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Similarity and Difference

Similarity and Difference. Pete Barnum January 25, 2006 Advanced Perception. Color. Texture. Visual Similarity. Uses for Visual Similarity Measures. Classification Is it a horse? Image Retrieval Show me pictures of horses. Unsupervised segmentation Which parts of the image are grass?.

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Similarity and Difference

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  1. Similarity and Difference Pete Barnum January 25, 2006 Advanced Perception

  2. Color Texture Visual Similarity

  3. Uses for Visual Similarity Measures • Classification • Is it a horse? • Image Retrieval • Show me pictures of horses. • Unsupervised segmentation • Which parts of the image are grass?

  4. Histogram Example Slides from Dave Kauchak

  5. Cumulative Histogram Normal Histogram Cumulative Histogram Slides from Dave Kauchak

  6. Joint vs Marginal Histograms Images from Dave Kauchak

  7. Joint vs Marginal Histograms Images from Dave Kauchak

  8. Adaptive Binning

  9. Clusters (Signatures)

  10. Higher Dimensional Histograms • Histograms generalize to any number of features • Colors • Textures • Gradient • Depth

  11. Distance Metrics y y - x x = Euclidian distance of 5 units - = Grayvalue distance of 50 values - = ?

  12. Bin-by-bin Bad! Good!

  13. Cross-bin Bad! Good!

  14. Distance Measures • Heuristic • Minkowski-form • Weighted-Mean-Variance (WMV) • Nonparametric test statistics •  2 (Chi Square) • Kolmogorov-Smirnov (KS) • Cramer/von Mises (CvM) • Information-theory divergences • Kullback-Liebler (KL) • Jeffrey-divergence (JD) • Ground distance measures • Histogram intersection • Quadratic form (QF) • Earth Movers Distance (EMD)

  15. Heuristic Histogram Distances • Minkowski-form distance Lp • Special cases: • L1: absolute, cityblock, or Manhattan distance • L2: Euclidian distance • L: Maximum value distance Slides from Dave Kauchak

  16. More Heuristic Distances • Weighted-Mean-Variance • Only includes minimal information about the distribution Slides from Dave Kauchak

  17. Nonparametric Test Statistics • 2 • Measures the underlying similarity of two samples Images from Kein Folientitel

  18. Nonparametric Test Statistics • Kolmogorov-Smirnov distance • Measures the underlying similarity of two samples • Only for 1D data

  19. Nonparametric Test Statistics • Kramer/von Mises • Euclidian distance • Only for 1D data

  20. Information Theory • Kullback-Liebler • Cost of encoding one distribution as another

  21. Information Theory • Jeffrey divergence • Just like KL, but more numerically stable

  22. Ground Distance • Histogram intersection • Good for partial matches

  23. Ground Distance • Quadratic form • Heuristic Images from Kein Folientitel

  24. Ground Distance • Earth Movers Distance Images from Kein Folientitel

  25. Summary Images from Kein Folientitel

  26. Moving Earth ≠

  27. Moving Earth ≠

  28. Moving Earth =

  29. The Difference? (amount moved) =

  30. The Difference? (amount moved) * (distance moved) =

  31. Linear programming P m clusters (distance moved) * (amount moved) Q All movements n clusters

  32. Linear programming P m clusters (distance moved) * (amount moved) Q n clusters

  33. Linear programming P m clusters * (amount moved) Q n clusters

  34. Linear programming P m clusters Q n clusters

  35. Constraints 1. Move “earth” only from P to Q P m clusters P’ Q Q’ n clusters

  36. Constraints 2. Cannot send more “earth” than there is P m clusters P’ Q Q’ n clusters

  37. Constraints 3. Q cannot receive more “earth” than it can hold P m clusters P’ Q Q’ n clusters

  38. Constraints 4. As much “earth” as possible must be moved P m clusters P’ Q Q’ n clusters

  39. Advantages • Uses signatures • Nearness measure without quantization • Partial matching • A true metric

  40. Disadvantage • High computational cost • Not effective for unsupervised segmentation, etc.

  41. Examples • Using • Color (CIE Lab) • Color + XY • Texture (Gabor filter bank)

  42. Image Lookup

  43. Image Lookup L1 distance Jeffrey divergence χ2 statistics Quadratic form distance Earth Mover Distance

  44. Image Lookup

  45. Concluding thought - - = it depends on the application -

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