We present a new approach to rigid-body motion segmentation from two views. We use a previously developed nonlinear embedding of two-view point correspondences into a 9-dimensional space and identify the different motions by segmenting lower-dimensional subspaces. In order to overcome nonuniform distributions along the subspaces, whose dimensions are unknown, we suggest the novel concept of global dimension and its minimization for clustering subspaces with some theoretical motivation. We propose a fast projected gradient algorithm for minimizing global dimension and thus segmenting motions from 2-views. We develop an outlier detection framework around the proposed method, and we present state-of-the-art results on outlier-free and outlier-corrupted two-view data for segmenting motion.
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Acknowledgments This work was supported by NSF Grants DMS-09-15064 and DMS-09-56072. GL was partially supported by the IMA during their annual program on the mathematics of information (2011– 2012) and BP benefited from participating in parts of this program and even presented an initial version of this work at an IMA seminar in Spring 2012. We thank the anonymous reviewers for their thoughtful comments, Shankar Rao for sharing with us the RAS database, and Tom Lou for his helpful suggestions in regards to our algorithm for minimizing global dimension. A very preliminary version of this work was submitted to CVPR 2012, we thank one of the anonymous reviewers for some insightful comments that made us modify the GDM algorithm and its theoretical support.
This work was supported by NSF Grants DMS-09-15064 and DMS-09-56072. Supplementary webpage: http://math.umn.edu/ ~lerman/gdm.
- Empirical dimension
- Global dimension
- Hybrid-linear modeling
- Motion segmentation
- Robust statistics
- Subspace clustering