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.