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

TL;DR

This paper proves the convergence and consistency of the blurring mean-shift algorithm, a popular method in computer vision, and demonstrates its superior efficiency over the nonblurring version through simulations.

Contribution

It provides the first rigorous proof of convergence and consistency for the blurring mean-shift algorithm, enhancing its theoretical foundation.

Findings

Proves convergence of the blurring mean-shift algorithm.

Establishes the consistency of the estimator.

Shows the blurring version is more efficient than the nonblurring one.

Abstract

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.