双目视觉立体匹配致密匹配算法的研究
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摘要
双目立体视觉是基于视差原理,由左右两幅视图获得匹配点对,根据匹配点对的视差计算出该点在空间中的高度,从而获取物体的三维几何信息。利用物体的三维信息根据不同的应用可以进行不同的后期处理,从而得到想要的结果。目前立体视觉已经在很多领域得到了广泛的应用,是国内外的一个研究热点。
本文研究了立体视觉中最困难也是最关键的部分——立体匹配问题,分析了现有各种匹配算法的特点和性能,并针对项目所需要的致密匹配,提出一种改进的基于图割的立体匹配算法。针对传统的图割算法计算量大的特点,该算法首先用分水岭算法将图像分成多个连通区域,得到每个区域的视差范围,在用a-扩展算法进行能量最小化时,先判断α是否在该像素的视差范围内,再决定是继续操作还是不予处理,从而可以减少计算量,有效地提高匹配速度。在匹配的过程中标记遮挡区域,然后再对该区域进行插值,最终得到整个图像的视差分布。
实验表明,本文提出的算法匹配的准确率较高,而且可以有效地提高匹配速度,最终获得较理想的致密的视差图。
Binocular stereo vision is a method of obtaining three-dimensional geometric information of objects based on the disparity principle. The height of a point is computed from the disparity of the corresponding matched pairs of pixels. Different postprocessing can be applied on objects' three-dimensional information based on different application to obtain desired outcome. Now stereo vision has been widely used in many fields and has been a research hotspot both in and abroad.
The thesis focuses on the key and most difficult part of stereo vision:stereo matching. Aiming at the dense matching which is needed, an improved stereo matching algorithm based on graph cut is presented in this paper on basis of in-depth study on all kinds of matching algorithms. Vast computation is a great disadvantage of the existing graph cut based algorithms. In proposed algorithm, the reference image is divided into many connected regions using watershed segmentation algorithm and then the disparity range of each region is computed. When minimizing the energy function,α-expansion operation depends on whether a is in or out the disparity range of the relevant pixel. The large computing cost for traditional graph cut algorithms can be reduced and the matching is speeded up efficiently. The occlusion regions are marked in the matching and will be covered by the closest value, thus the disparity distribution of the entire image is obtained.
The experimental results show that the accuracy of the proposed algorithm is high and it will take a shorter time to compute a preferable dense disparity mapping.
本文研究了立体视觉中最困难也是最关键的部分——立体匹配问题,分析了现有各种匹配算法的特点和性能,并针对项目所需要的致密匹配,提出一种改进的基于图割的立体匹配算法。针对传统的图割算法计算量大的特点,该算法首先用分水岭算法将图像分成多个连通区域,得到每个区域的视差范围,在用a-扩展算法进行能量最小化时,先判断α是否在该像素的视差范围内,再决定是继续操作还是不予处理,从而可以减少计算量,有效地提高匹配速度。在匹配的过程中标记遮挡区域,然后再对该区域进行插值,最终得到整个图像的视差分布。
实验表明,本文提出的算法匹配的准确率较高,而且可以有效地提高匹配速度,最终获得较理想的致密的视差图。
Binocular stereo vision is a method of obtaining three-dimensional geometric information of objects based on the disparity principle. The height of a point is computed from the disparity of the corresponding matched pairs of pixels. Different postprocessing can be applied on objects' three-dimensional information based on different application to obtain desired outcome. Now stereo vision has been widely used in many fields and has been a research hotspot both in and abroad.
The thesis focuses on the key and most difficult part of stereo vision:stereo matching. Aiming at the dense matching which is needed, an improved stereo matching algorithm based on graph cut is presented in this paper on basis of in-depth study on all kinds of matching algorithms. Vast computation is a great disadvantage of the existing graph cut based algorithms. In proposed algorithm, the reference image is divided into many connected regions using watershed segmentation algorithm and then the disparity range of each region is computed. When minimizing the energy function,α-expansion operation depends on whether a is in or out the disparity range of the relevant pixel. The large computing cost for traditional graph cut algorithms can be reduced and the matching is speeded up efficiently. The occlusion regions are marked in the matching and will be covered by the closest value, thus the disparity distribution of the entire image is obtained.
