Some approaches to shape analysis

作者: Washington Mio , Anuj Srivastava

DOI:

关键词: LandmarkPattern recognitionArtificial intelligenceMathematicsDiffeomorphismShape matchingPrincipal geodesic analysisHeat kernel signaturePoint distribution modelActive shape modelShape analysis (digital geometry)

摘要: Analysis of shapes is important for image analysis. The notion has been used in a variety ways across the literature. From definition shape, to derivation statistical procedures shape analysis, usage different among papers. In this paper, we summarize common attributes approaches, and compare few commonly ones. particular, focus on landmark-based diffeomorphism approach matching, geometric analyzing curves.

参考文章(14)
Ulf Grenander, Michael I. Miller, Computational anatomy: an emerging discipline Quarterly of Applied Mathematics. ,vol. 56, pp. 617- 694 ,(1998) , 10.1090/QAM/1668732
D. Barden, T. K. Carne, D. G. Kendall, Shape and Shape Theory ,(1999)
Rabi Bhattacharya, Vic Patrangenaru, Nonparametic estimation of location and dispersion on Riemannian manifolds Journal of Statistical Planning and Inference. ,vol. 108, pp. 23- 35 ,(2002) , 10.1016/S0378-3758(02)00268-9
Fred L. Bookstein, Size and Shape Spaces for Landmark Data in Two Dimensions Statistical Science. ,vol. 1, pp. 181- 222 ,(1986) , 10.1214/SS/1177013696
Yali Amit, Ulf Grenander, Mauro Piccioni, Structural Image Restoration through Deformable Templates Journal of the American Statistical Association. ,vol. 86, pp. 376- 387 ,(1991) , 10.1080/01621459.1991.10475053
Christopher G. Small, The statistical theory of shape ,(1996)
David G. Kendall, Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces Bulletin of the London Mathematical Society. ,vol. 16, pp. 81- 121 ,(1984) , 10.1112/BLMS/16.2.81
Michael Kass, Andrew Witkin, Demetri Terzopoulos, Snakes : Active Contour Models International Journal of Computer Vision. ,vol. 1, pp. 321- 331 ,(1988) , 10.1007/BF00133570
H. Karcher, Riemannian center of mass and mollifier smoothing Communications on Pure and Applied Mathematics. ,vol. 30, pp. 509- 541 ,(1977) , 10.1002/CPA.3160300502
Huiling Le, Locating Fréchet means with application to shape spaces Advances in Applied Probability. ,vol. 33, pp. 324- 338 ,(2001) , 10.1239/AAP/999188316