Similarity and Difference Pete Barnum January 25, 2006 Advanced Perception

Visual Similarity Color Texture

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?

Histogram Example Slides from Dave Kauchak

Cumulative Histogram Normal Histogram Cumulative Histogram Slides from Dave Kauchak

Joint vs Marginal Histograms Images from Dave Kauchak

Joint vs Marginal Histograms Images from Dave Kauchak

Adaptive Binning

Clusters (Signatures)

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

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

Bin-by-bin Bad! Good!

Cross-bin Bad! Good!

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)

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

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

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

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

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

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

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

Ground Distance Histogram intersection Good for partial matches

Ground Distance Quadratic form Heuristic Images from Kein Folientitel

Ground Distance Earth Movers Distance Images from Kein Folientitel

Summary Images from Kein Folientitel

Moving Earth ≠

Moving Earth ≠

Moving Earth =

The Difference? (amount moved) =

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

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

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

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

Linear programming P m clusters Q n clusters

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

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

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

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

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

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

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

Image Lookup

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

Image Lookup

Concluding thought - - = it depends on the application -