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

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Presentation on theme: "Similarity and Difference Pete Barnum January 25, 2006 Advanced Perception."— Presentation transcript:

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

2 Visual Similarity Color Texture

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 x y x y = Euclidian distance of 5 units = Grayvalue distance of 50 values = ?

12 Bin-by-bin Good! Bad!

13 Cross-bin Good! Bad!

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 L p Special cases:  L 1 : absolute, cityblock, or Manhattan distance  L 2 : Euclidian distance  L  : Maximum value distance Slides from Dave Kauchak

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

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

28 =

29 The Difference? = (amount moved)

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

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

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

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

34 Linear programming m clusters n clusters P Q

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

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

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

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

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 L1 distance Jeffrey divergence χ 2 statistics Quadratic form distance Earth Mover Distance

44 Image Lookup

45 Concluding thought = it depends on the application


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