  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.
