Non-Rigid Shape and Motion Recovery: Degenerate Deformations - Robotics Institute Carnegie Mellon University

Non-Rigid Shape and Motion Recovery: Degenerate Deformations

Conference Paper, Proceedings of (CVPR) Computer Vision and Pattern Recognition, pp. 668 - 675, June, 2004

Abstract

This paper studies the problem of 3D non-rigid shape and motion recovery from a monocular video sequence, under the degenerate deformations. The shape of a deformable object is regarded as a linear combination of certain shape bases. When the bases are non-degenerate, i.e. of full rank 3, a closed-form solution exists by enforcing linear constraints on both the camera rotation and the shape bases [18]. In practice, degenerate deformations occur often, i.e. some bases are of rank 1 or 2. For example, cars moving or pedestrians walking independently on a straight road refer to rank-1 deformations of the scene. This paper quantitatively shows that, when the shape is composed of only rank-3 and rank-1 bases, i.e. the 3D points either are static or independently move along straight lines, the linear rotation and basis constraints are sufficient to achieve a unique solution. When the shape bases contain rank-2 ones, imposing only the linear constraints results in an ambiguous solution space. In such cases, we propose an alternating linear approach that imposes the positive semi-definite constraint to determine the desired solution in the solution space. The performance of the approach is evaluated quantitatively on synthetic data and qualitatively on real videos.

BibTeX

@conference{Xiao-2004-8952,
author = {Jing Xiao and Takeo Kanade},
title = {Non-Rigid Shape and Motion Recovery: Degenerate Deformations},
booktitle = {Proceedings of (CVPR) Computer Vision and Pattern Recognition},
year = {2004},
month = {June},
pages = {668 - 675},
keywords = {structure from Motion, degenerate deformations, factorization},
}