The Normalized Subspace Inclusion: Robust Clustering of Motion Subspaces

Abstract

Perceiving dynamic scenes of rigid bodies, through affine projections of moving 3D point clouds, boils down to clustering the rigid motion subspaces supported by the points' image trajectories. For a physically meaningful interpretation, clusters must be consistent with the geometry of the underlying subspaces. Most of the existing measures for subspace clustering are ambiguous, or geometrically inconsistent. 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. Relying on this similarity, 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.