# Similarity and Difference

## Presentation on theme: "Similarity and Difference"— Presentation transcript:

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

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 - = ?

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

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 -