EXPLOITING LOW-DIMENSIONAL STRUCTURES IN MOTION PROBLEMS.

Abstract

VIDEO-RELATED PROBLEMS OFTEN INVOLVE HIGH-DIMENSIONAL DATA ANALYSIS. IN THIS THESIS, WE EXPLORE THE THEORETICAL AND ALGORITHMIC ASPECTS OF THEIR LOW-DIMENSIONAL STRUCTURES, INCLUDING SPARSITY IN VECTORS AND LOW RANK MATRICES, AMONG OTHERS. SPECIFICALLY, WE ADDRESS VARIOUS MOTION-RELATED PROBLEMS SUCH AS MOTION SEGMENTATION AND OBJECT TRACKING.

FOR THE MOTION SEGMENTATION PROBLEM, WE PROPOSE A JOINT SPARSITY MODEL, WHICH COMBINES AFFINITIES OF THE POINT CORRESPONDENCE IN MULTIPLE IMAGE PAIRS; IT IS CAPABLE OF HANDLING PERSPECTIVE EFFECT, WHILE SIMULTANEOUSLY LEVERAGING THE RICH INFORMATION ACROSS MULTIPLE FRAMES.

TO ESTIMATE THE NUMBER OF GROUPS IN THE ABOVE PROBLEM, WE PROPOSE A SIMULTANEOUS LOW-RANK AND SPARSE MODEL, WHERE THE RANK FUNCTION MODELS THE COMPLEXITY OF THE MODEL AND THE CARDINALITY FUNCTION IS USED TO AVOID THE TRIVIAL SOLUTION AND SUPPRESS SMALL AFFINITIES.

LASTLY, WE EXPLOIT THE LOW-DIMENSIONAL STRUCTURES PRESENT IN THE OBJECT TRACKING PROBLEM TO SPEED UP THE L