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Volumn , Issue , 2008, Pages

Robust statistics on Riemannian manifolds via the geometric median

Author keywords

[No Author keywords available]

Indexed keywords

CENTRAL POINT; DATA POINTS; EUCLIDEAN; EUCLIDEAN SPACES; EXISTENCE AND UNIQUENESS; GEODESIC DISTANCES; MEDIAN COMPUTATION; RIEMANNIAN MANIFOLDS; ROBUST ESTIMATORS; ROBUST STATISTICS; SHAPE SPACES; SUFFICIENT CONDITIONS; UNIQUE SOLUTION; VISION APPLICATIONS;

EID: 51949100053     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2008.4587747     Document Type: Conference Paper
Times cited : (96)

References (35)
  • 1
    • 0041062256 scopus 로고
    • The algebraic degree of geometric optimization problems
    • C. Bajaj. The algebraic degree of geometric optimization problems. Discrete and Computational Geometry, 3:177-191, 1988.
    • (1988) Discrete and Computational Geometry , vol.3 , pp. 177-191
    • Bajaj, C.1
  • 5
    • 84972512610 scopus 로고
    • Size and shape spaces for landmark data in two dimensions (with discussion)
    • F. L. Bookstein. Size and shape spaces for landmark data in two dimensions (with discussion). Statistical Science, 1(2):181-242, 1986.
    • (1986) Statistical Science , vol.1 , Issue.2 , pp. 181-242
    • Bookstein, F.L.1
  • 6
    • 84867943034 scopus 로고    scopus 로고
    • Fast approximations for sums of distances, clustering and the fermat-weber problem
    • P. Bose, A. Maheshwari, and P. Morin. Fast approximations for sums of distances, clustering and the fermat-weber problem. Comput. Geom. Theory Appl., 24(3):135-146, 2003.
    • (2003) Comput. Geom. Theory Appl , vol.24 , Issue.3 , pp. 135-146
    • Bose, P.1    Maheshwari, A.2    Morin, P.3
  • 7
    • 0003232417 scopus 로고    scopus 로고
    • Spherical averages and applications to spherical splines and interpolation
    • S. R. Buss and J. P. Fillmore. Spherical averages and applications to spherical splines and interpolation. ACM Transactions on Graphics, 20(2):95-126, 2001.
    • (2001) ACM Transactions on Graphics , vol.20 , Issue.2 , pp. 95-126
    • Buss, S.R.1    Fillmore, J.P.2
  • 8
    • 0025385328 scopus 로고
    • Algebraic optimization: The Fermat-Weber problem
    • R. Chandrasekaran and A. Tamir. Algebraic optimization: The Fermat-Weber problem. Mathematical Programming, 46:219-224, 1990.
    • (1990) Mathematical Programming , vol.46 , pp. 219-224
    • Chandrasekaran, R.1    Tamir, A.2
  • 11
    • 0000557601 scopus 로고
    • Weber's problem and Weiszfeld's algorithm in general spaces
    • U. Eckhardt. Weber's problem and Weiszfeld's algorithm in general spaces. Mathematical Programming, 18:186-196, 1980.
    • (1980) Mathematical Programming , vol.18 , pp. 186-196
    • Eckhardt, U.1
  • 12
    • 0019574599 scopus 로고
    • Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography
    • M. A. Fischler and R. C. Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-395, 1981.
    • (1981) Communications of the ACM , vol.24 , Issue.6 , pp. 381-395
    • Fischler, M.A.1    Bolles, R.C.2
  • 15
    • 0000315591 scopus 로고
    • Les éléments aléatoires de nature quelconque dans un espace distancié.
    • M. Fréchet. Les éléments aléatoires de nature quelconque dans un espace distancié. Ann. Inst. H. Poincaré, 10(3):215-310, 1948.
    • (1948) Ann. Inst. H. Poincaré , vol.10 , Issue.3 , pp. 215-310
    • Fréchet, M.1
  • 16
  • 18
    • 84980162923 scopus 로고
    • Riemannian center of mass and mollifier smoothing
    • H. Karcher. Riemannian center of mass and mollifier smoothing. Comm. on Pure and Appl. Math., 30:509-541, 1977.
    • (1977) Comm. on Pure and Appl. Math , vol.30 , pp. 509-541
    • Karcher, H.1
  • 19
    • 0002432238 scopus 로고
    • Shape manifolds, Procrustean metrics, and complex projective spaces
    • D. G. Kendall. Shape manifolds, Procrustean metrics, and complex projective spaces. Bulletin of the London Mathematical Society, 16:18-121, 1984.
    • (1984) Bulletin of the London Mathematical Society , vol.16 , pp. 18-121
    • Kendall, D.G.1
  • 21
    • 34250438259 scopus 로고
    • A note on Fermat's problem
    • H. W. Kuhn. A note on Fermat's problem. Mathematical Programming, 4:98-107, 1973.
    • (1973) Mathematical Programming , vol.4 , pp. 98-107
    • Kuhn, H.W.1
  • 22
    • 84980123632 scopus 로고
    • An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics
    • H. W. Kuhn and R. E. Kuenne. An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics. J. Regional Sci., 4:21-34, 1962.
    • (1962) J. Regional Sci , vol.4 , pp. 21-34
    • Kuhn, H.W.1    Kuenne, R.E.2
  • 24
    • 0001352378 scopus 로고
    • Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
    • H. P. Lopuhaa and P. J. Rousseeuw. Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. The Annals of Statistics, 19(1):229-248, 1991.
    • (1991) The Annals of Statistics , vol.19 , Issue.1 , pp. 229-248
    • Lopuhaa, H.P.1    Rousseeuw, P.J.2
  • 26
    • 31644434690 scopus 로고    scopus 로고
    • Riemannian geometries on spaces of plane curves
    • P. W. Michor and D. Mumford. Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc., 8:1-48, 2006.
    • (2006) J. Eur. Math. Soc , vol.8 , pp. 1-48
    • Michor, P.W.1    Mumford, D.2
  • 27
    • 0017995743 scopus 로고
    • On the convergence of a class of iterative methods for solving the Weber location problem
    • L. M. Ostresh. On the convergence of a class of iterative methods for solving the Weber location problem. Operations Research, 26:597-609, 1978.
    • (1978) Operations Research , vol.26 , pp. 597-609
    • Ostresh, L.M.1
  • 28
    • 33749642835 scopus 로고    scopus 로고
    • Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
    • X. Pennec. Intrinsic statistics on Riemannian manifolds: basic tools for geometric measurements. Journal of Mathematical Imaging and Vision, 25(1), 2006.
    • (2006) Journal of Mathematical Imaging and Vision , vol.25 , Issue.1
    • Pennec, X.1
  • 33
    • 0033189795 scopus 로고    scopus 로고
    • Robust parameter estimation in computer vision
    • C. V. Stewart. Robust parameter estimation in computer vision. SIAM Review, 41(3):513-537, 1999.
    • (1999) SIAM Review , vol.41 , Issue.3 , pp. 513-537
    • Stewart, C.V.1
  • 34
    • 0000281286 scopus 로고
    • Sur le point pour lequel la somme des distances de n points donnés est minimum.
    • E. Weiszfeld. Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. J., 43:355-386, 1937.
    • (1937) Tohoku Math. J , vol.43 , pp. 355-386
    • Weiszfeld, E.1
  • 35
    • 0032050058 scopus 로고    scopus 로고
    • Computable elastic distances between shapes
    • L. Younes. Computable elastic distances between shapes. SIAM J. Appl. Math., 58:565-586, 1998.
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 565-586
    • Younes, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.