Motion segmentation with missing data using PowerFactorization and GPCA

We consider the problem of segmenting multiple rigid motions from point correspondences in multiple affine views. We cast this problem as a subspace clustering problem in which the motion of each object lives in a subspace of dimension two, three or four. Unlike previous work, we do not restrict the motion subspaces to be four-dimensional or linearly independent. Instead, our approach deals gracefully with all the spectrum of possible affine motions: from two-dimensional and partially dependent to four-dimensional and fully independent. In addition, our method handles the case of missing data, meaning that point tracks do not have to be visible in all images. Our approach involves projecting the point trajectories of all the points into a 5-dimensional space, using the PowerFactorization method to fill in missing data. Then multiple linear subspaces representing independent motions is fitted to the points in R5 using GPCA. We test our algorithm on various real sequences with degenerate and nondegenerate motions, missing data, perspective effects, transparent motions, etc. Our algorithm achieves a misclassification error of less than 5% for sequences with up to 30% of missing data points.