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Mean Shift Theory and Applications

Mean Shift Theory and Applications. Reporter: Zhongping Ji. 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

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Mean Shift Theory and Applications

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  1. Mean ShiftTheory and Applications Reporter: Zhongping Ji

  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. Papers • Mean Shift: A Robust Approach Toward Feature Space Analysis Authors: Dorin Comaniciu, Peter Meer (Rutgers University EECS,Member IEEE). IEEE Trans. Pattern analysis and machine intelligence 24(5), 2002 Field: application of modern statistical methods to image understanding problems • A Topological Approach to Hierarchical Segmentation using Mean Shift Authors: Sylvain Paris, Fredo Durand. (MIT EECS, computer science and artificial intelligence laboratory) Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR'07) Field:most aspects of image processing

  4. Mean Shift Theory

  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 Mean Shift vector Objective : Find the densest region Distribution of identical billiard balls

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

  12. Data What is Mean Shift ? A tool for: Finding modes in a set of data samples, manifesting an underlying probability density function (PDF) in RN • PDF in feature space • Color space • Scale space • Actually any feature space you can conceive • … Non-parametric Density Estimation Discrete PDF Representation Non-parametric Density GRADIENT Estimation (Mean Shift) PDF Analysis

  13. Non-Parametric Density Estimation Assumption : The data points are sampled from an underlying PDF Data point density implies PDF value ! Assumed Underlying PDF Real Data Samples

  14. Non-Parametric Density Estimation Assumed Underlying PDF Real Data Samples

  15. Non-Parametric Density Estimation ? Assumed Underlying PDF Real Data Samples

  16. Parametric Density Estimation Assumption : The data points are sampled from an underlying PDF Estimate Assumed Underlying PDF Real Data Samples

  17. Data Kernel Density Estimation Parzen Windows - Function Forms A function of some finite number of data points x1…xn In practice one uses the forms: or Same function on each dimension Function of vector length only

  18. Data Kernel Density EstimationVarious Kernels A function of some finite number of data points x1…xn • Examples: • Epanechnikov Kernel • Uniform Kernel • Normal Kernel

  19. Gradient Kernel Density Estimation Give up estimating the PDF ! Estimate ONLYthe gradient Using the Kernel form: We get : Size of window

  20. Computing The Mean Shift Gradient Kernel Density Estimation

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

  22. Mean Shift Mode Detection What happens if we reach a saddle point ? Perturb the mode position and check if we return back • Updated Mean Shift Procedure: • Find all modes using the Simple Mean Shift Procedure • Prune modes by perturbing them (find saddle points and plateaus) • Prune nearby – take highest mode in the window

  23. Mean Shift Properties • Automatic convergence speed – the mean shift vector size depends on the gradient itself. • Near maxima, the steps are small and refined • Convergence is guaranteed for infinitesimal steps only  infinitely convergent, • For Uniform Kernel ( ), convergence is achieved in a finite number of steps • Normal Kernel ( ) exhibits a smooth trajectory, but is slower than Uniform Kernel ( ). Adaptive Gradient Ascent

  24. Real Modality Analysis Tessellate the space with windows Run the procedure in parallel

  25. Real Modality Analysis The blue data points were traversed by the windows towards the mode

  26. Real Modality AnalysisAn example Window tracks signify the steepest ascent directions

  27. Mean Shift Strengths & Weaknesses • Strengths : • Application independent tool • Suitable for real data analysis • Does not assume any prior shape (e.g. elliptical) on data clusters • Can handle arbitrary feature spaces • Only ONE parameter to choose • h (window size) has a physical meaning, unlike K-Means • Weaknesses : • The window size (bandwidth selection) is not trivial • Inappropriate window size can cause modes to be merged, or generate additional “shallow” modes  Use adaptive window size

  28. Mean Shift Applications

  29. Clustering Cluster : All data points in the attraction basin of a mode Attraction basin : the region for which all trajectories lead to the same mode Mean Shift : A robust Approach Toward Feature Space Analysis, by Comaniciu, Meer

  30. ClusteringSynthetic Examples Simple Modal Structures Complex Modal Structures

  31. Feature space: L*u*v representation Initial window centers ClusteringReal Example Modes found Modes after pruning Final clusters

  32. ClusteringReal Example L*u*v space representation

  33. ClusteringReal Example 2D (L*u) space representation Final clusters

  34. Discontinuity Preserving Smoothing Feature space : Joint domain = spatial coordinates + color space Meaning : treat the image as data points in the spatial and gray level domain Image Data (slice) Mean Shift vectors Smoothing result Mean Shift : A robust Approach Toward Feature Space Analysis, by Comaniciu, Meer

  35. z y Discontinuity Preserving Smoothing

  36. The effect of window size in spatial and range spaces Discontinuity Preserving Smoothing

  37. Discontinuity Preserving SmoothingExample

  38. Discontinuity Preserving SmoothingExample

  39. Object Contour DetectionRay Propagation Accurately segment various objects (rounded in nature) in medical images Vessel Detection by Mean Shift Based Ray Propagation, by Tek, Comaniciu, Williams

  40. Object Contour DetectionRay Propagation Use displacement data to guide ray propagation Discontinuity preserving smoothing Displacement vectors Vessel Detection by Mean Shift Based Ray Propagation, by Tek, Comaniciu, Williams

  41. Object Contour DetectionRay Propagation Speed function Normal to the contour Curvature

  42. Gray levels along red line Gray levels after smoothing Object Contour Detection Original image Displacement vectors Displacement vectors’ derivative

  43. Object Contour DetectionExample

  44. Object Contour DetectionExample Importance of smoothing by curvature

  45. Segmentation Segment = Cluster, or Cluster of Clusters • Algorithm: • Run Filtering (discontinuity preserving smoothing) • Cluster the clusters which are closer than window size Image Data (slice) Mean Shift vectors Segmentation result Smoothing result Mean Shift : A robust Approach Toward Feature Space Analysis, by Comaniciu, Meer http://www.caip.rutgers.edu/~comanici

  46. SegmentationExample …when feature space is only gray levels…

  47. SegmentationExample

  48. SegmentationExample

  49. SegmentationExample

  50. SegmentationExample

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