The experimental results show that the accuracy of the proposed algorithm is high and it will take a shorter time to compute a preferable dense disparity mapping.
引文
[1]高文,陈熙霖.计算机视觉-算法与系统原理.清华大学出版社,1999
[2]Marr, D. and T. Poggio. Cooperative computation of stereo disparity. Science, 1976,194(4262):283-287
[3]Myron Z. Brown,Darius Burschka, and G. D. Hager. Advances in Computational Stereo. IEEE Transactions on PAMI,2003,25(8):993-1008
[4]D. Scharstein, R. Szeliski. A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision,2002,47(1): 7-42
[5]P. Beardsley, P. Tort, A. Zisserma.3D model acquisition from extended image sequences. In Proceedings of the 4th European Conference on Computer Vision, LNCS 1065, Cambridge,1996:683-695
[6]Pritchett P, Zisserman A. Matching and reconstruction from widely separated views in 3D structure from multiple images of large-scale environments. Lecture Notes in Computer Science, Springer Verlag,1998:219-224
[7]Lhuillier Maxime, Quan Long. Robust Dense Matching using Local and Global Geometric Constraints. Proceedings of the 15th International Conference on Pattern Recognition, Barcelona,Spain,2000, vol.1:968-972
[8]Luigi Di Stefano, Massimiliano Marchinonni, Stefano Mattoccia. A fast area-based stereo matching algorithm. Image and Vision Computing,2004, 22(12):983-1005
[9]郭海涛,刘智,张保明.基于遗传算法的快速影像匹配技术的研究.测绘学院学报.2001,9,18(S1)：20-22
[10]熊兴华,钱曾波,王任享.遗传算法与最小二乘法相结合的遥感图像子像素匹配.测绘学报,2001,2,30(1)：54-59
[11]Yunde Zhong, Huaifeng Zhang. Control Points Based Semi-Dense Matching. The 5th Asian Conference on Computer Vision, MelBourne, Australia,2002
[12]陈明舟.主动光栅投影双目视觉传感器的研究.天津大学硕士学位论文,2002
[13]王磊.三维重构技术的研究与应用.清华大学硕士学位论文,2002
[14]马颂德,马正友.计算机视觉—计算理论与算法基础.北京：科学出版社,1998
[15]Marr D,姚国正译.视觉计算理论.科学出版社,1988
[16]刘正东.计算机视觉中立体匹配技术的研究.南京理工大学博士学位论文,
[17]Zitnick C, Kanade T. A Cooperative Algorithm for stereo Matching and Occlusion Detection. IEEE Transactions on PAMI,2000,22(7):675-684
[18]Myron Z. Brown, Darius Burschka, G. D. Hager. Advances in Computational Stereo. IEEE Transactions on PAMI,2003,25(8):993-1008
[19]Nakamura Y, Matsuura T, Satoh K. Occlusion detectable stereo-Occlusion patterns in camera matrix. IEEE Conf. on CVPR,1996:371-378
[20]B. Anderson, K. Nakayama. Toward a General Theory of Stereopsis:Binocular Matching Occluding Contours, and Fusion. Psychological Review,1994,101(3): 414-445
[21]K. Satoh, Y. Ohta. Occlusion Detectable Stereo-Systematic Comparison of Detection Algorithms. In ICRP,1996:280-286
[22]M. Pilon, P. Cohen. Occlusion Detection and Interpretation Based on Image Reprojection. in Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation,1996:166-171
[23]D. Geiger, B. Ladendorf, A. L. Yuille. Occlusion and binocular stereo. International Journal of Computer Vision,1995,14(3):211-226
[24]M. K. Reed, P. K. Allen. Constraint-Based Sensor Planning for Scene Modeling. IEEE Transactions on PAMI,2000,22:1460-1467
[25]S. Birchfield, C. Tomasi. Multiway Cut for Stereo and Motion with Slanted Surfaces. In ICCV. Kerkyra, Greece,1999:489-495
[26]D. N. Bhat, S. K. Nayar. Ordinal Measures for Image Correspondence. IEEE Transactions on PAMI,1998,20(4):415-423
[27]C. V. Stewart. Bias in Robust Estimation Caused by Discontinuous and Multiple Structures. IEEE Trans. PAMI,1997,19(8):818-833
