1. Mean-Shift Algorithm and Its Application Bohyung Han bhhan@cs.umd.edu

2. Introduction Computer vision applications and density estimation Computer vision applications and density estimation –Background subtraction –Model representation –Particle filter –Any other statistical method Issues for density estimation Issues for density estimation –How to represent density –How to extract the important information Local maxima, minima Local maxima, minima Gradient Gradient Mode Mode

3. Kernel Density Estimation Multivariate kernel density estimation Multivariate kernel density estimation Kernels Kernels –Gaussian –Epanechnikov

4. Mean-Shift Algorithm Basic idea Basic idea –Based on kernel density estimation –Finding local optimum (mode) –Density gradient estimation –Iterative hill climbing algorithm Benefit over the direct computation Benefit over the direct computation –Computational complexity Less density function evaluation Less density function evaluation Only local computation Only local computation

5. Finding Mean-Shift Vector Gradient computation Gradient computation –For Gaussian kernel Always converges to the local maximum! Always converges to the local maximum!

6. Variable Bandwidth Mean-Shift Motivation Motivation –Fixed bandwidth: specification of a scale parameter –Difficult to find the global optimal scale –Data-driven scale selection is required. Abramson’s rule Abramson’s rule – : fixed bandwidth for initial estimation – : geometric mean

7. Variable Bandwidth Mean-Shift (cont’d) Gradient computation Gradient computation –Also for Gaussian kernel

8. Applications Pattern recognition Pattern recognition –Clustering Image processing Image processing –Filtering –Segmentation Density estimation Density estimation –Density approximation –Particle filter Mid-level application Mid-level application –Tracking –Background subtraction

9. Application – Tracking (1) Target representation Target representation Candidate representation Candidate representation Bhattacharyya distance Bhattacharyya distance

10. Application – Tracking (2) Distance minimization Distance minimizationwhere Mean-Shift iteration Mean-Shift iteration

11. Application – Tracking (3) Mean-Shift tracking algorithm Mean-Shift tracking algorithm