Fast Segmentation of Sparse 3D Point Trajectories Using Group Theoretical Invariants

We present a novel approach for segmenting different motions from 3D trajectories. Our approach uses the theory of transformation groups to derive a set of invariants of 3D points located on the same rigid object. These invariants are inexpensive to calculate, involving primarily QR factorizations of small matrices. The invariants are easily converted into a set of robust motion affinities and with the use of a local sampling scheme and spectral clustering, they can be incorporated into a highly efficient motion segmentation algorithm. We have also captured a new multi-object 3D motion dataset, on which we have evaluated our approach, and compared against state-of-the-art competing methods from literature. Our results show that our approach outperforms all methods while being robust to perspective distortions and degenerate configurations.