[28]J. Sun. Symmetric Stereo Matching for Occlusion Handling. In CVPR.2005, vol.2:399-406
[29]T. Kanade, M. Okutomi. A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment. IEEE Transactions on PAMI,1994,16(9):920-932
[30]Mansouri, A. Mitiche, J. Konrad. Selective Image Diffusion:Application to Disparity Estimation. In International Conference of Image Processing,1998, vol.3:284-288
[31]S. Birchfield, C. Tomasi. Depth Discontinuities by Pixel-to-Pixel Stereo. In ICCV, 1998:1073-1080
[32]P. N. Belhumeur. A Bayesian-approach to Binocular Stereopsis. International Journal of Computer Vision,1996,19(3):237-260
[33]T. Kanade, M. Okutomi, T. Nakahara. A Multiple-Baseline Stereo Method. In the Proceeding of ARPA Image Understanding Workshop,1992:409-426
[34]S. D. Cochran, G. Medioni.3-D Surface Description from Binocular Stereo. IEEE Transactions on PAMI,1992,14(10):981-994
[35]L. G. Brown. A survey of image registration techniques. ACM Computing Surveys,1992,24:326-376
[36]宰小涛.基于SIFT特征描述子的立体匹配算法研究.上海交通大学硕士学位论文,2007
[37]Barnard Stephen T, Thompson William B. Disparity analysis of images. IEEE Transactions on PAMI,1980,2(4):33-40
[38]Kim C. A dense stereo matching using two-pass dynamic programming with generalized ground control points. In CVPR,2005, vol.2:1075-1082
[39]Kolmogorov V, Zabih R. Multi-Camera scene Reconstruction via Graph Cuts. European Conference on Computer Vision. Copenhagen,2002,2352(3):82-96
[40]Y. Boykov, O. Veksler, R. Zabih. Fast approximate energy minimization via graph cuts. IEEE Trans,2001, PAMI-23(11):1222-1239
[41]V. Kolmogorov, R. Zabih. Computing Visual Correspondence with Occlusions via Graph Cuts. In ICCV,2001,2:508-515
[42]J. Sun, Nan-Ning Zheng, Heung-Yeung Shum. Stereo Matching Using Belief Propagation. IEEE Trans. PAMI,2003,25(7):787-800
[43]P. F. Felzenszwalb, D. P. Huttenlocher. Efficient Belief Propagation for Early Vision. In CVPR,2004, vol.1:261-268
[44]Wang B, Shen C L. Dense disparity map estimation using genetic algorithms. Trans. of Nanjing University of Aeronautics & Astronau,2003,2(9):184-191
[45]Zhang W, Zhang Q B, Qu L. A stereo matching algorithm based on multiresolution and epipolar constraint. Image and Graphics,2004,18(20): 180-183
[46]徐彦君,杜利民,侯自强.基于相位的尺度自适应立体匹配方法.电子学报,1999,27(7)：38-41
[47]吕朝辉,张兆扬,安平.一种基于遗传算法的立体匹配方法.计算机工程,2003,11
[48]徐奕,周军,周源华.立体视觉匹配技术.计算机工程与应用,2003,39(15)：1-5
[49]Veksler O. Fast variable window for stereo correspondence using integral images. In CVPR,2003, vol.1:556-561
[50]Z. G. Zeng, H. Yan. Region matching and optimal matching pair theorem. Computer Graphics International,2001
[51]V. S. Kluth, G. W. Kunkel, U. A. Rauhala. Global Least Squares Matching. In Proceeding of International Geoscience and Remote Sensing Symp,1992, vol.2: 1615-1618
[52]吴铮.基于特征的图像配准算法研究.浙江大学硕士学位论文,2006
[53]王年.三维重构中关键算法研究.安徽大学博士学位论文,2005
[54]M. F. Tappen, W. T. Freeman. Comparison of Graph Cuts with Belief Propagation for stereo, using Identical MRF Parameters. In ICCV,2003, vol.2:900-906
[55]C. Tomasi, R. Manduchi. Stereo Matching as a Nearest-Neighbor Problem. IEEE Trans. PAMI,1998,20:333-340
[56]D. Scharstein, R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision,1998,28(2):155-174
[57]K. N. Kutulakos, S. M. Seitz. A Theory of Shape by Space Carving. International Journal of Computer Vision,2000,38(3):199-218
