Abstract
This paper casts the problem of point-set alignment and correspondence into a unified framework. The utility measure underpinning the work is the cross-entropy between probability distributions for alignment and assignment errors. We show how Procrustes alignment parameters and correspondence probabilities can be located using dual singular value decompositions. Experimental results using both synthetic and real images are given.
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Y. Amit and A. Kong. Graphical Templates for Model Registration. IEEE PAMI, 18:225–236, 1996.
T.F Cootes, C.J. Taylor, D.H. Cooper, and J. Graham. Active Shape Models-Their Training and Application. CVIU, 61:38–59, 1995.
A.D. J. Cross and E.R. Hancock. Graph Matching with a Dual-Step EM Algorithm. IEEE PAMI, 20(11):1236–1253, 1998.
O.D. Faugeras, E. Le Bras-Mehlman, and J-D. Boissonnat. Representing Stereo Data with the Delaunay Triangulation. Artificial Intelligence, 44:41–87, 1990.
A.M. Finch, R.C. Wilson, and E.R. Hancock. Matching delaunay graphs. Pattern Recognition, 30(1):123–140, January 1997.
S. Gold and A. Rangarajan. A graduated assignment algorithm for graph matching. IEEE PAMI, 18(4):377–388, 1996.
M.I. Jordan and R.A. Jacobs. Hierarchical mixture of experts and the EM algorithm. Neural Computation, 6:181–214, 1994.
D.G. Kendall. Shape Manifolds: Procrustean metrics and complex projective spaces. Bulletin of the London Mathematical Society, 16:81–121, 1984.
M. Lades, J.C. Vorbruggen, J. Buhmann, J. Lange, C. von der Maalsburg, R.P. Wurtz, and W. Konen. Distortion-invariant object-recognition in a dynamic link architecture. IEEE Transactions on Computers, 42:300–311, 1993.
B. Luo, A.D.J. Cross, and E.R. Hancock. Corner detection via topographic analysis of vector potential. Pattern Recognition Letters, 20:635–650, 1999.
A. Rangarajan and E. D. Mjolsness. A lagrangian relaxation network for graph matching. IEEE Transactions on Neural Networks, 7(6):1365–1381, November 1996.
S. Sclaroff and A.P. Pentland. Modal Matching for Correspondence and Recognition. IEEE PAMI, 17:545–661, 1995.
G.L. Scott and H.C. Longuet-Higgins. An Algorithm for Associating the Features of 2 Images. Proceedings of the Royal Society of London Series B-Biological, 244(1309):21–26, 1991.
L.S. Shapiro and J. M. Brady. Feature-based Correspondence-An Eigenvector Approach. Image and Vision Computing, 10:283–288, 1992.
L.S. Shapiro and J. M. Brady. Rejecting Outliers and Estimating Errors in an Orthogonal-regression Framework. Phil. Trans. Roy. Soc. A, 350:403–439, 1995.
S. Ullman. The Interpretation of Visual Motion. MIT Press, 1979.
S. Umeyama. An Eigen Decomposition Approach to Weighted Graph Matching Problems. IEEE PAMI, 10:695–703, 1988.
S. Umeyama. Least Squares Estimation of Transformation Parameters between Two Point sets. IEEE PAMI, 13(4):376–380, 1991.
S. Umeyama. Parameterised Point Pattern Matching and its Application to Recognition of Object Families. IEEE PAMI, 15:136–144, 1993.
M. Werman and D. Weinshall. Similarity and Affine Invariant Distances between 2D Point Sets. IEEE Trans. on PAMI, 17(8):810–814, 1995.
R.C. Wilson and E.R. Hancock. Structural matching by discrete relaxation. IEEE PAMI, 19(6):634–648, June 1997.
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© 2000 Springer-Verlag Berlin Heidelberg
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Luo, B., Hancock, E.R. (2000). Alignment and Correspondence Using Singular Value Decomposition. In: Ferri, F.J., Iñesta, J.M., Amin, A., Pudil, P. (eds) Advances in Pattern Recognition. SSPR /SPR 2000. Lecture Notes in Computer Science, vol 1876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44522-6_24
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DOI: https://doi.org/10.1007/3-540-44522-6_24
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