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Volumn 30, Issue 6-7, 2012, Pages 428-442

Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds

Author keywords

Activity recognition; Curve fitting; Diffusion tensor analysis; Interpolation; Pose tracking; Splines on manifolds

Indexed keywords

ALGORITHMS; CONTOUR MEASUREMENT; INTERPOLATION; OPTIMIZATION; SPLINES; TENSORS;

EID: 84862565323     PISSN: 02628856     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.imavis.2011.09.006     Document Type: Article
Times cited : (61)

References (48)
  • 1
    • 0038083371 scopus 로고    scopus 로고
    • The de Casteljau algorithm on SE(3)
    • C. Altafini The De Casteljau algorithm on SE(3) Nonlinear Control 258 2000 23 34
    • (2000) Nonlinear Control , vol.258 , pp. 23-34
    • Altafini, C.1
  • 4
    • 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 2001 95 126
    • (2001) ACM Transactions on Graphics , vol.20 , pp. 95-126
    • Buss, S.R.1    Fillmore, J.P.2
  • 6
    • 0033155646 scopus 로고    scopus 로고
    • De Casteljau algorithm on Lie groups and spheres
    • DOI 10.1023/A:1021770717822
    • P. Crouch, G. Kun, and F.S. Leite The De Casteljau algorithm on the Lie group and spheres Journal of Dynamical and Control Systems 5 1999 397 429 (Pubitemid 32080737)
    • (1999) Journal of Dynamical and Control Systems , vol.5 , Issue.3 , pp. 397-429
    • Crouch, P.1    Kun, G.2    Silva Leite, F.3
  • 8
    • 0001261818 scopus 로고
    • The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spaces
    • P. Crouch, and F.S. Leite The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces Journal of Dynamical and Control Systems 1 1995 177 202
    • (1995) Journal of Dynamical and Control Systems , vol.1 , pp. 177-202
    • Crouch, P.1    Leite, F.S.2
  • 9
    • 77649270180 scopus 로고    scopus 로고
    • Nonstationary shape activities: Dynamic models for landmark shape change and applications
    • S. Das, and N. Vaswani Nonstationary shape activities: dynamic models for landmark shape change and applications IEEE Transactions on PAMI 32 4 2010 579 592
    • (2010) IEEE Transactions on PAMI , vol.32 , Issue.4 , pp. 579-592
    • Das, S.1    Vaswani, N.2
  • 10
    • 77952417601 scopus 로고    scopus 로고
    • Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging
    • I.L. Dryden, A. Koloydenko, and D. Zhou Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging The Annals of Applied Statistics 3 3 2009 1102 1123
    • (2009) The Annals of Applied Statistics , vol.3 , Issue.3 , pp. 1102-1123
    • Dryden, I.L.1    Koloydenko, A.2    Zhou, D.3
  • 12
    • 33750164640 scopus 로고    scopus 로고
    • Riemannian geometry for the statistical analysis of diffusion tensor data
    • DOI 10.1016/j.sigpro.2005.12.018, PII S0165168406001691
    • P. Fletcher, and S. Joshi Riemannian geometry for the statistical analysis of diffusion tensor data Signal Processing 87 2 2007 250 262 (Pubitemid 44602252)
    • (2007) Signal Processing , vol.87 , Issue.2 , pp. 250-262
    • Fletcher, P.T.1    Joshi, S.2
  • 15
    • 35348870622 scopus 로고    scopus 로고
    • Energy-minimizing splines in manifolds
    • M. Hofer, and H. Pottmann Energy-minimizing splines in manifolds Proc. SIGGRAPH 2004 284 293
    • (2004) Proc. SIGGRAPH , pp. 284-293
    • Hofer, M.1    Pottmann, H.2
  • 20
    • 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 1984 81 121
    • (1984) Bulletin of the London Mathematical Society , vol.16 , pp. 81-121
    • Kendall, D.G.1
  • 24
    • 34548522151 scopus 로고    scopus 로고
    • Shape-space smoothing splines for planar landmark data
    • DOI 10.1093/biomet/asm047
