Generalized mean shift with triangular kernel profile
This work addresses a specific convergence issue in mean shift algorithms for clustering applications, representing an incremental improvement in the field.
The authors tackled the problem of proving convergence for mean shift algorithms by introducing a novel variant using triangular kernel profiles, and they proved that this variant converges after a finite number of iterations.
The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since its introduction, it underwent several practical improvements and generalizations, as well as deep theoretical analysis mainly focused on its convergence properties. In spite of encouraging results, this question has not received a clear general answer yet. In this paper we focus on a specific class of kernels, adapted in particular to the distributions clustering applications which motivated this work. We show that a novel Mean Shift variant adapted to them can be derived, and proved to converge after a finite number of iterations. In order to situate this new class of methods in the general picture of the Mean Shift theory, we alo give a synthetic exposure of existing results of this field.