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We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. Our key contribution is to show that, under...
We propose a novel algorithm for clustering data sampled from multiple submanifolds of a Riemannian manifold. First, we learn a representation of the data using generalizations of local nonlinear dimensionality reduction algorithms from Euclidean to Riemannian spaces. Such generalizations exploit geometric properties of the Riemannian space, particularly its Riemannian metric. Then, assuming that...
We propose a geometric approach to 3D motion segmentation from point correspondences in three perspective views. We demonstrate that after applying a polynomial embedding to the point correspondences, they become related by the so-called multibody trilinear constraint and its associated multibody trifocal tensor, which are natural generalizations of the trilinear constraint and the trifocal tensor...
Given point correspondences in multiple perspective views of a scene containing multiple rigid-body motions, we present an algorithm for segmenting the correspondences according to the multiple motions. We exploit the fact that when the depths of the points are known, the point trajectories associated with a single motion live in a subspace of dimension at most four. Thus motion segmentation with...
We propose a novel algorithm for segmenting multiple motions of different types from point correspondences in multiple affine or perspective views. Since point trajectories associated with different motions live in different manifolds, traditional approaches deal with only one manifold type: linear subspaces for affine views, and homographic, bilinear and trilinear varieties for two and three perspective...
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