Stereo Matching with Energy Minimizing Snake Grid for 3D Face Modeling

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1 Stereo Matching with Energy Minimizing Snake Grid for 3D Face Modeing Shafik Huq 1, Besma Abidi 1, Ardeshir Goshtasby 2, and Mongi Abidi 1 1 Imaging, Robotics, and Inteigent System (IRIS) Laboratory, Department of ECE, The University of Tennessee, Knoxvie, TN Inteigent Systems Laboratory, Wright State University, Dayton, OH ABSTRACT An energy minimizing snake agorithm that runs over a grid is designed and used to reconstruct high resoution 3D human faces from pairs of stereo images. The accuracy of reconstructed 3D data from stereo depends highy on how we stereo correspondences are estabished during the feature matching step. Estabishing stereo correspondences on human faces is often i posed and hard to achieve because of uniform texture, sow changes in depth, occusion, and ack of gradient. We designed an energy minimizing agorithm that accuratey finds correspondences on face images despite the aforementioned characteristics. The agorithm heps estabish stereo correspondences unambiguousy by appying a coarse-to-fine energy minimizing snake in grid format and yieds a high resoution reconstruction at neary every point of the image. Initiay, the grid is stabiized using matches at a few seected high confidence edge points. The grid then graduay and consistenty spreads over the ow gradient regions of the image to revea the accurate depths of object points. The grid appies its interna energy to approximate mismatches in occuded and noisy regions and to maintain smoothness of the reconstructed surfaces. The grid works in such a way that with every increment in reconstruction resoution, ess time is required to estabish correspondences. The snake used the curvature of the grid and gradient of image regions to automaticay seect its energy parameters and approximate the unmatched points using matched points from previous iterations, which aso acceerates the overa matching process. The agorithm has been appied for the reconstruction of 3D human faces, and experimenta resuts demonstrate the effectiveness and accuracy of the reconstruction. Keywords: Stereo images, 3D geometric modeing, face reconstruction, energy minimizing snake, east squares. 1. INTRODUCTION We perceive depth by using our two eyes when two sighty different and dispaced images of an object are formed on both retinas. The amount of dispacement between the two images depends on the distance of the object to the eyes. Distant objects are dispaced ess than coser objects and dispacement is usuay proportiona to the inverse of depth. Simiary, in stereo vision, two or more cameras are used to find the depth at each point of a scene. Stereo depth perception is the process by which a 3D structure is recovered from two or more images of a scene taken from sighty different view points. The key step in 3D reconstruction from stereo images is the matching or stereo correspondence, used to find the correspondence between 2D projected object points in the eft and right images. The output of a stereo correspondence agorithm is a disparity map, specifying the reative dispacement of matching points in the two images. The stereo correspondence probem is inherenty under-constrained and is usuay further compicated by the fact that typica images aso contain noise. In our work, we appy a cassica computer vision mode, i. e., energy minimizing snakes, aso caed active contour modes, to sove the stereo correspondence probem. Energy minimizing snakes are often used in medica imaging for automatic detection and ocaization of certain image regions such as esions and tumors 1. Facia feature extraction 2 and tracking of non-rigid objects 3 are aso some of the appications in which energy minimizing snakes are used. 3D reconstruction from stereo correspondences has been a subject of study for more than three decades. In a recent survey 4, Brown et a. discussed past work in stereo correspondence research, and cassified the techniques into oca and goba categories. Biometric Technoogy for Human Identification, edited by Ani K. Jain, Naini K. Ratha, Proceedings of SPIE Vo (SPIE, Beingham, WA, 2004) X/04/$15 doi: /

