Mean-Shift Algorithm and Its Application

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

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

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

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

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

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

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

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

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

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

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