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

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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.

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Acknowledgments

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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Authors and Affiliations

  1. Institute of Statistical Science, Academia Sinica, Taipei, 11529, Taiwan

    Ting-Li Chen

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  1. Ting-Li Chen
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Correspondence to Ting-Li Chen.

Additional information

This work is supported by the National Science Council, Taiwan, Grant Nos. NSC 96-2118-M-001-007-.

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Chen, TL. On the convergence and consistency of the blurring mean-shift process. Ann Inst Stat Math 67, 157–176 (2015). https://doi.org/10.1007/s10463-013-0443-8

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  • DOI: https://doi.org/10.1007/s10463-013-0443-8

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