IEEE Trans Pattern Anal Mach Intell - Shape Analysis of Elastic Curves in Euclidean Spaces.

Tópicos

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{ method(984) reconstruct(947) comput(926) }
{ featur(1941) imag(1645) propos(1176) }
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{ method(1969) cluster(1462) data(1082) }
{ detect(2391) sensit(1101) algorithm(908) }

Resumo

This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL(2) metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is the quotient space of (a submanifold of) the unit sphere, modulo rotation, and reparameterization groups, and we find geodesics in that space using a path straightening approach. These geodesics and geodesic distances provide a framework for optimally matching, deforming, and comparing shapes. These ideas are demonstrated using: 1) shape analysis of cylindrical helices for studying protein structure, 2) shape analysis of facial curves for recognizing faces, 3) a wrapped probability distribution for capturing shapes of planar closed curves, and 4) parallel transport of deformations for predicting shapes from novel poses.

Resumo Limpo

paper introduc squareroot veloc srv represent analyz shape curv euclidean space elast metric srv represent elast metric simplifi il metric reparameter group act isometri space unit length curv becom unit sphere shape space close curv quotient space submanifold unit sphere modulo rotat reparameter group find geodes space use path straighten approach geodes geodes distanc provid framework optim match deform compar shape idea demonstr use shape analysi cylindr helic studi protein structur shape analysi facial curv recogn face wrap probabl distribut captur shape planar close curv parallel transport deform predict shape novel pose

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