Multibody Nonrigid Structure from Motion Segmentation Based on Sparse Subspace Clustering

Sparse subspace clustering (SSC) is one of the latest methods of dividing data points into subspace joints, which has a strong theoretical guarantee. However, affine matrix learning is not very effective for segmenting multibody nonrigid structure from motion. To improve the segmentation performance and efficiency of the SSC algorithm in segmenting multiple nonrigid motions, we propose an algorithm that deploys the hierarchical clustering to discover the inner connection of data and represents the entire sequence using some of trajectories (in this paper, we refer to these trajectories as the set of anchor trajectories). Only the corresponding positions of the anchor trajectories have nonzero weights. Furthermore, in order to improve the affinity coefficient and strong connection between trajectories in the same subspace, we optimise the weight matrix by integrating the multilayer graphs and good neighbors. The experiments prove that our methods are effective.

Low-rank sparse subspace clustering with a clean dictionary

Low-Rank Representation (LRR) and Sparse Subspace Clustering (SSC) are considered as the hot topics of subspace clustering algorithms. SSC induces the sparsity through minimizing the l1-norm of the data matrix while LRR promotes a low-rank structure through minimizing the nuclear norm. In this paper, considering the problem of fitting a union of subspace to a collection of data points drawn from one more subspaces and corrupted by noise, we pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise. We propose a new algorithm, named Low-Rank and Sparse Subspace Clustering with a Clean dictionary (LRS2C2), by combining SSC and LRR, as the representation is often both sparse and low-rank. The effectiveness of the proposed algorithm is demonstrated through experiments on motion segmentation and image clustering.