2 In oca methods, correspondences are estabished by ooking at the image features ocay. Loca methods have reied on two major approaches: (1) Feature-based approaches 5 which ony match points and ines based on oca information such as intensity, and yied sparse disparity maps, and (2) Area-based approaches which yied dense disparity maps by matching sma image patches and reying on the assumption that nearby points usuay have simiar dispacements. A typica area-based stereo matching agorithm proceeds as foows: for each point in one image, the dispacement that aigns this point with one in the other image is found and the quaity of match is measured by comparing windows centered at the two points using, for instance, the sum of absoute differences or the cross correation 6. Athough areabased matching yieds dense disparity maps, the resuts of the match are usuay not accurate when the image gradient is ow. As an exampe, points on the forehead and cheeks of a human face ook amost the same everywhere. Another issue with area matching is the seection of the size of the search window and the determination that a match exists somewhere within this window. Goba methods, on the other hand, are generay based on dynamic programming and the optimization of a function of a arge number of correspondences. Dynamic programming methods treat stereo correspondence as the probem of finding an optima path on a two-dimensiona search pane. Successfu attempts using dynamic programming to sove the stereo correspondence probem were reported by Baker and Binford 7, and Ohta and Kanade 8. In both cases, the authors used edges as basic primitives but ony obtained sparse reconstructions. A fast and automatic stereo correspondence agorithm based on dynamic programming was aso proposed by Benshair and Debrie 9. One of the drawbacks of approaches based on dynamic programming is that they can ony be appied to a singe image pair and can t dispatch any tempora information to subsequent frames whie, for instance, tracking objects in stereo image sequences. In this paper, an agorithm combining oca and goba correspondence techniques is introduced. To sove the gradient probem, we introduce an energy minimizing grid-ike snake. The search area is usuay determined by introducing seed points at the beginning stage of the iterative agorithm. The sparsey distributed seed points were generated using fast aser scans over the face surface. The grid snake, starting with the seed points, iterativey finds more and more matches in a coarse-to-fine fashion. After estabishing the correspondences, camera caibration parameters are used to reconstruct the object. By its inherent architecture, the grid maintains two important characteristics - uniqueness and continuity. Marr and Poggio 10 were among the first to enforce uniqueness and continuity constraints to imit the search. They used a confidence measure for assigning a point in the eft image to a set of possibe corresponding points in the right image. This agorithm does not perform we on rea images, mosty because the tokens and the features used are not sufficient to dea with most rea and noisy data. In a work by Poard et a. 11 the disparity gradient constraint was used and the agorithm first extracts a number of tokens from both images with each token characterizing a number of features. For exampe, edge points are detected and characterized by their strength and orientation. Tokens are then matched using an iterative winner-take-a procedure that enforces uniqueness. In our work, we used the pixe intensity as a matching token. The snake, in the shape of a grid, converges to the possibe minimum goba energy after severa iterations whie aways maintaining the two constraints of uniqueness and ordering. Hence, our agorithm depoys both methods the oca method by using tempate matching and the goba method by stabiizing the grid snake to the minimum goba energy using the minimization of an objective function. Besides distributing the matches uniformy and unambiguousy over a arge image region where sufficient features are not avaiabe, the snake shows good performance in tracking when an object changes shape or its appearance in the images changes. The agorithm deas with genera shape objects and perspective camera modes. Another effort by Wong and Chung 12, enforces the epipoar and panarity constraints in the cost function to sove the stereo correspondence and reconstruction probem using an active contour mode. The agorithm is designed for objects with panar surfaces and approximates objects shapes by assuming a weak perspective camera mode. The reminder of this paper is organized according to the tasks needed to sove the 3D modeing from stereo, i.e., caibration, correspondence, and reconstruction. In section 2, we discuss the theory and impementation of binocuar stereo caibration used in our work. Section 3 describes a aspects of the energy minimizing agorithm, incuding the grid architecture, definitions of energies, seection of energy parameters, the energy minimizing equation, and the technique used to remove bad matches from the fina correspondence map. In section 4, we present and discuss some reconstruction resuts and then draw concusions in section CAMERA CALIBRATION The two cameras used in the stereo setup are first caibrated for ater use in the impementation of the reconstruction agorithm. Camera caibration in the broad sense reates the image coordinates of a point to its word coordinates through a camera parameter matrix, caed here an m-parameter matrix. The m-parameter matrix has eeven m unknown 340 Proc. of SPIE Vo. 5404

