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## Perceptual Vector Quantization of Binary Image Blocks for Pattern Analysis

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### Aiyesha Ma, Rishi Mukhopadhyay, and Ishwar K. Sethi ... [10] D. Stan and I. K. Sethi, 'Image Retrieval Using a Hierarchy of Clusters, ... – PowerPoint PPT presentation

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Title: Perceptual Vector Quantization of Binary Image Blocks for Pattern Analysis

1
Perceptual Vector Quantization of Binary Image
Blocks for Pattern Analysis
• Aiyesha Ma, Rishi Mukhopadhyay, and Ishwar K.
REU
• Intelligent Information Engineering
Laboratory Department of Computer Science and
Engineering Oakland University

2
Introduction
• Most Vector Quantization techniques have been
developed for compression.
• Previous VQ methods employ Euclidean metrics for
distance measures and averaging.
• These measures are unsuitable for the extraction
of descriptors where invariance to translation,
rotation, and scale is important.
• We focused on developing local descriptors
invariant to translation.

3
Introduction
• We present a vector quantization method that is
based on the Hausdorff metric of distance between
sets of points.
• The goal of our method is to cluster image blocks
containing line segments with similar shapes
together.

4
Data Sets
5
Clustering
• We used the K-means approach to clustering.
• K-means is of order n complexity, where n is the
size of the set of data being clustered.
• K-means algorithm
• Begin with an initial set of cluster means.
• Every element in the set is assigned to the
nearest cluster center.
• The center of each cluster is re-averaged based
on its constituents.
• The process of reassignment and re-averaging
repeats for some predefined number of iterations
or until the number of reassignments falls below
some threshold.

6
Distance Measures
• In VQ, the Euclidean or Mean Squared Error
distance is a popular distance metric.
• The Euclidean metric is inappropriate for
categorizing descriptors.
• Consider the following 7-by-7 image blocks with
their perceptual classifications

7
Distance Measures
• To group these images perceptually, the distance
between the two diagonal lines should be less
than the distance from either diagonal line to
either vertical line.
• The Mean Square Error distance measure
• In the case of binary images is equivalent to the
Hamming distance
• Results

8
Distance Measures
• Hausdorff metric of distance between sets of
points
• The Manhattan distance was selected for .

9
Distance Measures
• The Hausdorff metric results in
• a distance of 5 from image D1 to image V1
• a distance of 4 from image D1 to image D2
• a distance of 4 from image V1 to image V2 because
of translation
• a distance of 4 from image V2 to image D2.

10
Distance Measures
• Since, in cases of translation, all the nearest
neighbor distances are increased by the same
amount, we modify the Hausdorff distance to
• Results

11
Distance Measures
• Now consider the following noisy images
• Which results in distances of

12
Distance Measures
• So instead of taking the maximum and subtracting
the minimum, we take a percentile
• Then to mitigate the effects of asymmetry
inherent in the Hausdorff metric, we sum the
distance from A to B with the distance from B to
A

13
Distance Measures
• Yields the following result for the noisy images
• This modified Hausdorff measure yields a distance
measure invariant to translation.
• Although not impervious to noise, this measure is
still moderately robust.

14
Averaging Methods
• Previous methods for averaging binary images
include soft-centroids and hard centroids.
• These methods produce codewords that are an
accurate reflection of pixel distribution.
• They lack the ability to produce codewords that
represent the shape a set of pixels form.
• Consider the following images

15
Averaging Methods
• The ideal codeword
• Soft and hard centroid codewords

16
Averaging Methods
• Another averaging method is to take the Clustroid
as the codeword.
• Using our modified Hausdorff measure, the
Clustroid method results in the following
codeword
• We present a new averaging method based on the
Hausdorff mapping concept of the nearest neighbor
point.

17
Averaging Methods
• Given a set, , of binary images (where
each is a binary image and i ranges from 1 to
m, the number of images in the cluster) and the
set of points, , in the key-block (where
each is a coordinate pair representing one
of the black points in the key-block), then the
new average is defined as , where each new
coordinate pair
• and where is a function that
returns the coordinate of the nearest neighbor
point in image C relative to point P.

18
Averaging Methods
19
Averaging Methods
• Significant improvement over the Euclidean based
methods.
• Performs at least as well as the Clustroid method.

20
Data Sets
• 5-by-5, 7-by-7, 9-by-9 blocks
• Codebook size of 16 and 8, with one codeword
designated as a blank block.
• Clustroid method and HBA methods one and two with
the modified Hausdorff distance measure.
• Hard and Soft centroids, with Euclidean distance.
• 5-by-5 blocks with preset initial clusters,
• 5-by-5 and 7-by-7 blocks enlarged by a factor of
two.

