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

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  • Ting-Li Chen

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. Copyright The Institute of Statistical Mathematics, Tokyo 2015

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  • Ting-Li Chen, 2015. "On the convergence and consistency of the blurring mean-shift process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 157-176, February.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:1:p:157-176
    DOI: 10.1007/s10463-013-0443-8
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    References listed on IDEAS

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    1. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
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    Cited by:

    1. Chen, Ting-Li & Fujisawa, Hironori & Huang, Su-Yun & Hwang, Chii-Ruey, 2016. "On the weak convergence and Central Limit Theorem of blurring and nonblurring processes with application to robust location estimation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 165-184.
    2. Carlo Grillenzoni, 2016. "Design of Blurring Mean-Shift Algorithms for Data Classification," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 262-281, July.
    3. Jian Chen & Yongkun Shi & Jiaquan Sun & Jiangkuan Li & Jing Xu, 2023. "Base Station Planning Based on Region Division and Mean Shift Clustering," Mathematics, MDPI, vol. 11(8), pages 1-22, April.

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