3 parameters. In the same way, we wi have an n-parameter matrix with eeven n unknown parameters for the second camera. The m and n parameters are determined through correspondences of at east five and a haf points from the two images. We used the stereo pair of the caibration pattern shown in Figure 1 and a modified existing technique 13 that expicity extracts the caibration parameters from the projection matrix. (a) Figure 1: (a) Left stereo image, and Right stereo image of the caibration pattern used in our experiments. The red round dots were used to obtain more accurate correspondences. The user cicks anywhere inside two corresponding dots and the system finds the center of gravity of the red dots, thus providing a more accurate correspondence. The perspective projection can be described by the foowing equation: x y 1 M int M ext X Y Z 1 X Y M Z 1, (1) where (x, y) are the coordinates on the camera pane of a point whose word coordinates are (X, Y, Z) and m11 m12 m13 m14 M = m21 m22 m23 m24. m31 m32 m33 m34 The camera intrinsic and extrinsic parameters are combined into the m-parameters and the matrix M is defined up to an arbitrary scae factor. Therefore, by dividing a the eements m 11 through m 34 by m 34, M can be rewritten as: m1 m 2 m3 m 4 M ' = m8 m9 m10 m11. (2) m5 m 6 m 7 1 We define ( x, y ) as the coordinate of a point in the image captured by the first camera (we ca it eft camera). From equations (1) and (2), we obtain: Proc. of SPIE Vo

4 m1 X + m2y + m3z + m4 x and m X + m Y + m Z m8 X + m9y + m10z + m11 y. (3) m X + m Y + m Z In the same way, we have n parameters for the second or right camera and the corresponding matrix can be written as: Simiary, ( x r, y r ) is a point in the right image given by: n1 n 2 n 3 n 4 N = n 8 n 9 n10 n 11. n 5 n 6 n 7 1 n1 X + n2y + n3z + n4 n5 X + n6y + n7z + 1 x r and n8 X + n9y + n10z + n11 y r. (4) n5x + n6y + n7z + 1 A m and n parameters can be determined if the ( X, Y, Z) of at east five and a haf points on the caibration pattern, their corresponding image points ( x, y ) in the eft camera, and ( x r, y r ) in the right camera are a known. For this purpose, two images of the caibration pattern with known ( X, Y, Z) vaues of a set of marked points are captured by the eft and right cameras. To reduce computationa errors reated to inaccuracies in ocating ( x, y ) and ( x r, y r ), we used a higher number of points and appied the east squares method. Tabe 1 shows the m and n parameter vaues found from the caibration pattern of Figure 1 whie Tabe 2 shows the ( X, Y, Z) vaues measured from the pattern and their estimated ( X, Y, Z) vaues found by appying the recovered m and n parameter matrices. The rightmost coumn of Tabe 2 shows the distance between the measured and estimated ( X, Y, Z) coordinates. The average difference is found to be in the sub-miimeter range. Tabe 1: m and n parameter vaues cacuated using the caibration pattern of Figure 1. i=1 i=2 i=3 i=4 i=5 i=6 i=7 i=8 i=9 i=10 i=11 m i n i STEREO MATCHING WITH ENERGY MINIMIZING SNAKE GRID The energy minimizing snake grid agorithm described in this section finds the matching pairs of points on the two stereo images in two separate steps, by first estabishing sparse correspondences between points in the stereo images (even in the absence of sufficient gradient) and then refining the resuts by estabishing dense correspondences and performing interpoation. 3.1 Grid Setup and Initiaization Two separate grids are superimposed on each of the images of the stereo pair. The grids are identica and have the same number of rows and coumns. The grid on the eft image has a reguar shape with straight vertica and horizonta ines (ony the intersections of these ines wi be used in the matching process). The grids are started with a few matched seed points coected using a vertica aser ine swept over the individua s face whie two video sequences are captured by the two cameras. Each stereo frame pair contains corresponding vertica aser ines to indicate sparse correspondences. This sparseness comes from the facts that: (1) the eye-safe aser does not present a high contrast under ambient ighting conditions, (2) the faces usuay have areas of simiar intensities as that of the aser, and (3) the aser ine sometimes gets 342 Proc. of SPIE Vo. 5404