    • A. Kume, I.L. Dryden, and H. Le Shape-space smoothing splines for planar landmark data Biometrika 94 2007 513 528 (Pubitemid 47384247)
    • (2007) Biometrika , vol.94 , Issue.3 , pp. 513-528
    • Kume, A.1    Dryden, I.L.2    Le, H.3
  • 25
    • 3042571516 scopus 로고    scopus 로고
    • Optimal linear representations of images for object recognition
    • X. Liu, A. Srivastava, and K. Gallivan Optimal linear representations of images for object recognition IEEE Transactions on PAMI 26 5 2004 662 666
    • (2004) IEEE Transactions on PAMI , vol.26 , Issue.5 , pp. 662-666
    • Liu, X.1    Srivastava, A.2    Gallivan, K.3
  • 29
    • 0037281553 scopus 로고    scopus 로고
    • Means and averaging in the group of rotations
    • DOI 10.1137/S0895479801383877, PII S0895479801383877
    • M. Moakher Means and averaging in the group of rotations SIAM Journal of Matrix Analysis Applications 24 1 2002 1 16 (Pubitemid 36260148)
    • (2003) SIAM Journal on Matrix Analysis and Applications , vol.24 , Issue.1 , pp. 1-16
    • Moakher, M.1
  • 30
    • 22944439423 scopus 로고    scopus 로고
    • A differential geometric approach to the geometric mean of symmetric positive-definite matrices
    • DOI 10.1137/S0895479803436937
    • M. Moakher A differential geometric approach to the geometric mean of symmetric positive-definite matrices SIAM Journal of Matrix Analysis Applications 26 3 2005 735 747 (Pubitemid 41049842)
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.3 , pp. 735-747
    • Moakher, M.1
  • 33
    • 0001386011 scopus 로고
    • Morse theory on Hilbert manifolds
    • R.S. Palais Morse theory on Hilbert manifolds Topology 2 1963 299 340
    • (1963) Topology , vol.2 , pp. 299-340
    • Palais, R.S.1
  • 34
    • 0031189315 scopus 로고    scopus 로고
    • Smooth Invariant Interpolation of Rotations
    • F.C. Park, and B. Ravani Smooth invariant interpolation of rotations ACM Transactions on Graphics 16 3 1997 277 295 (Pubitemid 128445826)
    • (1998) ACM Transactions on Graphics , vol.16 , Issue.3 , pp. 277-295
    • Park, F.C.1    Ravani, B.2
  • 35
  • 45
    • 77949665332 scopus 로고    scopus 로고
    • Deform PF-MT: Particle filter with mode tracker for tracking nonaffine contour deformations
    • N. Vaswani, Y. Rathi, A. Yezzi, and A. Tannenbaum Deform PF-MT: particle filter with mode tracker for tracking nonaffine contour deformations IEEE Transactions on Image Processing 19 4 2010 841 857
    • (2010) IEEE Transactions on Image Processing , vol.19 , Issue.4 , pp. 841-857
    • Vaswani, N.1    Rathi, Y.2    Yezzi, A.3    Tannenbaum, A.4
  • 46
    • 27744441549 scopus 로고    scopus 로고
    • "Shape activity": A continous-state HMM for moving/deforming shapes with application to abnormal activity detection
    • DOI 10.1109/TIP.2005.852197
    • N. Vaswani, A.K. Roy-Chowdhury, and R. Chellappa Shape Activity: a continuous-state HMM for moving/deforming shapes with application to abnormal activity detection IEEE Transactions on Image Processing 14 10 2005 1603 1616 (Pubitemid 41623090)
    • (2005) IEEE Transactions on Image Processing , vol.14 , Issue.10 , pp. 1603-1616
    • Vaswani, N.1    Roy-Chowdhury, A.K.2    Chellappa, R.3
  • 48
    • 0032138442 scopus 로고    scopus 로고
    • On the generation of smooth three-dimensional rigid body motions
    • PII S1042296X98050186
    • M. Zefran, V. Kumar, and C. Croke On the generation of smooth three-dimensional rigid body motions IEEE Transactions on Robotics and Automation 14 4 1998 576 589 (Pubitemid 128743535)
    • (1998) IEEE Transactions on Robotics and Automation , vol.14 , Issue.4 , pp. 576-589
    • Zefran, M.1    Kumar, V.2    Croke, C.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.