★Mean shift a_robust_approach_to_feature_space_analysis

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★Mean shift a_robust_approach_to_feature_space_analysis

  1. 1. Mean Shift A Robust Approach to Feature Space Analysis Kalyan Sunkavalli 04/29/2008 ES251R
  2. 2. An Example Feature Space
  3. 3. An Example Feature Space
  4. 4. An Example Feature Space Parametric Density Estimation?
  5. 5. Mean Shift <ul><li>A non-parametric technique for analyzing complex multimodal feature spaces and estimating the stationary points (modes) of the underlying probability density function without explicitly estimating it . </li></ul>
  6. 6. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>An intuition </li></ul></ul><ul><ul><li>Kernel Density Estimation </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  7. 7. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>An intuition </li></ul></ul><ul><ul><li>Kernel Density Estimation </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  8. 8. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Mean Shift vector Objective : Find the densest region Slide Credit: Yaron Ukrainitz & Bernard Sarel
  9. 9. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Mean Shift vector Objective : Find the densest region
  10. 10. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Mean Shift vector Objective : Find the densest region
  11. 11. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Mean Shift vector Objective : Find the densest region
  12. 12. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Mean Shift vector Objective : Find the densest region
  13. 13. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Mean Shift vector Objective : Find the densest region
  14. 14. Intuitive Description Distribution of identical billiard balls Region of interest Center of mass Objective : Find the densest region
  15. 15. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>An intuition </li></ul></ul><ul><ul><li>Kernel Density Estimation </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  16. 16. Assumed Underlying PDF Estimate from data Data Samples Parametric Density Estimation The data points are sampled from an underlying PDF
  17. 17. Assumed Underlying PDF Data Samples Data point density Non-parametric Density Estimation PDF value
  18. 18. Assumed Underlying PDF Data Samples Non-parametric Density Estimation
  19. 19. Parzen Windows <ul><li>Kernel Properties </li></ul><ul><ul><li>Bounded </li></ul></ul><ul><ul><li>Compact support </li></ul></ul><ul><ul><li>Normalized </li></ul></ul><ul><ul><li>Symmetric </li></ul></ul><ul><ul><li>Exponential decay </li></ul></ul>
  20. 20. Kernels and Bandwidths <ul><li>Kernel Types </li></ul><ul><li>Bandwidth Parameter </li></ul>(product of univariate kernels) (radially symmetric kernel)
  21. 21. Various Kernels Epanechnikov Normal Uniform
  22. 22. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>An intuition </li></ul></ul><ul><ul><li>Kernel Density Estimation </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  23. 23. Density Gradient Estimation Epanechnikov  Uniform Normal  Normal Modes of the probability density
  24. 24. Mean Shift KDE Mean Shift Mean Shift Algorithm <ul><li>compute mean shift vector </li></ul><ul><li>translate kernel (window) by mean shift vector </li></ul>
  25. 25. Mean Shift <ul><li>Mean Shift is proportional to the normalized density gradient estimate obtained with kernel </li></ul><ul><li>The normalization is by the density estimate computed with kernel </li></ul>
  26. 26. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>An intuition </li></ul></ul><ul><ul><li>Kernel Density Estimation </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  27. 27. Properties of Mean Shift <ul><li>Guaranteed convergence </li></ul><ul><ul><li>Gradient Ascent algorithms are guaranteed to converge only for infinitesimal steps. </li></ul></ul><ul><ul><li>The normalization of the mean shift vector ensures that it converges. </li></ul></ul><ul><ul><li>Large magnitude in low-density regions, refined steps near local maxima  Adaptive Gradient Ascent. </li></ul></ul><ul><li>Mode Detection </li></ul><ul><ul><li>Let denote the sequence of kernel locations. </li></ul></ul><ul><ul><li>At convergence </li></ul></ul><ul><ul><li>Once gets sufficiently close to a mode of it will converge to the mode. </li></ul></ul><ul><ul><li>The set of all locations that converge to the same mode define the basin of attraction of that mode. </li></ul></ul>
  28. 28. Properties of Mean Shift <ul><li>Smooth Trajectory </li></ul><ul><ul><li>The angle between two consecutive mean shift vectors computed using the normal kernel is always less that 90° </li></ul></ul><ul><ul><li>In practice the convergence of mean shift using the normal kernel is very slow and typically the uniform kernel is used. </li></ul></ul>
  29. 29. Mode detection using Mean Shift <ul><li>Run Mean Shift to find the stationary points </li></ul><ul><ul><li>To detect multiple modes, run in parallel starting with initializations covering the entire feature space. </li></ul></ul><ul><li>Prune the stationary points by retaining local maxima </li></ul><ul><ul><li>Merge modes at a distance of less than the bandwidth. </li></ul></ul><ul><li>Clustering from the modes </li></ul><ul><ul><li>The basin of attraction of each mode delineates a cluster of arbitrary shape. </li></ul></ul>
  30. 30. Mode Finding on Real Data initialization detected mode tracks
  31. 31. Mean Shift Clustering
  32. 32. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>Density Estimation </li></ul></ul><ul><ul><li>What is mean shift? </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  33. 33. Joint Spatial-Range Feature Space <ul><li>Concatenate spatial and range (gray level or color) information </li></ul>
  34. 34. Discontinuity Preserving Smoothing
  35. 35. Discontinuity Preserving Smoothing
  36. 36. Discontinuity Preserving Smoothing
  37. 37. Discontinuity Preserving Smoothing
  38. 38. Outline <ul><li>Mean Shift </li></ul><ul><ul><li>Density Estimation </li></ul></ul><ul><ul><li>What is mean shift? </li></ul></ul><ul><ul><li>Derivation </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Applications of Mean Shift </li></ul><ul><ul><li>Discontinuity preserving Smoothing </li></ul></ul><ul><ul><li>Image Segmentation </li></ul></ul>
  39. 39. Clustering on Real Data
  40. 40. Image Segmentation
  41. 41. Image Segmentation
  42. 42. Image Segmentation
  43. 43. Image Segmentation
  44. 44. Image Segmentation
  45. 45. Acknowledgements <ul><li>Mean shift: A robust approach toward feature space analysis. D Comaniciu, P Meer Pattern Analysis and Machine Intelligence, IEEE Transactions on , Vol. 24, No. 5. (2002), pp. 603-619. </li></ul><ul><li>http://www.caip.rutgers.edu/riul/research/papers.html </li></ul><ul><li>Slide credits: Yaron Ukrainitz & Bernard Sarel </li></ul>
  46. 46. Thank You

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