메뉴 건너뛰기




Volumn 64, Issue 6, 2012, Pages 1227-1259

On the meaning of mean shape: Manifold stability, locus and the two sample test

Author keywords

Extrinsic mean; Horizontal lift; Intrinsic mean; Procrustes mean; Proper Lie group action; Schoenberg mean; Shape spaces; Slice theorem; Stratified spaces; Ziezold mean

Indexed keywords

EXTRINSIC MEAN; INTRINSIC MEAN; LIE GROUP ACTIONS; PROCRUSTES; SCHOENBERG MEAN; SHAPE SPACE; SLICE THEOREM; STRATIFIED SPACES; ZIEZOLD MEAN;

EID: 84870253371     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-012-0352-2     Document Type: Article
Times cited : (34)

References (45)
  • 4
    • 76849086044 scopus 로고    scopus 로고
    • Statistical analysis on manifolds: A nonparametric approach for inference on shape spaces
    • Bhattacharya, A. (2008). Statistical analysis on manifolds: A nonparametric approach for inference on shape spaces. Sankhya, Series A, 70(2), 223-266.
    • (2008) Sankhya, Series A , vol.70 , Issue.2 , pp. 223-266
    • Bhattacharya, A.1
  • 5
    • 21144443869 scopus 로고    scopus 로고
    • Large sample theory of intrinsic and extrinsic sample means on manifolds I
    • Bhattacharya, R. N., Patrangenaru, V. (2003). Large sample theory of intrinsic and extrinsic sample means on manifolds I. The Annals of Statistics, 31(1), 1-29.
    • (2003) The Annals of Statistics , vol.31 , Issue.1 , pp. 1-29
    • Bhattacharya, R.N.1    Patrangenaru, V.2
  • 6
    • 23744472179 scopus 로고    scopus 로고
    • Large sample theory of intrinsic and extrinsic sample means on manifolds II
    • Bhattacharya, R. N., Patrangenaru, V. (2005). Large sample theory of intrinsic and extrinsic sample means on manifolds II. The Annals of Statistics, 33(3), 1225-1259.
    • (2005) The Annals of Statistics , vol.33 , Issue.3 , pp. 1225-1259
    • Bhattacharya, R.N.1    Patrangenaru, V.2
  • 8
    • 0003306618 scopus 로고
    • Introduction to compact transformation groups
    • New York: Academic Press
    • Bredon, G. E. (1972). Introduction to compact transformation groups. In Pure and applied mathematics (Vol. 46). New York: Academic Press.
    • (1972) Pure and Applied Mathematics , vol.46
    • Bredon, G.E.1
  • 13
    • 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
  • 14
    • 0030080006 scopus 로고    scopus 로고
    • Asymptotic behaviour of sample mean location for manifolds
    • Hendriks, H., Landsman, Z. (1996). Asymptotic behaviour of sample mean location for manifolds. Statistics and Probability Letters, 26, 169-178.
    • (1996) Statistics and Probability Letters , vol.26 , pp. 169-178
    • Hendriks, H.1    Landsman, Z.2
  • 15
    • 0040678209 scopus 로고    scopus 로고
    • Mean location and sample mean location on manifolds: Asymptotics, tests, confidence regions
    • Hendriks, H., Landsman, Z. (1998). Mean location and sample mean location on manifolds: asymptotics, tests, confidence regions. Journal of Multivariate Analysis, 67, 227-243.
    • (1998) Journal of Multivariate Analysis , vol.67 , pp. 227-243
    • Hendriks, H.1    Landsman, Z.2
  • 19
    • 80051862101 scopus 로고    scopus 로고
    • Inference on 3D procrustes means: Tree boles growth, rank-deficient diffusion tensors and perturbation models
    • Huckemann, S. (2011). Inference on 3D Procrustes means: Tree boles growth, rank-deficient diffusion tensors and perturbation models. Scandinavian Journal of Statistics, 38(3), 424-446.
    • (2011) Scandinavian Journal of Statistics , vol.38 , Issue.3 , pp. 424-446
    • Huckemann, S.1
  • 20
    • 33745954917 scopus 로고    scopus 로고
    • Principal component analysis for riemannian manifolds with an application to triangular shape spaces
    • Huckemann, S., Ziezold, H. (2006). Principal component analysis for Riemannian manifolds with an application to triangular shape spaces. Advances of Applied Probability (SGSA), 38(2), 299-319.
