Half Quadratic Analysis for Mean Shift: with Extension to A Sequential Data Mode-Seeking Method

Theoretical understanding and extension of mean shift procedure has received much attention recently. In this paper, we present a theoretical exploration and an algorithm development on mean shift. In the theory part, we point out that convex profile based mean shift can be justified from the viewpoint of half-quadratic (HQ) optimization. Such analysis facilitates the convergence study and uni-mode bandwidth selection for the latest variation, annealed mean shift. In the algorithm development part of this paper, we extend annealed mean shift inside our HQ framework to a novel method, namely adaptive mean shift (Ada-MS), to detect multiple data modes sequentially from an arbitrary starting point in linear running time. To validate the performance, we couple the investigation with two applications: image segmentation and color constancy. Extensive experiments show that the proposed method is time efficient and initialization invariant.