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Pathfinder Networks for Computer Assisted Image Browsing

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Title: Pathfinder Networks for Computer Assisted Image Browsing


1
Pathfinder Networks for Computer Assisted Image
Browsing
  • Rishi Mukhopadhyay, Aiyesha Ma
  • and Ishwar K. Sethi 
  • Intelligent Information Engineering
    LaboratoryDepartment of Computer Science and
    EngineeringOakland University

2
Introduction
  • Recently, the amount of multimedia data available
    to users has exploded
  • Hand-annotations of existing databases is
    intractable
  • New methods for searching these databases in a
    semantically meaningful way are needed

3
Pathfinder Networks
  • Invented by Schvaneveldt, 1981
  • Given a similarity (distance) matrix between
    objects or concepts, it assembles a graph
  • This graph has the property that given a value of
    q, the network obeys the triangle inequality
    (w(a,b)ltw(a,c)w(c,b)) within q edges from every
    given node.

4
Pathfinder Networks
  • The distance between nodes is determined by the
    Minkowski metric which takes a value,
    0ltrltinfinity, as a parameter
  • In many applications, this process has been shown
    to preserve the semantically meaningful links.

5
r1, q2
6
r1, q12
7
r1, q24
8
r2, q24
9
r2, qinfinity
10
Distance Between Images
  • In order to use the pathfinder approach to
    organizing images, we would first have to
    generate a distance matrix between the images.
  • This approach should be automated so as that it
    is tractable to apply this method to large
    databases.
  • Cooccurrence matrix of local features

11
Cooccurrence Matrices
  • Given an image, and a local feature detector
    system, we can decompose it into a matrix of
    indices to a codebook of features

12
Cooccurrence Matrices
  • Once we have the images decomposed into feature
    matrices, we can calculate the cooccurrence
    matrix of each feature matrix.
  • In a coocurrence matrix, M, of radius r for a
    given feature matrix, entry M(i,j) is the number
    of times feature j occurred within a distance of
    r from each instance of feature i.

13
Cooccurrence Matrices
Feature matrix
Original image
Cooccurrence matrix
14
Cooccurrence Matrices
  • Cooccurrence matrices retain a lot of the
    structural information about the spatial
    organization of the features while being
    moderately robust to transformations.
  • Once we calculate the cooccurrence matrix for
    each image, we can use a euclidean or weighted
    euclidean distance to calculate a distance
    between the images for use by the pathfinder
    network.

15
Automated Local Feature Extraction
  • There are many current techniques for automated
    and semi-automated feature extraction.
  • We focused on local shape features since most of
    the work in the literature focuses on color or
    texture information.
  • Clustering 5 by 5 and 7 by 7 pixel blocks from
    the edge-analysis of the images in the database
    to automatically generate local features.

16
Clustering
  • Given a dataset, divide the set into subsets that
    are near eachother.
  • Need a definition of near
  • Used K-means clustering algorithm with clustroid
    averaging.
  • Used cluster centers as the feature codebook.

17
Data Sets
18
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

19
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

20
Distance Measures
  • Hausdorff metric of distance between sets of
    points
  • The Manhattan distance was selected for .

21
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.

22
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

23
Distance Measures
  • Now consider the following noisy images
  • Which results in distances of

24
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

25
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.

26
Results
  • The following are the results for pathfinder
    networks using q74, rinfinity
  • I used 5 by 5 blocks and tested the effects of
    varying the cooccurrence radius between 3, 4, and
    5.

27
Cooccurrence radius 3
28
Cooccurrence radius 4
29
Cooccurrence radius 5
30
Current/future work
  • Presently we are revisiting our vector
    quantization technique
  • Rather than modify the metric to mitigate the
    effects of translation, we are aligning the
    images based on their centroids and then using
    the standard Hausdorff metric
  • This has the benefit of being able to be scaled
    to larger sized blocks that tend to contain
    multiple line segments.

31
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. Gersho, On The Structure of Vector
    Quantizers, IEEE Trans. On Information Theory,
    pp. 157-166, Vol. IT-28, No. 2, Mar. 1982.
  • 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 P. Franti and T. Kaukoranta, Binary Vector
    Quantizer Design Using Soft Centroids, Signal
    Processing Image Communication, 14(1999),
    677-681.
  • 5 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.
  • 6 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.
  • 7 L. Zhu, A. Rao, and A. Zhang,Advanced
    Feature Extraction for Keyblock-Based Image
    Retrieval, pp. 179-182, ACM Multimedia Workshop,
    2000.
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