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**Similarity and Difference**

Pete Barnum January 25, 2006 Advanced Perception

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Visual Similarity Color Texture

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**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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Histogram Example Slides from Dave Kauchak

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**Cumulative Histogram Normal Histogram Cumulative Histogram**

Slides from Dave Kauchak

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**Joint vs Marginal Histograms**

Images from Dave Kauchak

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**Joint vs Marginal Histograms**

Images from Dave Kauchak

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Adaptive Binning

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**Clusters (Signatures)**

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**Higher Dimensional Histograms**

Histograms generalize to any number of features Colors Textures Gradient Depth Signatures Histograms

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

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

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Bin-by-bin Bad! Good!

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Cross-bin Bad! Good!

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**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)

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**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

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**More Heuristic Distances**

Weighted-Mean-Variance Only includes minimal information about the distribution Slides from Dave Kauchak

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**Nonparametric Test Statistics**

2 Measures the underlying similarity of two samples Images from Kein Folientitel

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**Nonparametric Test Statistics**

Kolmogorov-Smirnov distance Measures the underlying similarity of two samples Only for 1D data

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**Nonparametric Test Statistics**

Kramer/von Mises Euclidian distance Only for 1D data

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**Information Theory Kullback-Liebler**

Cost of encoding one distribution as another

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**Information Theory Jeffrey divergence**

Just like KL, but more numerically stable

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Ground Distance Histogram intersection Good for partial matches

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Ground Distance Quadratic form Heuristic Images from Kein Folientitel

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Ground Distance Earth Movers Distance Images from Kein Folientitel

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Summary Images from Kein Folientitel

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Moving Earth ≠

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Moving Earth ≠

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Moving Earth =

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The Difference? (amount moved) =

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

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

All movements n clusters

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

n clusters

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

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Linear programming P m clusters Q n clusters

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

n clusters

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

m clusters P’ Q Q’ n clusters

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

m clusters P’ Q Q’ n clusters

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

m clusters P’ Q Q’ n clusters

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**Advantages Uses signatures Nearness measure without quantization**

Partial matching A true metric

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**Disadvantage High computational cost**

Not effective for unsupervised segmentation, etc.

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

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Image Lookup

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**Image Lookup L1 distance Jeffrey divergence χ2 statistics**

Quadratic form distance Earth Mover Distance

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Image Lookup

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Concluding thought - - = it depends on the application -

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