Empirical Evaluation of Dissimilarity Measures for Color and Texture

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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_at_cs.ucsd.edu
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The Problem Image Dissimilarity
D(
) ?
,
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Where does this problem arise in computer vision?

• Image Classification
• Image Retrieval
• Image Segmentation

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Classification
?
?
?
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Retrieval
Jeremy S. De Bonet, Paul Viola (1997). Structure
Driven Image Database Retrieval. Neural
Information Processing 10 (1997).
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Segmentation
http//vizlab.rutgers.edu/comanici/segm_images.ht
ml
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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.

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Histogram Example
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Histogramming Image Features

• Color
• Texture
• Shape
• Others
• Create histogram through binning or some
  procedure to get a distribution

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Color
Which is more similar?
Lab was designed to be uniform in that
perceptual closeness corresponds to Euclidean
distance in the space.
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Lab
L lightness (white to black) a red-greeness b
yellowness-blueness
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Texture

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

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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)

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Examples of Gabor Filters
Scale 4 at 108
Scale 5 at 144
Scale 3 at 72
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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)

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Marginal Histograms

• Marginal histograms only deal with a single
  feature

Normal Binning
Marginal binning resulting in 2 histograms
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Cumulative Histogram
Normal Histogram
Cumulative Histogram
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Dissimilarity Measure Using the Histograms

• Heuristic Histogram Distances
• Non-parametric Test Statistics
• Information-Theoretic diverges
• Ground distance measures

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Notation

• 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

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Heuristic Histogram Distances

• Minkowski-form distance Lp
• Special cases
• L1 absolute, cityblock, or Manhattan distance
• L2 Euclidian distance
• L? Maximum value distance

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More heuristic distances

• Weighted-Mean-Variance (WMV)
• Only includes minimal information about
  distribution

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Non-parametric Test Statistics

• Kolmogorov-Smirnov distance (K-S)

• Cramer/von Mises type (CvM)

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Cumulative Difference Example
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Non-parametric Test Statistics (cont.)

• ?2-statistic (chi-square)
• Simple statistical measure to decide if two
  samples came from the same underlying distribution

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Information-Theoretic diverges

• How well can one distribution be coded using the
  other as a codebook?
• Kullback-Leibler divergence (KL)

• Jeffrey-divergence (JD)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Results Classification, color data set
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Results Classification, texture data set
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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

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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

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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

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Results Image Retrieval
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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

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Setup Segmentation

• 100 images
• Each image consists of 5 different Brodatz
  textures
• For multivariate, the bins are adapted to
  specific image

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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

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Results Segmentation
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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
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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

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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