Geometric Structure of Degeneracy for Multi-body Motion Segmentation

Abstract

Abstract. Many techniques have been proposed for segmenting feature point trajectories tracked through a video sequence into independent motions. It has been found, however, that methods that perform very well in simulations perform very poorly for real video sequences. This paper resolves this mystery by analyzing the geometric structure of the degeneracy of the motion model. This leads to a new segmentation algorithm: a multi-stage unsupervised learning scheme first using the degenerate motion model and then using the general 3-D motion model. We demonstrate by simulated and real video experiments that our method is superior to all existing methods in practical situations.

A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms

“…The Multi-Stage Learning (MSL) algorithm is a statistical approach proposed by Sugaya and Kanatani in [14]. It builds on Costeira and Kanade's factorization method (CK) [3] and Kanatani's subspace separation method (SS) [10,11].…”

“…For example, when two objects have the same rotational but different translational motion relative to the camera [14], or for articulated motions [20]. This has motivated the development of several algorithms for dealing with partially dependent motions, including statistical methods [6,14], spectral methods [21,22] and algebraic methods [16].…”

“…This has motivated the development of several algorithms for dealing with partially dependent motions, including statistical methods [6,14], spectral methods [21,22] and algebraic methods [16]. We review some of these methods in the next section.…”

Generalized projection based M-estimator: Theory and applications

“…Several approaches have been proposed which can be categorized into factorization based [22,23], clustering based [7,13], robust estimation based [9,17,5,19], algebraic [25] and statistical methods [20,11]. A brief review of most of these techniques can be found in [7].…”

Fast and accurate motion segmentation using Linear Combination of Views

“…[25]. Older methods such as LSA [23], ALC [10] MSL [16], GPCA [22] and RANSACtype subspace fitting approaches have since been surpassed. Of course, one is not limited to subspace methods for solving the motion segmentation problem, or indeed an affine camera model.…”