  The mean-shift algorithm is a popular algorithm in computer vision and image
processing. It can also be cast as a minimum gamma-divergence estimation. In
this paper we focus on the "blurring" mean shift algorithm, which is one
version of the mean-shift process that successively blurs the dataset. The
analysis of the blurring mean-shift is relatively more complicated compared to
the nonblurring version, yet the algorithm convergence and the estimation
consistency have not been well studied in the literature. In this paper we
prove both the convergence and the consistency of the blurring mean-shift. We
also perform simulation studies to compare the efficiency of the blurring and
the nonblurring versions of the mean-shift algorithms. Our results show that
the blurring mean-shift has more efficiency.
