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
Distance Metrics
x
y
x
y
-
-
-
= Euclidian distance of 5 units
= Grayvalue distance of 50 values
= ?
Bin-by-bin
Good!
Bad!
Cross-bin
Good!
Bad!
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)
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
More Heuristic Distances
r
rr
r
r JIJIJID rr
),(
Slides from Dave Kauchak
Weighted-Mean-Variance Only includes minimal information about
the distribution
Nonparametric Test Statistics
2
Measures the underlying similarity of two samples
2/;;ˆ,
ˆ
ˆ;,
2
JifIififif
ifIifJID
i
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
JIt
JIJID ffAff,
Images from Kein Folientitel
Ground Distance
Earth Movers Distance
Images from Kein Folientitel
jiij
jiijij
g
dg
JID
,
,,
Summary
Images from Kein Folientitel
Moving Earth
≠
Moving Earth
≠
Moving Earth
=
The Difference?
=
(amount moved)
The Difference?
=
(amount moved) * (distance moved)
Linear programming
m clusters
n clusters
P
Q All movements
(distance moved) * (amount moved)
Linear programming
m clusters
n clusters
P
Q
(distance moved) * (amount moved)
Linear programming
m clusters
n clusters
P
Q
* (amount moved)
Linear programming
m clusters
n clusters
P
Q
Constraints
m clusters
n clusters
P
Q
1. Move “earth” only from P to Q
P’
Q’
Constraints
m clusters
n clusters
P
Q
2. Cannot send more “earth” than there is
P’
Q’
Constraints
m clusters
n clusters
P
Q
3. Q cannot receive more “earth” than it can hold
P’
Q’
Constraints
m clusters
n clusters
P
Q
4. As much “earth” as possible must be moved
P’
Q’
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 LookupL1 distance
Jeffrey divergence
χ2 statistics
Quadratic form distance
Earth Mover Distance
Image Lookup
Concluding thought
-
-
-
= it depends on the application
