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

On the Convergence and Consistency of the Blurring Mean-Shift Process