Title: Empirical Evaluation of Dissimilarity Measures for Color and Texture
1Empirical Evaluation of Dissimilarity Measures
for Color and Texture
Jan Puzicha, Joachim M. Buhmann, Yossi Rubner
Carlo Tomasi
Presented by Dave Kauchak Department of Computer
Science University of California, San
Diego dkauchak_at_cs.ucsd.edu
2The Problem Image Dissimilarity
D(
) ?
,
3Where does this problem arise in computer vision?
- Image Classification
- Image Retrieval
- Image Segmentation
4Classification
?
?
?
5Retrieval
Jeremy S. De Bonet, Paul Viola (1997). Structure
Driven Image Database Retrieval. Neural
Information Processing 10 (1997).
6Segmentation
http//vizlab.rutgers.edu/comanici/segm_images.ht
ml
7Histograms for image dissimilarity
- Examine the distribution of features, rather than
the features themselves - General purpose (i.e. any distribution of
features) - Resilient to variations (shadowing, changes in
illumination, shading, etc.) - Can use previous work in statistics, etc.
8Histogram Example
9Histogramming Image Features
- Color
- Texture
- Shape
- Others
- Create histogram through binning or some
procedure to get a distribution
10Color
Which is more similar?
Lab was designed to be uniform in that
perceptual closeness corresponds to Euclidean
distance in the space.
11Lab
L lightness (white to black) a red-greeness b
yellowness-blueness
12Texture
- Texture is not pointwise like color
- Texture involves a local neighborhood
- Gabor Filters are commonly used to identify
texture features
13Gabor Filters
- Gabor filters are Gaussians modulated by
sinusoids - They can be tuned in both the scale (size) and
the orientation - A filter is applied to a region and is
characterized by some feature of the energy
distribution (often mean and standard deviation)
14Examples of Gabor Filters
Scale 4 at 108
Scale 5 at 144
Scale 3 at 72
15Creating Histograms from Features
- Regular Binning
- Simple
- Choosing bins important. Bins may be too large
or too small - Adaptive Binning
- Bins are adapted to the distribution (usually
using some form of K-means)
16Marginal Histograms
- Marginal histograms only deal with a single
feature
Normal Binning
Marginal binning resulting in 2 histograms
17Cumulative Histogram
Normal Histogram
Cumulative Histogram
18Dissimilarity Measure Using the Histograms
- Heuristic Histogram Distances
- Non-parametric Test Statistics
- Information-Theoretic diverges
- Ground distance measures
19Notation
- D(I,J) is the dissimilarity of images I and J
- f(iJ) is histogram entry i in histogram of image
J - fr(iJ) is marginal histogram entry i of image J
- Fr(iJ) is the cumulative histogram
20Heuristic Histogram Distances
- Minkowski-form distance Lp
- Special cases
- L1 absolute, cityblock, or Manhattan distance
- L2 Euclidian distance
- L? Maximum value distance
21More heuristic distances
- Weighted-Mean-Variance (WMV)
- Only includes minimal information about
distribution
22Non-parametric Test Statistics
- Kolmogorov-Smirnov distance (K-S)
- Cramer/von Mises type (CvM)
23Cumulative Difference Example
24Non-parametric Test Statistics (cont.)
