Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 26, Issue 3, 2004, Pages 372-383

  Klassen, Eric ^a   Srivastava, Anuj ^a   Mio, Washington ^a   Joshi, Shantanu H ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Geodesic paths; Intrinsic mean shapes; Shape interpolation; Shape metrics; Shape statistics; Shape based clustering

Indexed keywords

GEODESIC PATHS; INTRINSIC MEAN SHAPES; SHAPE ANALYSIS; SHAPE INTERPOLATION; SHAPE METRICS; SHAPE SPACES; SHAPE STATISTICS; SHAPE-BASED CLUSTERING;

APPROXIMATION THEORY; DATABASE SYSTEMS; ESTIMATION; EXTRAPOLATION; IMAGE ANALYSIS; IMAGE QUALITY; INTERPOLATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION; STATISTICAL METHODS; TOPOLOGY;

PATTERN RECOGNITION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BAYES THEOREM; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; EVALUATION; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; PATTERN RECOGNITION; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; STATISTICAL MODEL; VALIDATION STUDY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BAYES THEOREM; COMPUTER GRAPHICS; FORM PERCEPTION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SUBTRACTION TECHNIQUE;

EID: 1342345777     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2004.1262333     Document Type: Article

References (30)

1. R. Bhattacharya and V. Patrangenaru, "Nonparametric Estimation of Location and Dispersion on Riemannian Manifolds," J. Statistical Planning and Inference, vol. 108, pp. 23-36, 2002.
2. F.L. Bookstein, "Size and Shape Spaces for Landmark Data in Two Dimensions," Statistical Science, vol. 1, pp. 181-242, 1986.
3. M.P. Do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, 1976.
4. I. Cohen and I. Herlin, "Tracking Meteorological Structures through Curve Matching Using Geodesic Paths," Proc. Int'l Conf. Computer Vision, pp. 396-401, 1998.
5. D. Cremers, T. Kohlberg, and C. Schnorr, "Nonlinear Shape Statistics in Mumford-Shah Based Segmentation," Proc. European Conf. Computer Vision, pp. 93-108, June 2002.
6. D. Cremers and S. Soatto, "A Pseudo Distance for Shape Priors in Level Set Segmentation," Proc. Second IEEE Workshop Variational, Geometric, and Level Set Methods in Computer Vision, 2003.
7. I.L. Dryden and K.V. Mardia, Statistical Shape Analysis. John Wiley and Son, 1998.
8. M.A.T. Figueiredo and A.K. Jain, "Unsupervised Learning of Finite Mixture Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 3, Mar. 2002.
9. U. Grenander, General Pattern Theory. Oxford Univ. Press, 1993.
10. U. Grenander and M.I. Miller, "Computational Anatomy: An Emerging Discipline," Quarterly of Applied Math., vol. LVI, no. 4, pp. 617-694, 1998.
11. U. Grenander, A. Srivastava, and M.I. Miller, "Asymptotic Performance Analysis of Bayesian Object Recognition," IEEE Trans. Information Theory, vol. 46, no. 4, pp. 1658-1666, 2000.
12. S. Joshi and A. Srivastava, "A Geometric Approach to Shape Clustering and Learning," Proc. 12th IEEE Workshop Statistical Signal Processing, 2003.
13. H. Karcher, "Riemann Center of Mass and Mollifier Smoothing," Comm. Pure and Applied Math., vol. 30, pp. 509-541, 1977.
14. D.G. Kendall, "Shape Manifolds, Procrustean Metrics and Complex Projective Spaces," Bull. of London Math. Soc., vol. 16, pp. 81-121, 1984.
15. J.T. Kent and K.V. Mardia, "Shape, Procrustes Tangent Projections and Bilateral Symmetry," Biometrika, vol. 88, pp. 469-485, 2001.
16. S. Lang, Fundamentals of Differential Geometry. Springer, 1999.
17. L.J. Latecki and R. Lakamper, "Shape Similarity Measure Based on Correspondence of Visual Parts," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1185-1190, Oct. 2000.
18. H. Le, "Locating Frechet Means with Application to Shape Spaces," Advances in Applied Probability, vol. 33, no. 2, pp. 324-338, 2001.
19. J.S. Marques and A.J. Abrantes, "Shape Alignment - Optimal Initial Point and Pose Estimation," Pattern Recognition Letters, vol. 18, pp. 49-53, 1997.
20. P. Maurel and G. Sapiro, "Dynamic Shapes Average," Proc. Second IEEE Workshop Variational, Geometric, and Level Set Methods in Computer Vision, 2003.
21. M.I. Miller and L. Younes, "Group Actions, Homeomorphisms, and Matching: A General Framework," Int'l J. Computer Vision, vol. 41, nos. 1/2, pp. 61-84, 2002.
22. W. Mio, A. Srivastava, and E. Klassen, "Interpolation by Elastica in Euclidean Spaces," Quarterly of Applied Math., to be published.
23. F. Mokhtarian, S. Abbasi, and J. Kittler, "Efficient and Robust Shape Retrieval by Shape Content through Curvature Scale Space," Proc. First Int'l Conf. Image Database and Multi-Search, pp. 35-42, 1996.
24. T.B. Sebastian, P.N. Klein, and B.B. Kimia, "On Aligning Curves," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 1, pp. 116-125, Jan. 2003.
25. A. Srivastava, S. Joshi, W. Mio, and X. Liu, "A Geometric Approach to Shape Clustering, Learning and Testing," Technical Report TC03, Dept. of Statistics, Florida State Univ., 2003.
26. A. Srivastava and E. Klassen, "Monte Carlo Extrinsic Estimators for Manifold-Valued Parameters," IEEE Trans. Signal Processing, vol. 50, no. 2, pp. 299-308, Feb. 2001.
27. A. Srivastava, W. Mio, E. Klassen, and X. Liu, "Geometric Analysis of Constrained Curves for Image Understanding," Proc. Second IEEE Workshop Variational, Geometric, and Level Sets Methods in Computer Vision, Oct. 2003.
28. H.D. Tagare, D. O'Shea, and D. Groisser, "Nonrigid Shape Comparison of Plane Curves in Images," J. Math. Imaging and Vision, vol. 16, pp. 57-68, 2002.
29. R.P. Woods, "Characterizing Volume and Surface Deformations in an Atlas Framework," technical report, Dept. of Neurology and Physiology, Univ. of California at Los Angeles, 2002.
30. L. Younes, "Optimal Matching between Shapes via Elastic Deformations," J. Image and Vision Computing, vol. 17, nos. 5/6, pp. 381-389, 1999.