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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Abstract
This paper empirically compares nine image dissimilarity measures that are based on distributions of color and texture features summarizing over 1,000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and via an image partitioning method for texture.
Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measures. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images.
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Goals
compare distribution-based image dissimilarity measures
evaluate dependency on parameter settings
develop generic and statistically sound benchmarking methodology
examine influence in different applications:classification, retrieval, annotation and unsupervised segmentation
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Image Representation
Distributions:– adaptive binning (multivariate histograms)
– marginal histograms
– cumulative marginal histograms
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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Image Representation
dissimilarity measures:
for multivariate (full) distributions
for marginal distributions
• Color: CIELab color space • Texture: Gabor filter responses
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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Heuristic Dissimilarity Measures
• Minkowski-distance
e.g. p = 1 [see 8] (Histogram Intersection), [see 9]
• Weighted-Mean-Variance (WMV)
[see 4]
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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Statistical Dissimilarity Measures
• Kolmogorov-Smirnoff distance (KS)
[see 2]
• Cramer/Von Mises (CvM)
• -statistic
[see 6]
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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Information-Theoretic Measures
• Kullback-Leibler divergence (KL)
[see 5]
• Jeffrey divergence (JD)
[see 6]
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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Ground Distance Measures
• Quadratic Form (QF)via similarity matrix A to incorporate similarities between bins
[see 3]
• Earth Movers Distance (EMD)by solving the transportation problem for the optimal admissible flow gij between the two distributions. dij is the dissimilarity between bins.
[see 7]
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Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Properties
Lp WMV KS/CvM 2 KL JD QF EMD
Symmetrical + + + + - + + +
Triangle inequality + + + - - - + +
Computation Medium Low Medium Medium Medium Medium High High
Ground Distance - - + - - - + +
Multivariate + - - + + + + +
Individual binning - + - - - - - +
Partial Matches - - - - - - - +
Non-Parametric + - + + + + + +
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Methodology
• quality measure: separating into different tasks (classification, retrieval, segmentation)
• parameters: select best possible for every measure by exhaustive evaluation
• evaluate processing steps separately: such as representation, dissimilarity measures, application
• ground truth: collected by sampling given images
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Parameter Settings
• exhaustive search over parameter values:– K nearest neighbors (k = 1, 3, 5, 7)
– sample size: (color: 4, 8, 16, 32, 64 pixels
texture: 82 , 162 , 322 , 642 , 1282 , 2562 pixels)
– number of bins: (4, 8, 16, 32, 64, 128, 256; for EMD only for 4, 8, 16, 32)
– number of Gabor filters: (12, 24, 40)
• quality measures:– classification: K-NN classifier with leave-one-out
– image retrieval: precision vs. number of retrieved images
– unsupervised segmentation: pixel-wise error
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Texture Segmentation
L1 - adaptive JD - adaptive
2 - marginal L1 - marginal JD - marginal KS
original
Unsupervised Grouping by normalized pairwise clustering [6]
.....
Original
Image Representation
Feature Extraction
Grouping by Optimization
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Color Classification
20
40
60
80
100
4 8 16 32 64
Classification Results for Color, Full Histograms, 8 Bins
2
2
L1
L1EMD
QF
L2
0
20
40
60
80
100
4 8 16 32 64
Classification Results for Color, Full Histograms, 256 Bins
L
L
Cla
ssif
icat
ion
Err
or [
%]
EMD
94 images from Corel Database, 16 Samples from each image
Full distributions:
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Color Classification
2
L1
L1
L2
0
20
40
60
80
100
4 8 16 32 64
Classification Results for Color, Marginal Histograms, 8 Bins/dim
CvM
EMD
0
20
40
60
80
100
4 8 16 32 64
Classification Results for Color, Marginal Histograms, 256 Bins/dim
CvM
L
Cla
ssif
icat
ion
Err
or [
%]
Sample size Sample size
KS
WMV
Marginal distributions:
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Texture Classification
10
20
30
40
50
60
8 16 32 64 128 256
Classification Results for Texture, Multivariate Histograms, 8 Bins
JD2
KL
L1
L2
QFEMD
0
10
20
30
40
50
60
8 16 32 64 128 256
Classification Results for Texture, Multivariate Histograms, 256 Bins
JD2
KL
L1
L2
QF
L
Cla
ssif
icat
ion
erro
r [%
]
Sample size
EMD
94 images from Brodatz Album, 16 samples from each image
Full distributions:
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Texture Classification
10
20
30
40
50
60
8 16 32 64 128 256
Classification Results for Texture, Marginal Histograms, 8 Bins
JD2
KL
L1
L2
CvMKS
0
10
20
30
40
50
60
8 16 32 64 128 256
Classification Results for Texture, Marginal Histograms, 256 Bins
JD2
KL
L1
L2
CvM
KS
WMVL
Cla
ssif
icat
ion
erro
r [%
]
Sample size Sample size
Marginal distributions:
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Color Retrieval
20
40
60
80
100
0 20 40 60 80 100
Retrieval Results for Color Images, Sample Size 16
2 Marginals
CvM
WMV
2 Full
EMD FullQF Full
Number of retrieved images
Prec
isio
n
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Results: Texture RetrievalRetrieval Result for Textured Images, Sample Size 8x8
2 Full
2 MarginalEMD Full
QF Full
WMV
L 2 Full
Full
CvM
L
0
10
20
30
40
50
60
0 20 40 60 80 100
Prec
isio
n
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Conclusion
• no overall best measure, but different tools for different tasks
• marginal histograms and aggregate measures good for large feature spaces and small samples
• multivariate histograms effective on large sample sizes and/or well-adapted binning
• EMD attractive for moderate similarities
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
Literature
[1] M.Flickner et al. Query by image and video content: The cubic system. IEEE Computer 1995.
[2] D. Geman et al. Boundary detection by constraint optimization. PAMI 1990.
[3] J. Hafner et al. Efficient color histogram indexing for quadratic form distance function. PAMI 1995.
[4] B. Manjunath and W. Ma. Texture features for browsing and retrieval of image data. PAMI 1996.
[5] T. Ojala et al. A comparative study of texture measures with classification based on feature distributions. Pattern Recognition 1996.
[6] J. Puzicha et al. Non-parametric similarity measures for unsupervised texture segmentation and image retrieval. CVPR 1997.
[7] Y. Rubner et al. A metric for distributions with applications to image databases. ICCV 1998.
[8] M. Swain and D. Ballard. Color indexing. IJCV 1991.
[9] H. Voorhees and T. Poggio. Computing texture boundaries from images. Nature 1988.
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
77
9
11
13
15
17
1 3
L 1 Marginals
L 1 Marginals
L 1 Full
L 1 Full
EMD
EMD
2 Marginals
2 Marginals
2 Full
2 Full
Classification Results for Color Classification Results for Texture
5 7K K
Cla
ssif
icat
ion
erro
r [%
]
5
7
9
11
13
15
1 3
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
L 1 Marginals
EMD
2 Marginals
2 Full
Number of filters
Cla
ssif
icat
ion
erro
r [%
]
6
10
14
18
22
12 24 40
Classification Results for Texture
Computer Vision Group, University of Bonn Vision Laboratory, Stanford University
L inf Marginals
L inf Full
L inf Full
L 1 Full
L 1 Full
EMD
EMD
2 Marginals
2 Marginals
2 Full
2 Full
Classification Results for Color, Sample Size 16 Classification Results for Texture, Sample Size 2562
Number of bins Number of bins
Cla
ssif
icat
ion
erro
r [%
]
0
20
40
60
80
4 8 16 32 64 128 2560
10
20
30
4 8 16 32 64 128 256