    • (2006) Advances of Applied Probability (SGSA) , vol.38 , Issue.2 , pp. 299-319
    • Huckemann, S.1    Ziezold, H.2
  • 21
    • 77649243364 scopus 로고    scopus 로고
    • Intrinsic MANOVA for riemannian manifolds with an application to kendall's space of planar shapes
    • Huckemann, S., Hotz, T., Munk, A. (2010a). Intrinsic MANOVA for Riemannian manifolds with an application to Kendall's space of planar shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(4), 593-603.
    • (2010) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.32 , Issue.4 , pp. 593-603
    • Huckemann, S.1    Hotz, T.2    Munk, A.3
  • 22
    • 77949381107 scopus 로고    scopus 로고
    • Intrinsic shape analysis: Geodesic principal component analysis for riemannian manifolds modulo lie group actions (with discussion)
    • Huckemann, S., Hotz, T., Munk, A. (2010b). Intrinsic shape analysis: Geodesic principal component analysis for Riemannian manifolds modulo Lie group actions (with discussion). Statistica Sinica, 20(1), 1-100.
    • (2010) Statistica Sinica , vol.20 , Issue.1 , pp. 1-100
    • Huckemann, S.1    Hotz, T.2    Munk, A.3
  • 23
    • 0000971145 scopus 로고
    • Residuals for directional data
    • Jupp, P. E. (1988). Residuals for directional data. Journal of Applied Statistics, 15(2), 137-147.
    • (1988) Journal of Applied Statistics , vol.15 , Issue.2 , pp. 137-147
    • Jupp, P.E.1
  • 27
    • 84960586494 scopus 로고
    • Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence
    • Kendall, W. S. (1990). Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence. Proceedings of the London Mathematical Society, 61, 371-406.
    • (1990) Proceedings of the London Mathematical Society , vol.61 , pp. 371-406
    • Kendall, W.S.1
  • 33
    • 0035360021 scopus 로고    scopus 로고
    • Locating fréchet means with an application to shape spaces
    • Le, H. (2001). Locating Fréchet means with an application to shape spaces. Advances of Applied Probability (SGSA), 33(2), 324-338.
    • (2001) Advances of Applied Probability (SGSA) , vol.33 , Issue.2 , pp. 324-338
    • Le, H.1
  • 35
    • 0004143760 scopus 로고    scopus 로고
    • Testing statistical hypotheses
    • New York: Springer
    • Lehmann, E. L. (1997). Testing statistical hypotheses. In Springer texts in statistics. New York: Springer.
    • (1997) Springer Texts in Statistics
    • Lehmann, E.L.1
  • 39
    • 0002702476 scopus 로고
    • The imbedding problem for riemannian manifolds
    • Nash, J. (1956). The imbedding problem for Riemannian manifolds. The Annals of Mathematics, 63, 20-63.
    • (1956) The Annals of Mathematics , vol.63 , pp. 20-63
    • Nash, J.1
  • 40
    • 0001441560 scopus 로고
    • On the existence of slices for actions of non-compact lie groups
    • Palais, R. S. (1961). On the existence of slices for actions of non-compact Lie groups. The Annals of Mathematics 2nd Series, 73(2), 295-323.
    • (1961) The Annals of Mathematics 2nd Series , vol.73 , Issue.2 , pp. 295-323
    • Palais, R.S.1
  • 41
    • 33750251165 scopus 로고    scopus 로고
    • Shape matching by variational computation of geodesics on a manifold
    • Berlin: Springer
    • Schmidt, F. R., Clausen, M., Cremers, D. (2006). Shape matching by variational computation of geodesics on a manifold. In Pattern recognition (Proceedings DAGM), LNCS (Vol. 4174, pp. 142-151). Berlin: Springer.
    • (2006) Pattern Recognition (Proceedings DAGM), LNCS , vol.4174 , pp. 142-151
    • Schmidt, F.R.1    Clausen, M.2    Cremers, D.3
  • 45
    • 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 Journal, 36, 491-510.
    • (1994) Biometrical Journal , vol.36 , pp. 491-510
    • Ziezold, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.