empirical evaluation of dissimilarity measures for color and texture presented by: dave kauchak...
TRANSCRIPT
Empirical Evaluation of Dissimilarity Measures for Color
and Texture
Presented by:
Dave Kauchak
Department of Computer Science
University of California, San Diego
Jan Puzicha, Joachim M. Buhmann, Yossi Rubner & Carlo Tomasi
The Problem: Image Dissimilarity
D( ) = ?,
Where does this problem arise in computer vision?
Image Classification Image Retrieval Image Segmentation
Classification
?
?
?
Retrieval
Jeremy S. De Bonet, Paul Viola (1997). Structure Driven Image Database Retrieval. Neural Information Processing 10 (1997).
Segmentation
http://vizlab.rutgers.edu/~comanici/segm_images.html
Histograms 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.
Histogram Example
Histogramming Image Features
Color Texture Shape Others… Create histogram through binning or some
procedure to get a distribution
Color
Which is more similar?
L*a*b* was designed to be uniform in that perceptual “closeness” corresponds to Euclidean distance in the space.
L*a*b*
L – lightness (white to black)
a – red-greeness
b – yellowness-blueness
Texture
Texture is not pointwise like color
Texture involves a local neighborhood
Gabor Filters are commonly used to identify texture features
Gabor 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)
Examples of Gabor Filters
Scale: 4 at 108° Scale: 5 at 144°Scale: 3 at 72°
Creating 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)
Marginal Histograms
Marginal histograms only deal with a single feature
Normal Binning
Marginal binning resulting in 2 histograms
Cumulative Histogram
Normal Histogram
Cumulative Histogram
Dissimilarity Measure Using the Histograms
Heuristic Histogram Distances Non-parametric Test Statistics Information-Theoretic diverges Ground distance measures
Notation
D(I,J) is the dissimilarity of images I and J f(i;J) is histogram entry i in histogram of image
J fr(i;J) is marginal histogram entry i of image J Fr(i;J) is the cumulative histogram
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
),(),(),(
More heuristic distances
Weighted-Mean-Variance (WMV)
– Only includes minimal information about distribution
r
rr
r
r JIJIJID rr
),(
Non-parametric Test Statistics
Kolmogorov-Smirnov distance (K-S)
);();(max),( JiFIiFJID rrr
Cramer/von Mises type (CvM)
i
rrr JiFIiFJID 2));();((),(
Cumulative Difference Example
Histogram 1 Histogram 2 Difference
- =
K-S = CvM =
Non-parametric Test Statistics (cont.)
2-statistic (chi-square)– Simple statistical measure to decide if two samples
came from the same underlying distribution
i JifIif
JifIifJID
);();(
);();(),(
2
Information-Theoretic diverges
How well can one distribution be coded using the other as a codebook?
Kullback-Leibler divergence (KL)
Jeffrey-divergence (JD)
i Jif
IifIifJID
);(
);(log);(),(
i if
JifJif
if
IifIifJID
)('
);(log);(
)('
);(log);(),(
Ground 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
EMD
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
Transportation 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
Various 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
Key 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
Data 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
Data 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
Setup: 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
Setup: 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
Results: Classification, color data set
Results: Classification, texture data set
Results: 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
Results: 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
Setup: 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
Results: Image Retrieval
Results: 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
Setup: Segmentation
100 images Each image consists of 5 different Brodatz textures For multivariate, the bins are adapted to specific image
Setup: 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
Results: Segmentation
Results: 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%
Results: 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
Conclusions
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