[58]M. Kisworo, S. Venkatesh, G West. Modeling edges at subpixel accuracy using local energy approach. Theory and experiment,1994, PAMI-16(4):405-410
[59]D. Rosenholm. Multi-point matching using the least-squares technique for an evaluation of three-dimensional models. Photogrammatic Engineering and Remote Sensing,1987,53(6):1214-1218
[60]C. D. Kuglin, D. C. Hines. The phase correlation image alignment method. Proc. of IEEE International Conf. on Cybernetics and Society,1975:163-165
[61]Zhou J, Xu Y, Yu W R. Phase matching with multi-resolution wavelet transform. Proceeding of SPIE,2002,61(10):82-91
[62]D. J. Fleet, A. D. Jepson, M. R. M. Jenkin. Phase-based disparity measurement. CVGIP Image Understanding,1991,53(2):198-210
[63]张强.图像匹配算法研究.西安电子科技大学硕士学位论文,2006
[64]Y. Ohta, T. Kanade. Stereo by Inter-and Intra-Scanline Search Using Dynamic Programming. IEEE Transactions on PAMI,1985,7:139-154
[65]S. S. Intille, A. F. Bobick. Incorporating Intensity Edges in the recovery of occlusion regions. In ICPR,1994, vol.1:674-677
[66]I. J. Cox. A Maximum Likelihood Stereo Algorithm. Computer Vision and Image Understanding,1996,63:542-567
[67]C. Chang, S. Chatterjee, P. R. Kube. On an analysis of Static Occlusion in Stereo Vision. In ICPR,1991:722-723
[68]Y. Deng. A Symmetric Patch-Based Correspondence Model for Occlusion Handling. In ICCV,2005, vol.2:1316-1322
[69]V. Kolmogorov. Graph Based Algorithms for Scene Reconstruction from Two or More Views. Cornell University,2004
[70]邦迪,默蒂.图论及其应用.科学出版社,1976
[71]L. Vincent, P. Soille. Watershed in digital space:an efficient algorithm based on immerosin simulation. IEEE Transaction on PAMI,1991, (13):583-598
[72]www.middlebury.edu/stereo
[2]Marr, D. and T. Poggio. Cooperative computation of stereo disparity. Science, 1976,194(4262):283-287
[3]Myron Z. Brown,Darius Burschka, and G. D. Hager. Advances in Computational Stereo. IEEE Transactions on PAMI,2003,25(8):993-1008
[4]D. Scharstein, R. Szeliski. A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision,2002,47(1): 7-42
[5]P. Beardsley, P. Tort, A. Zisserma.3D model acquisition from extended image sequences. In Proceedings of the 4th European Conference on Computer Vision, LNCS 1065, Cambridge,1996:683-695
[6]Pritchett P, Zisserman A. Matching and reconstruction from widely separated views in 3D structure from multiple images of large-scale environments. Lecture Notes in Computer Science, Springer Verlag,1998:219-224
[7]Lhuillier Maxime, Quan Long. Robust Dense Matching using Local and Global Geometric Constraints. Proceedings of the 15th International Conference on Pattern Recognition, Barcelona,Spain,2000, vol.1:968-972
[8]Luigi Di Stefano, Massimiliano Marchinonni, Stefano Mattoccia. A fast area-based stereo matching algorithm. Image and Vision Computing,2004, 22(12):983-1005
[9]郭海涛,刘智,张保明.基于遗传算法的快速影像匹配技术的研究.测绘学院学报.2001,9,18(S1)：20-22
[10]熊兴华,钱曾波,王任享.遗传算法与最小二乘法相结合的遥感图像子像素匹配.测绘学报,2001,2,30(1)：54-59
[11]Yunde Zhong, Huaifeng Zhang. Control Points Based Semi-Dense Matching. The 5th Asian Conference on Computer Vision, MelBourne, Australia,2002
[12]陈明舟.主动光栅投影双目视觉传感器的研究.天津大学硕士学位论文,2002
[13]王磊.三维重构技术的研究与应用.清华大学硕士学位论文,2002
[14]马颂德,马正友.计算机视觉—计算理论与算法基础.北京：科学出版社,1998
[15]Marr D,姚国正译.视觉计算理论.科学出版社,1988