21
Cluster Separation
• The ratio between the average inter-cluster
distance (codeword to codeword) and the average
intra-cluster distance (cluster member to
codeword) for each data set was calculated.
• This ratio is an indicator of the degree of
separation of the clusters from each other.
• A ratio greater than one indicates that the
codewords are more separated from each other than
they are from the blocks they represent.

22
Cluster Separation
16 Codewords
23
Cluster Separation
8 Codewords
24
Cluster Separation
5-by-5 blocks, preset initial codewords
25
Visual Comparison of Methods
Two clusters from 5-by-5 blocks with 8 means,
HBA method 1, without enlargement.
Two clusters from 5-by-5 blocks with 8 means,
HBA method 1, with enlargement.
26
Visual Comparison of Methods
Two clusters from 5-by-5 blocks with 8 means,
Clustroid method, with enlargement.
27
Visual Comparison of Methods
Four clusters from 5-by-5 blocks with 8 means,
Hard centroid method.
Three clusters from 5-by-5 blocks with 8 means,
Soft centroid method.
28
Visual Comparison of Methods
5-by-5 blocks with 8 means, Hard centroid
method.
5-by-5 blocks with 8 means, Soft centroid
method.
29
Visual Comparison of Methods
5-by-5 blocks without enlargement, 8 means, HBA
1 method.
5-by-5 blocks with enlargement, 8 means, HBA 1
method.
30
Visual Comparison of Methods
5-by-5 blocks without enlargement, 8 means,
Clustroid method.
5-by-5 blocks with enlargement, 8 means,
Clustroid method.
31
Computational Complexity
• The assignment portion of each cycle in the
k-means algorithm is of order
• where b is the total number of blocks, k is the
number of clusters and where each block is n
pixels by n pixels.
• The averaging portion of each cycle for both HBA
methods is of order
• For the Clustroid algorithm, the averaging
portion of the cycle takes order
• where is the number of members in the ith
cluster.

32
Using Perceptual Descriptors
• Represent the original images as matrices of
indices to the generated codebook.
• Two approaches for grouping the representative
images
• Co-occurrence matrices
• Frequency histograms
• The co-occurrence matrix approach successfully
separated 6 images into two groups.

33
Using Perceptual Descriptors
• Taking blocks from the representative image
matrix and clustering them can be used to build a
hierarchy of relationships.
• Using the frequency histogram approach on a
second level representation of 6 images the
images were accurately separated into two groups.

34
Conclusion
• Presented a method for obtaining perceptually
meaningful descriptors for use in pattern
analysis.
• These methods appear to be better suited than
previously established methods for obtaining
descriptors.
• Initial progress using these descriptors seems
promising.

35
References
• 1 N.M. Nasrabadi and R.A. King, Image Coding
Using Vector Quantization A Review, IEEE Trans.
Commun., pp. 957-971, Vol. 36, No. 8, Aug. 1988.
• 2 A.K. Jain, M.N. Murty, and P.J. Flynn, Data
Clustering A Review, ACM Computing Surveys,
Vol. 31, No. 3, Sept. 1999.
• 3 Y. Linde, A. Buzo, and R.M. Gray, An
Algorithm for Vector Quantizer Design, IEEE
Trans. Communications, pp. 84-95, Vol. COM-28,
No. 1, Jan. 1980
• 4 S.P. Lloyd, Least Squares Quantization in
PCM, IEEE Trans. On Information Theory, pp.
129-137, Vol. IT-28, No. 2, Mar. 1982.
• 5 A. Gersho, On The Structure of Vector
Quantizers, IEEE Trans. On Information Theory,
pp. 157-166, Vol. IT-28, No. 2, Mar. 1982.
• 6 P. Franti and T. Kaukoranta, Binary Vector
Quantizer Design Using Soft Centroids, Signal
Processing Image Communication, 14(1999),
677-681.

36
References
• 7 D.P. Huttenlocher, G.A. Klanderman, and W.J.
Rucklidge, Comparing Images Using the Hausdorff
Distance, IEEE Trans. On Pattern Analysis and
Machine Intelligence, pp 850-863, Vol. 15, No. 9,
Sept. 1993.
• 8 Q. Iqbal and J.K. Aggarwal, Applying
Perceptual Grouping to Content-Based Image
Retrieval Building Images, Proceedings of the
IEEE International Conference on Computer Vision
and Pattern Recognition, June 23-26, 1999, pp.
42-48.
• 9 L. Zhu, A. Rao, and A. Zhang,Advanced
Feature Extraction for Keyblock-Based Image
Retrieval, pp. 179-182, ACM Multimedia Workshop,
2000.
• 10 D. Stan and I. K. Sethi, Image Retrieval
Using a Hierarchy of Clusters, Lecture Notes in