Duc-Son Pham, Saha Budhaditya, Dinh Phung, and Svetha Venkatesh. Improved sparse subspace clustering via exploitation of spatial constraints. In Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), Province, Rhode Island, USA, June 2012.

We propose a novel approach to subspace clustering, which has important applications in motion segmentation. Our method makes an important exploitation of the spatial constraints to improve clustering results. Intuitively, we observe that tracked points that belong to a rigid moving object are likely close in proximity. Hence, using this information as a prior knowledge, we propose a weighted formulation which gives the subspace clustering as a posterior solution evidenced on the observed data. Our proposed approach is flexible and treats the previously proposed sparse subspace clustering algorithm as a special case. We also give a full treatment for the noisy case and with missing data and two modes of corruptions: random and column. On the Johns Hopkins 155 dataset, we present state-of-the-arts motion segmentation results, which demonstrate the power of the proposed approach.

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