Download presentation

Presentation is loading. Please wait.

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 Signatures Histograms

11
**Distance Metrics - - - = Euclidian distance of 5 units**

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 Nonparametric test statistics**

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 Q m clusters (distance moved) * (amount moved)**

All movements n clusters

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

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 P’ Q Q’ m clusters**

n clusters

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

m clusters P’ Q Q’ n clusters

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

m clusters P’ Q Q’ n clusters

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

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 -

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google