CAIP 1999: Computer Analysis of Images and Patterns pp 623-631 | Cite as
Procrustes Alignment with the EM Algorithm
Abstract
This paper casts the problem of point-set alignment via Pro- crustes analysis into a maximum likelihood framework using the EM algorithm. The aim is to improve the robustness of the Procrustes alig- nment to noise and clutter. By constructing a Gaussian mixture model over the missing correspondences between individual points, we show how alignment can be realised by applying singular value decomposition to a weighted point correlation matrix. Moreover, by gauging the relational consistency of the assigned correspondence matches, we can edit the point sets to remove clutter. We illustrate the effectiveness of the method matching stereogram. We also provide a sensitivity analysis to demonstrate the operational advantages of the method.
Keywords
Gaussian Mixture Model Delaunay Triangulation Alignment Parameter Proximity Matrix Procrustes DistancePreview
Unable to display preview. Download preview PDF.
References
- 1.N. Ahuja, Dot Pattern Processing using Voronoi Neighbourhoods, IEEE PAMI, 4(1982), 336–343.Google Scholar
- 2.N. Ahuja and B. An and B. Schachter, Image Representation using Voronoi Tessellation, CVGIP, 29(1985), 286–295.Google Scholar
- 3.N. Ahuja and M. Tuceryan, Extraction of Early Perceptual Structure in Dot Patterns: Integrating Region, Boundary and Component Gestalt, CVGIP, 48(1989), 304–356.Google Scholar
- 4.Amit, Y. and Kong, A., Graphical Templates For Model Registration, PAMI, 18(1996), 225–236.Google Scholar
- 5.T.F Cootes and C.J. Taylor and D.H. Cooper and J. Graham, Active Shape Models — Their Training and Application, CVIU, 61(1995), 38–59.Google Scholar
- 6.A.P. Dempster and N.M. Laird and D.B. Rubin, Maximum-likelihood from incomplete data via the EM algorithm, J. Royal Statistical Soc. Ser. B (methodological), 39(1977), 1–38.MATHMathSciNetGoogle Scholar
- 7.O.D. Faugeras and E. Le Bras-Mehlman and J-D. Boissonnat, Representing Stereo Data with the Delaunay Triangulation, Artificial Intelligence, 44(1990), 41–87.CrossRefMathSciNetMATHGoogle Scholar
- 8.D. G. Kendall, Shape manifolds,Procrustean metrics, and complex projective spaces, Bulletin of the London Mathematical Society, 16(1984), 81–121.MATHCrossRefMathSciNetGoogle Scholar
- 9.M. Lades and J.C. Vorbruggen and J. Buhmann and J. Lange and C. von der Maalsburg and R.P. Wurtz and W. Konen, Distortion-invariant object-recognition in a dynamic link architecture, IEEE Transactions on Computers, 42(1993), 300–311.CrossRefGoogle Scholar
- 10.S. Sclaroff and A.P. Pentland, Modal Matching for Correspondence and Recognition, IEEE PAMI, 17(1995), 545–661.Google Scholar
- 11.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(1991), 21–26.CrossRefGoogle Scholar
- 12.L.S. Shapiro and J. M. Brady, Feature-based Correspondence — An Eigenvector Approach, IVC, 10(1992), 283–288.CrossRefGoogle Scholar
- 13.L.S. Shapiro and J. M. Brady, Rejecting Outliers and Estimating Errors in an Orthogonal-regression Framework, Phil. Trans. Roy. Soc. A, 350(1995), 403–439.CrossRefGoogle Scholar
- 14.M. Tuceryan and T Chorzempa, Relative Sensitivity of a Family of Closest Point Graphs in Computer Vision Applications, Pattern Recognition, 25(1991), 361–373.CrossRefGoogle Scholar
- 15.S. Ullman, The Interpretation of Visual Motion, MIT Press,(1979).Google Scholar
- 16.S. Umeyama, An Eigen Decomposition Approach to Weighted Graph Matching Problems, IEEE PAMI, 10(1988), 695–703.MATHGoogle Scholar
- 17.S. Umeyama, Least Squares Estimation of Transformation Parameters between Point sets, IEEE PAMI, 13(1991), 376–380.Google Scholar
- 18.S. Umeyama, Parameterised Point Pattern Matching and its Application to Recognition of Object Families, IEEE PAMI, 15(1993), 136–144.Google Scholar
- 19.R.C. Wilson and E.R. Hancock, Structural Matching by Discrete Relaxation, IEEE PAMI, 19(1997), 634–648.Google Scholar