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Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes. These bases are object dependent and therefore have to be estimated anew for each video sequence. In contrast, we propose a dual approach to describe the evolving 3D structure in trajectory space by a linear combination of basis trajectories. We...
We introduce locally-rigid motion, a general framework for solving the M-point, N-view structure-from-motion problem for unknown bodies deforming under orthography. The key idea is to first solve many local 3-point, N-view rigid problems independently, providing a “soup” of specific, plausibly rigid, 3D triangles. The main advantage here is that the extraction of 3D triangles requires only very weak...
In factorization approaches to nonrigid structure from motion, the 3D shape of a deforming object is usually modeled as a linear combination of a small number of basis shapes. The original approach to simultaneously estimate the shape basis and nonrigid structure exploited ortho-normality constraints for metric rectification. Recently, it has been asserted that structure recovery through ortho-normality...
This paper proposes a method to recover the embedding of the possible shapes assumed by a deforming nonrigid object by comparing triplets of frames from an orthographic video sequence. We assume that we are given features tracked with no occlusions and no outliers but possible noise, an orthographic camera and that any 3D shape of a deforming object is a linear combination of several canonical shapes...
We present a practical algorithm that provably achieves the global optimum for a class of bilinear programs commonly arising in computer vision applications. Our approach relies on constructing tight convex relaxations of the objective function and minimizing it in a branch and bound framework. A key contribution of the paper is a novel, provably convergent branching strategy that allows us to solve...
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