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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.
    Sethi   Undergraduate Computer Research Program,
    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,
    instead of randomly chosen.
  • 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
    Computer Science Advances in Pattern
    Recognition, ICAPR, 2001, Springer-Verlag Ltd.
    (ed.), pg. 377-388, 2001.
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