Geometrical Consistent Clustering of Linear Subspaces
نویسندگان
چکیده
The perception of rigid-bodies from affine views of moving 3D point clouds, boils down to clustering the rigid motion subspaces supported by the image trajectories. For a physically meaningful interpretation, clusters must be consistent with the geometry of the underlying subspaces. We find that proper subspace clustering requires invariance both to the orthogonal and the inclusion relationship between subspaces. Most of the existing measures for subspace comparison do not comply with this observation. A practical consequence is that methods based on such (dis)similarities are unstable when the number of rigid bodies increase. This paper introduces the Normalized Subspace Inclusion (NSI) criterion to resolve these issues. Combining it with a robust segmentation method, we propose a robust methodology for rigid motion segmentation, and test it, extensively, on the Hopkins155 database. The geometric consistency of the NSI assures the method’s accuracy when the number of rigid bodies increases, while robustness proves to be suitable for dealing with challenging imaging conditions.
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