[16]刘正东.计算机视觉中立体匹配技术的研究.南京理工大学博士学位论文,
[17]Zitnick C, Kanade T. A Cooperative Algorithm for stereo Matching and Occlusion Detection. IEEE Transactions on PAMI,2000,22(7):675-684
[18]Myron Z. Brown, Darius Burschka, G. D. Hager. Advances in Computational Stereo. IEEE Transactions on PAMI,2003,25(8):993-1008
[19]Nakamura Y, Matsuura T, Satoh K. Occlusion detectable stereo-Occlusion patterns in camera matrix. IEEE Conf. on CVPR,1996:371-378
[20]B. Anderson, K. Nakayama. Toward a General Theory of Stereopsis:Binocular Matching Occluding Contours, and Fusion. Psychological Review,1994,101(3): 414-445
[21]K. Satoh, Y. Ohta. Occlusion Detectable Stereo-Systematic Comparison of Detection Algorithms. In ICRP,1996:280-286
[22]M. Pilon, P. Cohen. Occlusion Detection and Interpretation Based on Image Reprojection. in Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation,1996:166-171
[23]D. Geiger, B. Ladendorf, A. L. Yuille. Occlusion and binocular stereo. International Journal of Computer Vision,1995,14(3):211-226
[24]M. K. Reed, P. K. Allen. Constraint-Based Sensor Planning for Scene Modeling. IEEE Transactions on PAMI,2000,22:1460-1467
[25]S. Birchfield, C. Tomasi. Multiway Cut for Stereo and Motion with Slanted Surfaces. In ICCV. Kerkyra, Greece,1999:489-495
[26]D. N. Bhat, S. K. Nayar. Ordinal Measures for Image Correspondence. IEEE Transactions on PAMI,1998,20(4):415-423
[27]C. V. Stewart. Bias in Robust Estimation Caused by Discontinuous and Multiple Structures. IEEE Trans. PAMI,1997,19(8):818-833
[28]J. Sun. Symmetric Stereo Matching for Occlusion Handling. In CVPR.2005, vol.2:399-406
[29]T. Kanade, M. Okutomi. A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment. IEEE Transactions on PAMI,1994,16(9):920-932
[30]Mansouri, A. Mitiche, J. Konrad. Selective Image Diffusion:Application to Disparity Estimation. In International Conference of Image Processing,1998, vol.3:284-288
[31]S. Birchfield, C. Tomasi. Depth Discontinuities by Pixel-to-Pixel Stereo. In ICCV, 1998:1073-1080
[32]P. N. Belhumeur. A Bayesian-approach to Binocular Stereopsis. International Journal of Computer Vision,1996,19(3):237-260
[33]T. Kanade, M. Okutomi, T. Nakahara. A Multiple-Baseline Stereo Method. In the Proceeding of ARPA Image Understanding Workshop,1992:409-426
[34]S. D. Cochran, G. Medioni.3-D Surface Description from Binocular Stereo. IEEE Transactions on PAMI,1992,14(10):981-994
[35]L. G. Brown. A survey of image registration techniques. ACM Computing Surveys,1992,24:326-376
[36]宰小涛.基于SIFT特征描述子的立体匹配算法研究.上海交通大学硕士学位论文,2007
[37]Barnard Stephen T, Thompson William B. Disparity analysis of images. IEEE Transactions on PAMI,1980,2(4):33-40
[38]Kim C. A dense stereo matching using two-pass dynamic programming with generalized ground control points. In CVPR,2005, vol.2:1075-1082
[39]Kolmogorov V, Zabih R. Multi-Camera scene Reconstruction via Graph Cuts. European Conference on Computer Vision. Copenhagen,2002,2352(3):82-96
[40]Y. Boykov, O. Veksler, R. Zabih. Fast approximate energy minimization via graph cuts. IEEE Trans,2001, PAMI-23(11):1222-1239
[41]V. Kolmogorov, R. Zabih. Computing Visual Correspondence with Occlusions via Graph Cuts. In ICCV,2001,2:508-515
[42]J. Sun, Nan-Ning Zheng, Heung-Yeung Shum. Stereo Matching Using Belief Propagation. IEEE Trans. PAMI,2003,25(7):787-800
