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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

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

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Bin-by-bin Good! Bad!

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Cross-bin Good! Bad!

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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)

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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

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

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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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≠

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=

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The Difference? = (amount moved)

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

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

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

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

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Linear programming m clusters n clusters P Q

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

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

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

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

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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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L1 distance Jeffrey divergence χ 2 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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