the left side 10 September 2014 / Vol. 53, No. 26 / APPLIED OPTICS

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will only correspond to one rectangle in the right side on the epipolar line if the homologous one is in the field of view of the right camera. Once we find the homologous rectangles, that means the two fringes that the small rectangles are located in are the corresponding ones. Given a pair of rectified BFP stereo images, we extract the pixel index and center coordinates of the rectangles by morphological analysis at first. If a pair of rectangles meet the following three conditions, then they will be determined as homologous ones: (1) Two rectangles have a similar area. Because of the angle difference between the two cameras, the left and right images of the same rectangular have different areas. If the area difference between the two rectangles is less than 50%, this pair of rectangles will be selected as candidates:

points_Left points_Right

100

200

300

400

500

600

SL − SR < 50%: SL

700

(8)

800

900

(2) The position shifted in the vertical direction between the center coordinates of the candidates is not more than 5 pixels. In the ideal case, homologous points have the same row coordinates in the rectified images. Because of the same reason as the first condition, we relax this condition to 5 pixels: jyL − yR j < 5:

200

400

600

800

1000

1200

(9)

(3) Two rectangles have the same color properties, i.e., both white or black. We determine that two rectangles are homologous when the above three conditions are met. In some cases, because of occlusion or other reasons, it is difficult to find the corresponding rectangle. Therefore, arranging a plurality of rectangles at different positions in each stripe improves the robustness of this algorithm. In other words, as long as a pair of homologous rectangles exists, the stripes will be determined homologous. Figures 6(a) and 6(b) show the stripes and rectangles extracted from the BFP image. Figure 6(c) displays an overlay of a pair of stereo images with a color-coded plot of the corresponding stripes connected by yellow lines. Figure 6(d) explains the search strategy based on initial matching. At last, we find 15 pairs of corresponding stripes that have been connected by yellow lines. Red and cyan represent the left and right images, respectively. As a comparison, we introduce another search range optimization method, which is based on an estimate of disparity. As shown in Fig. 7, the steps are as follows: (1) We compute the centroid of each row of ROI. (2) Estimated disparity is obtained by simply subtracting the column coordinates of the left centroid from the right: 6088

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Fig. 6. (a) Stripes extracted from the BFP image. (b) Rectangles extracted from the BFP image. (c) An overlay of a pair of stereo images. (d) The search strategy based on initial matching.

dE  xR − xL :

(10)

(3) We evaluate the similarity measure along the epipolar line in a certain range centered on the estimated disparity and within a radius of 100 pixels. So the search range can be defined as follows:

Fig. 7. Search strategy based on estimated disparity.

dmin  maxdE − 100; xL  dmax  dE  100:

(11)

In the case of no search range optimization, the number of similarity measure is 61132183. The simplified algorithm based on estimated disparity reduces this number from 61,132,183 to 29,369,918 by roughly one half. By contrast, the search strategy based on initial matching has such an excellent performance that the number of similarity measures is reduced from 61,132,183 to 15,576,354, roughly 25%. D.

Exhaustive Matching

After initial matching, we process the pixels that belong to the corresponding stripes at first. As shown in Fig. 6(d), for a pixel P belonging to stripe A in the left image, we can find the corresponding stripe B in the right image according to the result of initial matching. Afterward, we search the homologous pixel of P among the pixels that have the same row coordinate with pixel P in the stripe B using a logical comparison-based temporal correlation technique (LTCT): LTCTx; y; d 

N X

f I BWL x; y; t; I BWR x  d; y; t;

t1

(12)  f I 1 ; I 2  

1 0

I1  I2 ; I1 ≠ I2

(13)

where I BW x; y; t; t ∈ 1; N is the pixel in binarized rectified image. Instead of the complicated floating-point operation in Eq. (7), LTCT evaluates the similarity measure using an integer logical operation that is faster and simpler than floating-point operation. When using N  15 projected BBLP, we choose 13 as the threshold. Once the LTCT values reach the maximum and above the threshold, we tempted to use the disparity as the match for current pixel. Indeed, there are still some stripes that do not find the corresponding ones. The remaining pixels belonging to those stripes will be analyzed later. Finally, disparity data will be output to calculate the 3D coordinates using triangulation methods. E.

Fig. 8. (a) Disparity map. (b) Distribution of disparity.

defined as a ratio between the disparities of pixels and the average disparity of a small square window around them: di < 5%; dAVE

dAVE 

Pm

i−m

Pm

j−m

disx  i; y  j

2m  12

(14)

;

(15)

Outliers Filter

After obtaining the original homologous point set, there are still some outliers that are not physically homologous mixed in the points set. Therefore, it is necessary to find additional criterion to removing them from output homologous points set.

where di is the disparity of the pixel and disx; y is the disparity map. This assumption is based on the fact that the disparity gradient for correct matches is small in most cases of binocular stereo.

(1) A distribution map of disparity will be drawn [as shown in Figs. 8(a) and 8(b)], and the points whose disparities are associated with a less than 20 pixel number will not be accepted as homologous points. (2) We place a limit of the disparity gradient for acceptable matches, where a disparity gradient is

Disparities obtained from the above operations are integers, and point pairs that have the same disparities correspond to the same depths. This leads to obvious stratification of the point cloud. Indeed, corresponding points are not often located at integer coordinates, so subpixel interpolation is performed to obtain the precise measurements. In image

F.

Subpixel Interpolation

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standard deviation (RMS) is smaller than 60 μm. This experimental result demonstrated the effectiveness of optimized stereo matching with significantly reduced searching area for practical binocular 3D measurement. The authors acknowledge the support of the National Natural Science Foundation of China (grant numbers 61127013, 61308073, and 61307064) and the Foundation of State Administration of Culture Heritage (grant number 20120228). References Fig. 9. Result of 3D reconstruction.

processing, bicubic interpolation is often chosen over bilinear interpolation or the nearest neighbor in image resampling. In contrast to bilinear interpolation, which only takes 4 pixels (2 × 2) into account, bicubic interpolation considers 16 pixels (4 × 4). Images resampled with bicubic interpolation are smoother and have fewer interpolation artifacts. During subpixel interpolation, we use Eq. (5) as the similarity evaluation function. Figure 9 gives the result of a measured plaster statuette of a woman’s head. The related point cloud consists of more than 2.2 × 105 points. It is worth noting that this plaster statuette occupies a region of 2.5 × 105 pixels in the entire image. In other words, more than 90% of pixels in the ROI have successfully completed the stereo matching. 4. Conclusion

An optimized stereo-matching method used in active binocular 3D measurement system is proposed. A series of N BBLP and one BFP are projected on the target objects. ROI, which represents the object, is extracted using image segmentation and morphological operations. Then SAB in time domain is performed to eliminate the harmful impact caused by uneven brightness, defocus, or texture of the object itself for a simplified calculation process. With the help of BFP, we divide the ROI into several vertical stripes and determine the corresponding relationship among them. Based on the initial matching of vertical stripes, the search range of homologous pixels is greatly reduced. The search strategy based on initial matching can reduce three-quarters of the amount of calculation and suppress mismatch. Afterward, homologous pixels are determined according to the similarity evaluation using the LTCT. A 3D point cloud can be calculated using triangulation methods. Finally, subpixel interpolation based on bicubic interpolation is used to increase reconstruction accuracy. A high flatness granite plate is used to check the absolute measurement accuracy. The absolute error of the full field is less than 0.3 mm whereas the

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Optimized stereo matching in binocular three-dimensional measurement system using structured light.

In this paper, we develop an optimized stereo-matching method used in an active binocular three-dimensional measurement system. A traditional dense st...
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