메뉴 건너뛰기




Volumn 38, Issue 2, 2006, Pages 299-319

Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces

Author keywords

Geodesic; Principal component analysis; Riemannian manifold; Shape analysis

Indexed keywords

DIFFERENTIATION (CALCULUS); GEOMETRY; NUMERICAL METHODS;

EID: 33745954917     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1151337073     Document Type: Article
Times cited : (85)

References (22)
  • 2
    • 0002702986 scopus 로고
    • Training models of shape from sets of examples
    • eds D. C. Hogg and R. D. Boyle, Springer, Berlin
    • Cootes, T. F., Taylor, C. J., Cooper, D. H. and Graham, J. (1992). Training models of shape from sets of examples. In Proc. British Mach. Vision Conf., eds D. C. Hogg and R. D. Boyle, Springer, Berlin, pp. 9-18.
    • (1992) Proc. British Mach. Vision Conf. , pp. 9-18
    • Cootes, T.F.1    Taylor, C.J.2    Cooper, D.H.3    Graham, J.4
  • 4
    • 0030371910 scopus 로고    scopus 로고
    • Extremal properties of principal curves in the plane
    • Ducham, T. and Stuetzle W. (1996). Extremal properties of principal curves in the plane. Ann. Statist. 24, 1511-1520.
    • (1996) Ann. Statist. , vol.24 , pp. 1511-1520
    • Ducham, T.1    Stuetzle, W.2
  • 5
    • 84944893332 scopus 로고    scopus 로고
    • Gaussian distributions on Lie groups and their applications to statistical shape analysis
    • Preprint
    • Fletcher, P. T., Joshi, S., Lu, C. and Pizer, S. (2004). Gaussian distributions on Lie groups and their applications to statistical shape analysis. Preprint.
    • (2004)
    • Fletcher, P.T.1    Joshi, S.2    Lu, C.3    Pizer, S.4
  • 6
    • 0041438457 scopus 로고    scopus 로고
    • Statistics of shapes via principal geodesic analysis on Lie groups
    • IEEE, Piscataway, NJ
    • Fletcher, P. T., Lu, C. and Joshi, S. (2003). Statistics of shapes via principal geodesic analysis on Lie groups. Proc. Computer Vision and Pattern Recognition 2003, Vol. 1, IEEE, Piscataway, NJ, pp. 95-101.
    • (2003) Proc. Computer Vision and Pattern Recognition 2003 , vol.1 , pp. 95-101
    • Fletcher, P.T.1    Lu, C.2    Joshi, S.3
  • 7
    • 0007302835 scopus 로고    scopus 로고
    • Growth curve models for correlated triangular shapes
    • Interface Foundation, Fairfax Station, VA
    • Goodall, C. R. and Lange N. (1998). Growth curve models for correlated triangular shapes. In Proc. 21st INTERFACE Symp., Interface Foundation, Fairfax Station, VA, pp. 445-454.
    • (1998) Proc. 21st INTERFACE Symp. , pp. 445-454
    • Goodall, C.R.1    Lange, N.2
  • 8
    • 0001886818 scopus 로고
    • Generalized Procrustes analysis
    • Gower, J. C. (1975). Generalized Procrustes analysis. Psychometrika 40, 33-51.
    • (1975) Psychometrika , vol.40 , pp. 33-51
    • Gower, J.C.1
  • 9
    • 84980162923 scopus 로고
    • Riemannian center of mass and mollifier smoothing
    • Karcher, H. (1977). Riemannian center of mass and mollifier smoothing. Commun. Pure Appl. Math. 30, 509-541.
    • (1977) Commun. Pure Appl. Math. , vol.30 , pp. 509-541
    • Karcher, H.1
  • 11
    • 0001034467 scopus 로고
    • The complex Bingham distribution and shape analysis
    • Kent, J. T. (1994). The complex Bingham distribution and shape analysis. J. R. Statist. Soc. B 56, 285-299.
    • (1994) J. R. Statist. Soc. B , vol.56 , pp. 285-299
    • Kent, J.T.1
  • 14
    • 0344944944 scopus 로고    scopus 로고
    • On Fréchet means in simplex shape space
    • Kume, A. and Le, H. (2003). On Fréchet means in simplex shape space. Adv. Appl. Prob. 35, 885-897,
    • (2003) Adv. Appl. Prob. , vol.35 , pp. 885-897
    • Kume, A.1    Le, H.2
  • 15
    • 0035360021 scopus 로고    scopus 로고
    • Locating Fréchet means with application to shape spaces
    • Le, H. (2001). Locating Fréchet means with application to shape spaces. Adv. Appl. Prob. 33, 324-338.
    • (2001) Adv. Appl. Prob. , vol.33 , pp. 324-338
    • Le, H.1
  • 16
    • 0004474095 scopus 로고    scopus 로고
    • On simplex shape spaces
    • Le, H. and Barden, D. (2001). On simplex shape spaces. J. London Math. Soc. 64, 501-512.
    • (2001) J. London Math. Soc. , vol.64 , pp. 501-512
    • Le, H.1    Barden, D.2
  • 17
    • 0033739089 scopus 로고    scopus 로고
    • Detection of shape changes in biological features
    • Le, H. and Kume, A. (2000). Detection of shape changes in biological features. J. Microscopy 200, 140-147.
    • (2000) J. Microscopy , vol.200 , pp. 140-147
    • Le, H.1    Kume, A.2
  • 18
    • 0032878120 scopus 로고    scopus 로고
    • Multidimensional scaling of simplex shapes
    • Le, H. and Small, C. G. (1999). Multidimensional scaling of simplex shapes. Pattern Recognition 32, 1601-1613.
    • (1999) Pattern Recognition , vol.32 , pp. 1601-1613
    • Le, H.1    Small, C.G.2
  • 19
    • 0002702476 scopus 로고
    • The imbedding problem for Riemannian manifolds
    • Nash, J. (1956). The imbedding problem for Riemannian manifolds. Ann. Math. 63, 20-63.
    • (1956) Ann. Math. , vol.63 , pp. 20-63
    • Nash, J.1
  • 21
    • 0001913628 scopus 로고
    • On expected figures and a strong law of large numbers for random elements in quasi-metric spaces
    • Reidel, Dordrecht
    • Ziezold, H. (1977). On expected figures and a strong law of large numbers for random elements in quasi-metric spaces. In Trans. 7th Prague Conf. Inf. Theory, Statist. Decision Functions, Random Process., Vol. A, Reidel, Dordrecht, pp. 591-602.
    • (1977) Trans. 7th Prague Conf. Inf. Theory, Statist. Decision Functions, Random Process. , vol.A , pp. 591-602
    • Ziezold, H.1
  • 22
    • 84985656305 scopus 로고
    • Mean figures and mean shapes applied to biological figure and shape distributions in the plane
    • Ziezold, H. (1994). Mean figures and mean shapes applied to biological figure and shape distributions in the plane. Biometrical J. 36, 491-510.
    • (1994) Biometrical J. , vol.36 , pp. 491-510
    • Ziezold, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.