Polynomial Regression on Riemannian Manifolds

被引：0
|
作者：
Hinkle, Jacob [1 ]
Muralidharan, Prasanna [1 ]
Fletcher, P. Thomas [1 ]
Joshi, Sarang [1 ]
机构：
[1] Univ Utah, SCI Inst, Salt Lake City, UT 84112 USA
来源：
COMPUTER VISION - ECCV 2012, PT III | 2012年 / 7574卷
关键词：
FITTING SMOOTH PATHS; EQUATIONS; SPLINES;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds. The theory enables parametric analysis in a wide range of applications, including rigid and non-rigid kinematics as well as shape change of organs due to growth and aging. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein and the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.
引用
收藏
页码：1 / 14
页数：14
相关论文
共 50 条
  • [31] On the symmetry of Riemannian manifolds
    Deng, Shaoqiang
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 680 : 235 - 256
  • [32] Mechanics on Riemannian manifolds
    Oliva, WM
    NONLINEAR ANALYSIS AND ITS APPLICATIONS TO DIFFERENTIAL EQUATIONS, 2001, 43 : 65 - 84
  • [33] CONVEXITY IN RIEMANNIAN MANIFOLDS
    TRIBUZY, I
    ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 1978, 50 (03): : 269 - 271
  • [34] Separability in Riemannian Manifolds
    Benenti, Sergio
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2016, 12
  • [35] On δ-homogeneous Riemannian manifolds
    Berestovskii, V. N.
    Nikonorov, Yu. G.
    DOKLADY MATHEMATICS, 2007, 76 (01) : 596 - 598
  • [36] Traces on Riemannian Manifolds
    Schneider, Cornelia
    BEYOND SOBOLEV AND BESOV: REGULARITY OF SOLUTIONS OF PDES AND THEIR TRACES IN FUNCTION SPACES, 2021, 2291 : 295 - 313
  • [37] On δ-homogeneous Riemannian manifolds
    Berestovskii, V. N.
    Nikonorov, Yu. G.
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2008, 26 (05) : 514 - 535
  • [38] Knots in Riemannian manifolds
    Fang, Fuquan
    Mendonca, Sergio
    MATHEMATISCHE ZEITSCHRIFT, 2011, 267 (1-2) : 425 - 431
  • [39] Flowers on Riemannian manifolds
    Regina Rotman
    Mathematische Zeitschrift, 2011, 269 : 543 - 554
  • [40] EQUIMORPHISMS OF RIEMANNIAN MANIFOLDS
    EFREMOVI.VA
    LOGINOV, EA
    TIKHOMIR.ES
    DOKLADY AKADEMII NAUK SSSR, 1971, 197 (01): : 25 - +
12345