5 diffused by hairy regions on the face. For these reasons, it is usuay impossibe to detect a continuous aser ine as it runs from the top to the bottom of the face. The sparse correspondence map of matched points resuting from this process provides the seed points to initiaize the grid which is originay set at very ow resoution. About 50% of the grid points can initiay be matched using these seed points. Increasing the number of seed points did not necessariy resut in an improvement of the fina matching resut. Figure 2 (a)-(d) show a frame pair from the eft and right video sequences and the detected aser ines from this pair. When initiaized with seed points, the eft grid is kept and the right grid becomes distorted because of differences in disparities at matching points from the intersection of vertica and horizonta ines. Tabe 2: Measured and estimated ( X, Y, Z) vaues using the caibration pattern of Figure 1 and the recovered vaues in Tabe 1. Measured 3D points (cm), P G Estimated 3D points (cm), P E Error X Y Z X Y Z P G -P E (mm) Average error = mm To separate the face region from the background, haf an eiptica area is manuay defined using three mouse cicks, two at the outer ends of both eyes and a third at the bottom of the chin. The grid shown in Figure 3 was defined in this manner. If a point P i in the eft image is to be matched in the right image, the search for a match is performed on both sides of the corresponding grid point P i in the right image and the search area is defined to be within eft point P i-1 and right point P i The Energy Minimizing Agorithm The goa now is to refine the matches obtained from the aser scans and fi up the missing parts on both grids for a more accurate reconstruction. Since the seed points may not be distributed uniformy and some points correspondences may remain unknown, this creates hoes in the grid as seen in Figure 4 (a) and. Points in these hoes are ater interpoated from surrounding points as seen in Figure 5 (a) and. The grid initiaization step described in subsection 3.1 resuted in two ow resoution grids, one reguar on the eft image and one irreguar on the right image. Disparities in this case are differences in distances measured in the horizonta direction, which makes ony vertica ines on the right grid distort to the eft or right from their initia position seen on the eft grid. In the stereo setup, both cameras were focused on the same scan ine and the energy minimizing agorithm is appied by ooking at the grid points one by one in the eft image and finding the ocation where they match best in the right image. This approach raises the questions: 1) what image feature shoud be used for the search, and 2) where and how much area needs to be searched to find a match? These two questions wi be addressed by introducing two energy terms in our agorithm, the externa and interna energies denoted respectivey by E ext and E int. The energy minimizing agorithm can then be described as foows: Proc. of SPIE Vo

6 (a) (c) (d) Figure 2: (a) One frame taken from eft stereo aser scan image sequence, Corresponding frame from right stereo image sequence, (c) Detected aser from (a), and (d) Detected aser from. P i-1 P i P i+1 P i-1 P i P i+1 (a) Figure 3: Grid setup and initiaization using seed points; (a) Straight grid set on eft camera image, distorted grid after performing seed point correspondences on right camera image. (a) Figure 4: Missing data creating hoes after initiaization of eft (a) and right image grids with seed points obtained from aser scan. 344 Proc. of SPIE Vo. 5404

7 1. Deveop an energy function E i by combining E ext and E int to evauate the energy of a match between two corresponding points in the eft and the right images. E ext is rewarded with a negative sign whie E int is penaized with a positive sign so that ess energy indicates a better match. 2. Define the grid points P Li in the eft image to be used to search for matches in the right image. 3. For a grid point P Li in the eft image, compute a energies E i within a neighborhood A of a points, p Ri, in the right image. A match for P Li is expected to exist inside A and A is defined in such a way that the ordering and uniqueness constraints are maintained. The architecture of the grid heps in expicity maintaining these constraints. 