Affine motion segmentation from feature point trajectories using rank minimization

In this paper, we examine the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this motion segmentation problem can be cast as the problem of segmenting samples drawn from a union of linear subspaces. We pose this problem as a rank minimization problem, where the goal is to decompose the corrupted data matrix as the sum of a low-rank dictionary plus a matrix of noise. Given a set of data vectors, low rank representation seeks the lowest rank representation among all the linear combination of the bases in a dictionary. For noisy data, this non-convex problem can be solved very efficiently in the inexact Augmented Lagrange Multiplier method. Our algorithm amounts to an SVD of the data matrix and a shrinkage-thresholding of its singular values. We have experimented on real image sequence, where we show good segmentation result, comparable to the state-of-the-art in literature.