Mean Shift 算法 原理和在目标跟踪上的应用

1. Mean Shift算法原理和在目标跟踪上的应用

2. Agenda • Mean Shift Theory • What is Mean Shift ? • Density Estimation Methods • Deriving the Mean Shift • Mean shift properties • Applications • Clustering • Discontinuity Preserving Smoothing • Object Contour Detection • Segmentation • Object Tracking

3. Mean Shift Theory

4. Region of interest Intuitive Description Center of mass Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

5. Region of interest Intuitive Description Center of mass Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

6. Region of interest Intuitive Description Center of mass Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

7. Region of interest Intuitive Description Center of mass Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

8. Region of interest Intuitive Description Center of mass Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

9. Region of interest Intuitive Description Center of mass Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

10. Region of interest Intuitive Description Center of mass Objective : Find the densest region Distribution of identical billiard balls

11. 研究现状 Mean shift算法是Fukunaga于1975年提出的，其含义即偏移的均值向量。随着Mean shift理论的发展，它的含义也发生了变化。现在一般是指一个迭代的步骤，即先算出当前点的偏移均值，移动该点到其偏移均值,然后以此为新的起始点，继续移动，直到满足一定的条件结束。Cheng Yizong定义了一族核函数 ，将Mean shift算法引入到计算机视觉领域。Bradski G R对Mean shift算法进行改进，发展建立了Camshift算法，将Mean shift方法扩展应用到了目标跟踪中来。

12. Mean shift的基本形式 给定d维空间 中的n个样本点,i=1,…,n,在点 的Mean Shift向量的基本形式定义为: 其中， 是一个半径为h的高维球区域， k表示在这n个样本点中，有k个点落入区域 中.

13. Mean shift的扩展 核函数： 代表一个d维的欧氏空间， 是该空间中的一个点，用一列向量表示。 的模 。 表示实数域。如果一个函数 存在一个剖面函数 ，即 剖面函数的性质： （1） 是非负的 ； （2） 是非增的； （3） 是分段连续的,并且

14. Kernel Density EstimationVarious Kernels 在选定的空间中，x1…xn 是有限的样本点。 • 例: • Epanechnikov Kernel • Uniform Kernel • （均匀核函数） • Normal Kernel • （高斯核函数）

15. 梯度 核密度估计 使用核函数 的形式: 得到 : 窗宽带宽

16. Computing The Mean Shift Yet another Kernel density estimation ! • Simple Mean Shift procedure: • Compute mean shift vector • Translate the Kernel window by m(x)

17. Non-Rigid Object Tracking … …

18. Choose a reference model in the current frame Choose a feature space Represent the model in the chosen feature space … … Current frame Mean-Shift Object TrackingGeneral Framework: Target Representation

19. Search in the model’s neighborhood in next frame Find best candidate by maximizing a similarity func. Model Candidate … … Current frame Mean-Shift Object TrackingGeneral Framework: Target Localization Start from the position of the model in the current frame Repeat the same process in the next pair of frames

20. Choose a reference target model Choose a feature space Represent the model by its PDF in the feature space Quantized Color Space Mean-Shift Object TrackingTarget Representation Kernel Based Object Tracking, by Comaniniu, Ramesh, Meer

21. SimilarityFunction: Mean-Shift Object TrackingPDF Representation Target Model (centered at 0) Target Candidate (centered at y)

22. candidate model y 0 • A differentiable, isotropic, convex, monotonically decreasing kernel • Peripheral pixels are affected by occlusion and background interference The color bin index (1..m) of pixel x Probability of feature u in model Probability of feature u in candidate Normalization factor Normalization factor Pixel weight Pixel weight Mean-Shift Object TrackingFinding the PDF of the target model Target pixel locations

23. The Bhattacharyya Coefficient 1 1 Mean-Shift Object TrackingSimilarity Function Target model: Target candidate: Similarity function:

24. Search in the model’s neighborhood in next frame Find best candidate by maximizing a similarity func. Mean-Shift Object TrackingTarget Localization Algorithm Start from the position of the model in the current frame

25. Linear approx. (around y0) Mean-Shift Object TrackingApproximating the Similarity Function Model location: Candidate location: Independent of y Density estimate! (as a function of y)

26. Important Assumption: The target representation provides sufficient discrimination One mode in the searched neighborhood Mean-Shift Object TrackingMaximizing the Similarity Function The mode of = sought maximum

27. Extended Mean-Shift: using Find mode of Mean-Shift Object TrackingApplying Mean-Shift The mode of = sought maximum Original Mean-Shift: Find mode of using

28. A special class of radially symmetric kernels: The profile of kernel K Extended Mean-Shift: using Find mode of Mean-Shift Object TrackingAbout Kernels and Profiles

29. Uniform kernel(单位均匀核函数): Mean-Shift Object TrackingChoosing the Kernel A special class of radially symmetric kernels: Epanechnikov kernel: Extended Mean-Shift:

30. Solution: Run localization 3 times with different h Choose h that achieves maximum similarity Mean-Shift Object TrackingAdaptive Scale Problem: The scale of the target changes in time The scale (h) of the kernel must be adapted

31. 完 谢谢