4. The point p Ri with the minimum vaue of E i is considered to be the best match for P Li in the current iteration. Redefine A in the surrounding of the new ocation of p Ri. 5. For a grid points seected in the eft image in step 2, foow steps 3 and 4 to find their matches and cacuate ocay the minimum E i for each. 6. Sum a minimum energy vaues for a P Li points. Assuming E n is the vaue of this sum, where n denotes the nth iteration, if E n-1 - E n > ε, where ε is a sma threshod vaue, go to Step 4. Otherwise quit. The energy minimizing agorithm is iterative and stops ony when the goba minimum energy E n stops decreasing beyond a given threshod. (a) Figure 5: Corrected eft (a) and right image grids after fiing hoes using interpoation techniques. 3.3 Externa and interna energies Assume that P i,j is a point at the i-th row and the j-th coumn of the grid in the eft image. It is assumed that the intensity map of a sma window around P i,j wi remain amost unchanged in the right image. This property aows us to use a we-known method caed tempate matching, where the intensity vaues within the tempate area in the eft image are compared to intensity vaues of the same size tempate in the right image. The cross correation (CC) vaue is used as a measure of the externa energy as given in equation 5 and incudes the correation of a three coor channes in the same formua. E ext ( (( I L C ( i, I L C ) ( I R C ( i, I R C ))) C = R, G, B i = 1.. k, j = 1.. = 2 2 ( (( I L C ( i, I L C ) (( I R C ( i, I R C ) ) C= R, G, B i = 1.. k, j = 1.. i = 1.. k, j = 1... (5) Figure 6 (a) shows the behavior of the externa energy curve when a eft grid point tempate is matched within ±20 pixes of the corresponding grid point in the right image. The curve presents a maxima at or near 1.0 if a good match is found. The shape and smoothness of the curve depends on the smoothness of the intensity map. Most face images ack contrast especiay in areas ike the forehead and cheeks where the externa energy by itsef wi be insufficient to find a correct match, since the ow gradient causes a eft image tempate to match in severa ocations in the right image. In this case, an additiona term, the interna energy, is used to assist in correcting fase matches. Figure 6 shows the interna energy curve, which has a vaue of zero in the midde of the search area and increases ineary from the center in both directions to reach a maximum of 1.0 at both ends. A fase match generay causes a grid point to move away from its correct matching position as seen in Figure 7, where the tempate at X i,j commits a fase match and moves away to X i,j. The interna energy term was introduced to avoid these fase matches by puing the tempate towards its correct matching position assumed to be situated somewhere cose to the center of the surrounding eight grid points. Proc. of SPIE Vo

8 E Ext E int Distance in pixe Distance in pixe (a) Figure 6: (a) Externa energy curve and Interna energy curve as functions of the distances in pixes from the best matches. X i-1,j-1 X i-1,j X i-1,j+1 X i,j-1 X i,j X i,j+1 X i+1,j-1 X i+1,j X i+1,j+1 Figure 7: Iustration of the resut of a fase match at X i,j. The objective is to find a match somewhere near X i,j which is simpy the center of gravity of the surrounding grid points defined as: 1 X i, j = ( Xi+ k, j+ ). 8 (6) k= 1,0,1 = 1,0,1 The interna energy of the searched grid point (i, is defined by Eint '' ' X i, j X i, j =, (7) max X i, j X i, j where X i, j is an image point between grid points X i,j-1 and X i,j+1 in the right image. The best match, X i,j, is expected to yied the smaest interna energy vaue (0). 346 Proc. of SPIE Vo. 5404

9 As mentioned earier, the best matches are those with the highest externa energy and the owest interna energy. In some instances, both conditions may not be satisfied at the same time. A compromise between the two conditions can be achieved by using the foowing energy equation: E ( i, = α E( i, int β E( i,, (6) where α and β are energy parameters and the vaues of E(i, are computed by matching the tempate centered at grid point X i,j in the eft image with tempates centered at grid points between X i,j-1 and X i,j+1 in the right image. The point with the minimum vaue of E(i, is seected as the best match or the nearest point to the actua X i,j obtained from the puing power exerted by the interna energy towards the center. In equation 6, α and β contro the importance of one energy term against the other. A arge vaue of α with respect to β provides a arge interna energy to the grid, making it stiff. On the other hand, a arge vaue of β emphasizes the externa energy, thus providing the grid with more easticity. In our agorithm, β is proportiona to the tota