Similarity and Difference
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Transcript of Similarity and Difference
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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 Lp
Special cases: L1: absolute, cityblock, or
Manhattan distance L2: Euclidian distance L: Maximum value distance
p
i
pJifIifJID
/1
),(),(),(
Slides from Dave Kauchak
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More Heuristic Distances
r
rr
r
r JIJIJID rr
),(
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
2/;;ˆ,
ˆ
ˆ;,
2
JifIififif
ifIifJID
i
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
JIt
JIJID ffAff,
Images from Kein Folientitel
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Ground Distance
Earth Movers Distance
Images from Kein Folientitel
jiij
jiijij
g
dg
JID
,
,,
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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
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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Image LookupL1 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