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Title: Subspace Procrustes Analysis
Author: Perez-Sala, Xavier
De la Torre, Fernando
Igual Muñoz, Laura
Escalera Guerrero, Sergio
Angulo, Cecilio
Keywords: Estadística matemàtica
Mathematical statistics
Issue Date: 15-Sep-2016
Publisher: Springer Verlag
Abstract: Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.
Note: Versió postprint del document publicat a:
It is part of: International Journal of Computer Vision, 2016, vol. 121, num. 3, p. 1-17
Related resource:
ISSN: 0920-5691
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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