gradient of the tempate in the eft image. Thus, in ow gradient regions, the grid has more easticity and the grid points can be eveny distributed by reying mosty on the interna energy. In high gradient regions, the grid points mosty rey on the externa energy. This choice was based on the fact that image regions with high gradients correate we and unambiguousy. A noise remova step was performed on the tempate before measuring the gradient using an edge operator. The seection of β is aso dependent on the curvature of the vertica ines of the grid. Large curvature usuay resuts from mismatches. Hence, when the curvature is bigger than a threshod, β is decreased so that α can dominate and pu the mismatched points toward the correct match positions. The goba minimum energy, E n, is the summation of E ( i, for a grid points. As iterations continue, the grid finds better matches and E n decreases. After severa iterations, when E n does not decrease any further, it is concuded that the grid has become stabe with the best matches at a its points. Convergence of the grid to the goba minimum energy is shown in Figure 8. ext Figure 8: Goba energy convergence as function of the number of iterations. At every few iterations, when the grid has stabiized, the resoution of the grid is doubed by inserting new coumns and new rows. The new points introduced in the grid are assigned average disparities computed from the disparities of their neighboring points. The grid goes through iterations again to stabiize with the newy introduced points. After an expected resoution of the grid is obtained and the grid has stabiized, the points within the corresponding eft and right grid ces are simpy interpoated and mapped to obtain correspondence for each image point. The corresponding points from eft and right images are then pugged into the set of equations (3) and (4) for reconstruction. The four equations in (3) and (4) are used to compute the three unknowns X, Y, and Z using a east squares method for higher accuracy. During the matching process, bad matches are introduced due to occusion and variations in iumination in both images. On a human face, occusion may appear near the nose. Bad matches aso may appear on eyeids because of hair or very thin objects making the face surface discontinuous. Hair on eyes introduces sharp changes in depth, which vioates the ordering constraint. Bad matches are usuay those points with sharp changes in disparity with respect to surrounding good matches. Good matches usuay come very cose to the center of their surrounding points after severa iterations of energy minimizing agorithm, whie bad matches seem to appear far away from the center. At the fina step of the agorithm, the bad matches are corrected by dragging them cose to the center of their surrounding non-occuded points and forcing the grid points to be distributed eveny. As mentioned earier the energy minimizing Proc. of SPIE Vo

10 agorithm can appy a force to create a smoothed overay of grid ines on image regions not having enough feature points and gradient. For this purpose, we update the interna energy curve as shown in Figure 9. q E int Distance in pixes Linear part of the interna energy Noninear part of the interna energy Figure 9: Updated interna energy curve for correction of bad matches. Near the center, the energy sti varies ineary, but bends exponentiay into both directions away from the center. These two different shapes of the curve serve two different purposes: (1) the exponentia part of the curve forces the bad q matches to stay cose to the center. In this part the energy minimizing equation becomes E = α E int β Eext with q being an assigned exponent vaue for the interna energy E int. (2) The inearity around the center is sti maintained so that good matches that are not in the midde but cose to it are not forced to dispace. 4. EXPERIMENTS AND RECONSTRUCTION RESULTS A stereo pair is acquired from a person standing sti in front of two stereo video cameras whie a aser is swept horizontay over their face. This produces two stereo sequences. The ast two frames from the two sequences after the aser has been removed are used for matching and reconstruction. Prior frames are used to coect the seed points. Each pair of these frames has a aser ine iuminating the face verticay aong a ine hence giving correspondences of points ying on the vertica ine. The seed points from this ine are fed into the energy minimizing agorithm for dense matching. Figure 10 shows a zoomed in portion of the face s stereo pair. The eft image has the reguar grid aid on it. The right image shows the grid after seed point matching. The vertica ines are bent to the eft or right depending on depth variations on the face. (a) Figure 10: (a) Left stereo image of the face with the grid, corresponding right stereo image with grid after matching. Figure 11 shows the reconstruction of a face rendered at different anges. The accuracy of the reconstruction is found to be in the sub-miimeter range. Accuracy vaues were observed during the caibration process when the pattern points were reconstructed to see how they match with pre-measured X, Y, Z vaues. 348 Proc. of SPIE Vo. 5404

