Correntropy metric-based robust low-rank subspace clustering for motion segmentation

The subspace clustering methods for motion segmentation are widely used in the field of computer vision. However, the existing methods ignore the low-rank property of motion trajectory with nonlinear structure and are sensitive to non-Gaussian noise. To this end, we seek to improve the performance of motion segmentation by effectively modeling some important characteristics of the motion trajectories, such as nonlinear structure and contained non-Gaussian noise. Specifically, we propose to use kernel function to model motion trajectory, design a variant of the correntropy-induced metric to measure noise, and integrate the block diagonal regularizer into the kernel subspace clustering to strengthen the block diagonal structure of the learned affinity matrix. More importantly, we propose a unified rank-constrained block diagonal subspace clustering method for motion segmentation, which can handle not only rigid body motion segmentation, but also non-rigid motion segmentation. And we further extend this method to deal with various noises in motion data, such as missing trajectories, corrupted trajectory and outlying trajectory. An effective algorithm HQ& AM, which is integrated by Half-quadratic theory and alternating minimization, is designed to optimize these models. Experimental results on several commonly used motion datasets indicate the effectualness and robustness of our methods.