This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Stereo Matching as a Nearest-Neighbor Problem
March 1998 (vol. 20 no. 3)
pp. 333-340

Abstract—We propose a representation of images, called intrinsic curves, that transforms stereo matching from a search problem into a nearest-neighbor problem. Intrinsic curves are the paths that a set of local image descriptors trace as an image scanline is traversed from left to right. Intrinsic curves are ideally invariant with respect to disparity. Stereo correspondence then becomes a trivial lookup problem in the ideal case. We also show how to use intrinsic curves to match real images in the presence of noise, brightness bias, contrast fluctuations, moderate geometric distortion, image ambiguity, and occlusions. In this case, matching becomes a nearest-neighbor problem, even for very large disparity values.

[1] R.D. Arnold and T.O. Binford, "Geometric Constraints in Stereo Vision," Proc. SPIE, vol. 238, pp. 281-292,San Diego, Calif., 1978.
[2] Y. Ohta and T. Kanade, "Stereo by Intra- and Inter-Scanline Search Using Dynamic Programming," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, no. 2, pp. 139-154, Mar. 1985.
[3] M.H. Kass, "Computing Stereo Correspondence," master's thesis, Massachusetts Institute of Tech nology, 1984.
[4] D.G. Jones and J. Malik, "A Computational Framework for Determining Stereo Correspondence From a Set of Linear Spatial Filters," Proc. EECV '92, pp. 395-410,Santa Margherita Ligure, Italy, 1992.
[5] J. Weng,N. Ahuja,, and T. S. Huang,“Matching two perspective views,” Trans. Pattern Analysis and Machine Intelligence Intell., vol. 14, no. 8, pp. 806-825, 1992.
[6] A. Blake and C. Marinos, "Shape From Texture: Estimation, Isotropy and Moments," Artificial Intelligence, vol. 45, pp. 323-380, 1990.
[7] B.J. Super and A.C. Bovik,“Shape-from-texture by wavelet-based measurement of local spectral moments,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 296-301,Champaign, Ill., June 1992.
[8] R. Manmatha, "A Framework for Recovering Affine Transforms Using Points, Lines, or Image Brightnesses," Proc. Conf. Computer Vision and Pattern Recognition, pp. 141-146, 1994.
[9] J. Sato and R. Cipolla, "Extracting the Affine Transformation From Texture Moments," Proc. ECCV '94, pp. 165-172,Stockholm, 1994.
[10] J.J. Koenderink and A.J. Van Doorn, "Geometry of Binocular Vision and a Model for Stereopsis," Biological Cybernetics, vol. 21, pp. 29-35, 1976.
[11] K. Kanatani, "Detection of Surface Orientation and Motion From Texture by a Stereological Technique," Artificial Intelligence, vol. 23, pp. 213-237, 1984.
[12] M. Campani and A. Verri, "Motion Analysis From First-Order Properties of Optical Flow," CVGIP: Image Understanding, vol. 56, no. 1, pp. 90-107, 1992.
[13] D.G. Jones and J. Malik, "Determining Three-Dimensional Shape From Orientation and Spatial Frequency Disparities," Proc. EECV '92, pp. 661-669,Santa Margherita Ligure, Italy, 1992.
[14] S.G. Mallat,“A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.
[15] J. Malik and P. Perona, "Preattentive Texture Discrimination With Early Vision Mechanisms," J. Optical Soc. of Am.-A, vol. 7, no. 5, pp. 923-932, 1990.
[16] V.I. Arnold, Ordinary Differential Equations.Cambridge, Mass.: MIT Press, 1990.
[17] D.J. Struik, Lectures on Classical Differential Geometry.New York: Dover, 1988.
[18] P.S. Toh and A.K. Forrest, "Occlusion Detection in Early Vision," Proc. Third Int'l Conf. Computer Vision, pp. 126-132,Osaka, Japan, 1990.
[19] J.J. Little and W.E. Gillet, "Direct Evidence for Occlusion in Stereo and Motion," Proc. ECCV '90, pp. 336-340,Antibes, France, 1990.
[20] P.N. Belhumeur and D. Mumford, "A Bayesian Treatment of the Stereo Correspondence Problem Using Half-Occluded Regions," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 506-512, June 1992.
[21] D. Geiger, B. Ladendorf, and A. Yuille, "Occlusions and Binocular Stereo," Proc. EECV '92, pp. 425-433,Santa Margherita Ligure, Italy, 1992.
[22] S.S. Intille and A.F. Bobick, "Disparity-Space Images and Large Occlusion Stereo," Proc. ECCV '94, pp. 179-186,Stockholm, 1994.
[23] Y. Xion and L. Matthies, "Error Analysis of a Real-Time Stereo System," Proc. CVPR '97, pp. 1,087-1,093,Puerto Rico, 1997.
[24] C. Tomasi and R. Manduchi, "Stereo Without Search," Technical Report STAN-CS-TR-95-1543, Stanford Univ., 1995.
[25] J.K. Uhlmann, "Satisfying General Proximity/Similarity Queries With Metric Trees," Information Processing Letters, vol. 40, pp. 175-179, 1991.
[26] P.N. Yianilos, "Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces," Proc. Fourth ACM-SIAM Symp. Discrete Algorithms, 1993.
[27] I.J. Cox, S. Hingorani, B.M. Maggs, and S.B. Rao, "A Maximum Likelihood Stereo Algorithm," Computer Vision and Image Understanding, vol. 63, no. 3, pp. 542-567, 1996.
[28] S.B. Pollard, J.E. Mayhew, and G.P. Frisby, "PMF: A Stereo Correspondence Algorithm Using a Disparity Gradient Limit," Perception, vol. 14, pp. 449-470, 1985.
[29] D.E. Knuth, The Art of Computer Programming, 2nd ed. Reading, Mass.: Addison-Wesley, 1973.
[30] H.H. Baker and T.O. Binford, "Depth From Edge and Intensity Based Stereo," Proc. Seventh Int'l Joint Conf. Artificial Intelligence, pp. 631-636, 1981.
[31] W.E.L. Grimson, "Computational Experiments With a Feature Based Stereo Algorithm," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, no. 1, pp. 17-34, 1985.

Index Terms:
Stereo vision, stereo matching, correspondence problem, disparity, ambiguity, occlusions, search, nearest-neighbor search, dynamic programming.
Citation:
Carlo Tomasi, Roberto Manduchi, "Stereo Matching as a Nearest-Neighbor Problem," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 3, pp. 333-340, March 1998, doi:10.1109/34.667890
Usage of this product signifies your acceptance of the Terms of Use.