11 Figure 11: Reconstructed 3D face from stereo rendered at different anges. 5. CONCLUSIONS An energy minimizing agorithm for stereo matching was discussed. This agorithm combines oca and goba techniques to produce a dense and accurate disparity map from ow contrast face images, where traditiona matching methods usuay fai. The agorithm is iterative and takes about 20 seconds on a 2.4 GHz Pentium IV machine to match a stereo image pair at sub-miimeter accuracy. The agorithm can be improved in a number of ways: (1) by using a ookup tabe where pre-cacuated cross correation coefficients can be stored, which reduces the agorithm s runtime; (2) by first segmenting out the face from the background using depth information found initiay in the coarse matching phase, hence correating ony points on the face region (this technique is depoyabe ony when there are no obstaces between the person and the camera); (3) by coecting seed points automaticay instead of using a aser sweep. These improvements woud make the agorithm fuy automatic and speed up the processing time required for the reconstruction. Energy minimizing snakes are aso efficient toos for tracking. The agorithm described in this paper can potentiay be used for tracking faces or any other object in mutipe stereo image sequences to produce 3D animation of a moving object. Objects moving at reativey ow speed can be tracked and reconstructed in rea time since the size of the search areas can be significanty reduced in subsequent frames. For more detais on our work, the reader is referred to reference 14. REFERENCES 1. L. Yin, S. Deshpande, and J. Chang, Automatic esion/tumor detection using inteigent mesh-based active contour, in Proc. 15th IEEE Internationa Conference on Toos with Artificia Inteigence, pp , Sacramento, CA, USA (3-5 Nov, 2003). 2. M. Haseyama, S. Yoneyama, and H. Kitajima, A shape-constraint-based active contour mode with a spitting mechanism for face-feature extraction, Journa of the Institute of Image Information and Teevision Engineers, 57(6), pp (June 2003). 3. D. Xu and J. Hwang, A topoogy independent active contour tracking, Neura Networks for Signa Processing IX, Proceedings of the 1999 IEEE Signa Processing Society Workshop, Cat. No. 98TH8468, pp (1999). 4. M. Z. Brown, D. Burschka, and G. D. Hager, Advances in computationa stereo, IEEE Transactions on Pattern Anaysis and Machine Inteigence, 25(8), pp (Aug 2003). 6. O. Faugeras, B. Hotz, H. Matthieu, T. Viei, Z. Zhang, P. Fua, E. Theron, L. Mo, G. Berry, J. Vuiemin, P. Bertin, and C. Proy, Rea Time Correation-based Stereo: Agorithm, Impementations and Appications, INRIA Technica Report 2013 (1993). 5. C. Schmid and A. Zisserman, The Geometry and Matching of Curves in Mutipe Views, Proc. European Conf. Computer Vision, pp (1998). Proc. of SPIE Vo

12 7. H. H. Baker and T.O. Binford, Depth from edge and intensity based stereo, Proceedings of the 7 th Internationa Joint Conference On Artificia Inteigence, pp ; Vancouver, Canada (1981). 8. Y. Ohta and T. Kanade, Stereo by intra- and inter-scanine search using dynamic programming, IEEE Transactions, Pattern Anaysis and Machine Inteigence, 7(2), pp (1985). 9. A. Benshair, P. Miche, and R. Debrie, Fast and automatic stereo vision matching agorithm based on dynamic programming method, Pattern Recognition Letters 17, pp (1996). 10. D. Marr and T. Poggio, Cooperative computation of stereo disparity, Science 194, pp (1976). 11. S. B. Poard, J. E. W. Mayhew, and J. P. Frisby, A stereo correspondence agorithm using a disparity gradient constraint, Perception, 14, pp (1985). 12. H. S. Wong and R. Chung, Three-dimensiona shape recovery across two views using approximate geometric constraints, Optica Engineering, 42(3), pp (March 2003). 13. O. Faugeras, Three-Dimensiona Computer Vision: A Geometric Viewpoint. MIT Press, Cambridge (MA) (1993). 14. M. Huq, 3D Reconstruction and Tracking of Human Faces from Stereo image sequences. MS Thesis, Department of Computer Science and Engineering, Wright State University (May 2001). 350 Proc. of SPIE Vo. 5404