On the convergence and consistency of the blurring mean-shift process

  • Ting-Li ChenEmail author


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.


Mean-shift Convergence Consistency Clustering Super robustness  \(\upgamma \)-Divergence 



The author would like to thank Pei Lun Tseng for suggesting a shorter proof on Lemma 2, and Professor Chii-Ruey Hwang and Professor Su-Yun Huang for inputs and discussions.


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2013

Authors and Affiliations

  1. 1.Institute of Statistical ScienceAcademia SinicaTaipeiTaiwan

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