[43]P. F. Felzenszwalb, D. P. Huttenlocher. Efficient Belief Propagation for Early Vision. In CVPR,2004, vol.1:261-268
[44]Wang B, Shen C L. Dense disparity map estimation using genetic algorithms. Trans. of Nanjing University of Aeronautics & Astronau,2003,2(9):184-191
[45]Zhang W, Zhang Q B, Qu L. A stereo matching algorithm based on multiresolution and epipolar constraint. Image and Graphics,2004,18(20): 180-183
[46]徐彦君,杜利民,侯自强.基于相位的尺度自适应立体匹配方法.电子学报,1999,27(7)：38-41
[47]吕朝辉,张兆扬,安平.一种基于遗传算法的立体匹配方法.计算机工程,2003,11
[48]徐奕,周军,周源华.立体视觉匹配技术.计算机工程与应用,2003,39(15)：1-5
[49]Veksler O. Fast variable window for stereo correspondence using integral images. In CVPR,2003, vol.1:556-561
[50]Z. G. Zeng, H. Yan. Region matching and optimal matching pair theorem. Computer Graphics International,2001
[51]V. S. Kluth, G. W. Kunkel, U. A. Rauhala. Global Least Squares Matching. In Proceeding of International Geoscience and Remote Sensing Symp,1992, vol.2: 1615-1618
[52]吴铮.基于特征的图像配准算法研究.浙江大学硕士学位论文,2006
[53]王年.三维重构中关键算法研究.安徽大学博士学位论文,2005
[54]M. F. Tappen, W. T. Freeman. Comparison of Graph Cuts with Belief Propagation for stereo, using Identical MRF Parameters. In ICCV,2003, vol.2:900-906
[55]C. Tomasi, R. Manduchi. Stereo Matching as a Nearest-Neighbor Problem. IEEE Trans. PAMI,1998,20:333-340
[56]D. Scharstein, R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision,1998,28(2):155-174
[57]K. N. Kutulakos, S. M. Seitz. A Theory of Shape by Space Carving. International Journal of Computer Vision,2000,38(3):199-218
[58]M. Kisworo, S. Venkatesh, G West. Modeling edges at subpixel accuracy using local energy approach. Theory and experiment,1994, PAMI-16(4):405-410
[59]D. Rosenholm. Multi-point matching using the least-squares technique for an evaluation of three-dimensional models. Photogrammatic Engineering and Remote Sensing,1987,53(6):1214-1218
[60]C. D. Kuglin, D. C. Hines. The phase correlation image alignment method. Proc. of IEEE International Conf. on Cybernetics and Society,1975:163-165
[61]Zhou J, Xu Y, Yu W R. Phase matching with multi-resolution wavelet transform. Proceeding of SPIE,2002,61(10):82-91
[62]D. J. Fleet, A. D. Jepson, M. R. M. Jenkin. Phase-based disparity measurement. CVGIP Image Understanding,1991,53(2):198-210
[63]张强.图像匹配算法研究.西安电子科技大学硕士学位论文,2006
[64]Y. Ohta, T. Kanade. Stereo by Inter-and Intra-Scanline Search Using Dynamic Programming. IEEE Transactions on PAMI,1985,7:139-154
[65]S. S. Intille, A. F. Bobick. Incorporating Intensity Edges in the recovery of occlusion regions. In ICPR,1994, vol.1:674-677
[66]I. J. Cox. A Maximum Likelihood Stereo Algorithm. Computer Vision and Image Understanding,1996,63:542-567
[67]C. Chang, S. Chatterjee, P. R. Kube. On an analysis of Static Occlusion in Stereo Vision. In ICPR,1991:722-723
[68]Y. Deng. A Symmetric Patch-Based Correspondence Model for Occlusion Handling. In ICCV,2005, vol.2:1316-1322
[69]V. Kolmogorov. Graph Based Algorithms for Scene Reconstruction from Two or More Views. Cornell University,2004
[70]邦迪,默蒂.图论及其应用.科学出版社,1976
[71]L. Vincent, P. Soille. Watershed in digital space:an efficient algorithm based on immerosin simulation. IEEE Transaction on PAMI,1991, (13):583-598
[72]www.middlebury.edu/stereo