- ?2-statistic (chi-square)
- Simple statistical measure to decide if two
samples came from the same underlying distribution
25Information-Theoretic diverges
- How well can one distribution be coded using the
other as a codebook? - Kullback-Leibler divergence (KL)
26Ground Distance Measure
- Based on some metric of distance between
individual features - Earth Movers Distance (EMD)
- Minimal cost to transform one distribution to the
other - Only measure that works on distributions with a
different number of bins
27EMD
- One distribution can be seen as a mass of earth
properly spread in space, the other as a
collection of holes in that same space - Distributions are represented as a set of
clusters and an associated weight - Computing the dissimilarity then becomes the
transportation problem
28Transportation Problem
- Some number of suppliers with goods
- Some other number of consumers wanting goods
- Each consumer-supplier pair has an associated
cost to deliver one unit of the goods - Find least expensive flow of goods from supplier
to consumer
29Various properties of the metrics
- K-S, CvM and WMV are only defined for marginal
distributions - Lp, WMV, K-S, CvM and, under constraints, EMD all
obey the triangle inequality - WMV is particularly quick because the calculation
is quick and the values can be pre-computed
offline - EMD is the most computationally expensive
30Key Components for Good Comparison
- Meaningful quality measure
- Subdivision into various tasks/applications
(classification, retrieval and segmentation) - Wide range of parameters should be measured
- An uncontroversial ground truth should be
established
31Data Set Color
- Randomly chose 94 images from set of 2000
- 94 images represent separate classes
- Randomly select disjoint set of pixels from the
images - Set size of 4, 8, 16, 32, 64 pixels
- 16 disjoint samples per set per image
32Data Set Texture
- Brodatz album
- Collection of wide range of texture (e.g. cork,
lawn, straw, pebbles, sand, etc.) - Each image is considered a class (as in color)
- Extract sets of 16 non-overlapping blocks
- sizes 8x8, 16x16,, 256x256
33Setup Classification
- k-Nearest Neighbor classifier is used
- Nearest Neighbor classification given a
collection of labeled points S and a query point
q, what point belonging to S is closest to q? - k nearest is a majority vote of the k closest
points - k 1, 3, 5 and 7
- Average misclassification rate percentage using
leave-one-out
34Setup Classification (cont.)
- Bins 4, 8, 16, 32, 64, 128, 256
- Texture case, three sets of filters were used of
sizes 12, 24 and 40 filters - 1000 CPU hours of computation
35Results Classification, color data set
36Results Classification, texture data set
37Results Classification
- For small sample sizes, the WMV measure performs
best in the texture case. - WMV only estimates means and variances
- Less sensitive to sampling noise
- EMD also performs well for small sample sizes
- Local binning provides additional information
- For large sample sizes ?2 test performs best
38Results Classification (cont.)
- For texture classification, marginal
distributions do better than multidimensional
distributions except for very large sample sizes
(256x256) - Binning is not well adapted to the data since it
is fixed for all the 94 classes - EMD, which uses local adaption does much better
- For multidimensional histograms, the more bins
the better the performance - For texture, usually 12 filters is enough
39Setup Image Retrieval
- Vary sample size
- Vary number of images retrieved
- Performance measured based on precision (i.e.
percent correct of the images retrieved) vs. the
number of images retrieved
40Results Image Retrieval
41Results Image Retrieval (cont.)
- Similar to classification
- EMD, WMV, CvM and K-S performed well for small
sample sizes - JD, ?2 and KL perform better for larger sizes
42Setup Segmentation
- 100 images
- Each image consists of 5 different Brodatz
textures - For multivariate, the bins are adapted to
specific image
43Setup Segmentation (cont.)
- Image is divided into 16384 sites (128 x 128
grid) - A histogram is calculate for each site
- Each site histogram is then compared with 80
randomly selected sites - Image sites with high average similarity are then
grouped
44Results Segmentation
45Results Segmentation (cont.)
Median 20 Quantile
L1 marginal 8.2 12
?2 marginal 8.1 13
JD marginal 8.1 12
KS marginal 10.8 20
CvM marginal 10.9 22
L1 full 6.8 9
?2 full 6.6 10
JD full 6.8 10
46Results Segmentation (cont.)
- Binning can be adapted to image
- Increased accuracy in representing
multidimensional distributions - Adaptive multivariate outperforms marginal
- Best results were obtained by ?2
- EMD suffers from high computational complexity
47Conclusions
- No measure is overall best
- Marginal histograms and aggregate measures are
best for large feature spaces - Multivariate histograms perform well with large
sample sizes - EMD performs generally well for both
classification and retrieval, but with a high
computational cost - ?2 is a good overall metric (particularly for
larger sample sizes