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Empirical 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@cs.ucsd.edu. The Problem: Image Dissimilarity. D(.

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empirical evaluation of dissimilarity measures for color and texture

Empirical 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


where does this problem arise in computer vision
Where does this problem arise in computer vision?
  • Image Classification
  • Image Retrieval
  • Image Segmentation

Jeremy S. De Bonet, Paul Viola (1997). Structure Driven Image Database Retrieval. Neural Information Processing 10 (1997).



histograms for image dissimilarity
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.
histogramming image features
Histogramming Image Features
  • Color
  • Texture
  • Shape
  • Others…
  • Create histogram through binning or some procedure to get a distribution

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 is not pointwise like color
  • Texture involves a local neighborhood
  • Gabor Filters are commonly used to identify texture features
gabor filters
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
Examples of Gabor Filters

Scale: 3 at 72°

Scale: 4 at 108°

Scale: 5 at 144°

creating histograms from features
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

Marginal histograms only deal with a single feature

Normal Binning

Marginal binning resulting in 2 histograms

cumulative histogram
Cumulative Histogram

Normal Histogram

Cumulative Histogram

dissimilarity measure using the histograms
Dissimilarity Measure Using the Histograms
  • Heuristic Histogram Distances
  • Non-parametric Test Statistics
  • Information-Theoretic diverges
  • Ground distance measures
  • 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
Heuristic Histogram Distances
  • Minkowski-form distance Lp
  • Special cases:
    • L1: absolute, cityblock, or Manhattan distance
    • L2: Euclidian distance
    • L: Maximum value distance
more heuristic distances
More heuristic distances
  • Weighted-Mean-Variance (WMV)
    • Only includes minimal information about distribution
non parametric test statistics
Non-parametric Test Statistics
  • Kolmogorov-Smirnov distance (K-S)
  • Cramer/von Mises type (CvM)
cumulative difference example

Histogram 1

Histogram 2




CvM =

K-S =

Cumulative Difference Example
non parametric test statistics cont
Non-parametric Test Statistics (cont.)
  • 2-statistic (chi-square)
    • Simple statistical measure to decide if two samples came from the same underlying distribution
information theoretic diverges
Information-Theoretic diverges
  • How well can one distribution be coded using the other as a codebook?
  • Kullback-Leibler divergence (KL)
  • Jeffrey-divergence (JD)
ground distance measure
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
  • 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
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
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
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
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
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
Setup: Classification
  • k-Nearest Neighbor classifier is used
    • Nearest Neighbor classification: given a collection of labeled points S and a query point q, what pointbelonging 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
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
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
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
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 cont
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
Setup: Segmentation
  • 100 images
  • Each image consists of 5 different Brodatz textures
  • For multivariate, the bins are adapted to specific image
setup segmentation cont
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 cont46
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
  • 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