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| 均值漂移算法的收敛性 |
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李乡儒1,2, 吴福朝1,2, 胡占义1,2
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1.中国科学院,自动化研究所,模式识别国家重点实验室,北京,100080;2.中国科学院,研究生院,北京,100039
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| 摘要: |
| 均值漂移是一种有效的统计迭代算法,已广泛应用于聚类分析、跟踪、图像分割、图像平滑、滤波、图像边缘提取和信息融合等方面.但是,其收敛性仍没有得到严格的证明,而收敛性是任何迭代算法的必要前提.推广并严格证明了该算法的收敛性.首先将均值漂移算法做了以下推广:反映不同样本点处局部空间结构的差异及其各向异性.然后,在推广的条件下从数学上严格证明了均值漂移算法的收敛性.最后,探讨了均值漂移算法中参数的自适应选择方法.从而为该算法的应用奠定了理论基础. |
| 关键词: 均值漂移 收敛性 聚类分析 图像处理 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60375006 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2003AA133060 (国家高技术研究发展计划(863)) |
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| Convergence of a Mean Shift Algorithm |
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LI Xiang-Ru,WU Fu-Chao,HU Zhan-Yi
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| Abstract: |
| Mean shift is an effective iterative algorithm widely used in clustering, tracking, segmentation, discontinuity preserving smoothing, filtering, edge detection, and information fusion etc. However, its convergence, a key property of any iterative method, has not been rigorously proved till now. In this paper, the traditional mean shift algorithm is first extended to account for both the local property at different sampling points and the anisotropic property at different directions, then a rigorous convergence proof is provided under these extended conditions. Finally, some approaches to adaptively selecting the algorithm’s parameters are outlined. The results in this paper contribute substantially to the establishment of a sound theoretical foundation for the mean shift algorithm. |
| Key words: mean shift convergence clustering analysis image processing |
