Texture Classification Using Wavelets

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Texture ClassificationUsing Wavelets

• Lindsay Semler

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Research Goal
To investigate the use of the Haar wavelet
in the texture classification of human organs in
CT scans.
Organ/Tissue segmentation in CT images
Wavelet Coefficients
Classification rules for tissue/organs in CT
images
Decision Trees
Texture Descriptors
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Step 1 Segmentation and Cropping
cropping
segmentation
Segmented Heart Slice
Data 340 Dicom Images
Active Contour Mapping (Snakes) a boundary
based segmentation algorithm
The image must be cropped, since wavelets are
extremely sensitive to areas of high contrast
(background)
Organs Backbone Heart Liver Kidney Spleen
Segmented 140 50 56 55 39
Cropped 665 103 122 183 55
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Step 2 Texture Analysis and Classification
Texture Descriptors Mean, Standard Deviation,
Energy, Entropy, Contrast, Homogeniety, Variance,
Maximum Probability, Inverse Difference Moment,
Cluster Tendency, and Summean
Classification The process of identifying a
region as part of a class based on its texture
properties. (Decision Trees)
Wavelet coefficientsHaar

• Other Possible Descriptors
• Run-Length Statistics
• Spectral Measures
• Fractal Dimension
• Statistical Moments
• Co-occurrence Matrices

Sample Decision Tree
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Wavelets

• A mathematical function that can decompose a
  signal or an image with a series of averaging and
  differencing calculations.
• Wavelets calculate average intensity properties
  as well as several detailed contrast levels
  distributed throughout the image.
• They are sensitive to the spatial distribution of
  grey level pixels, but are also able to
  differentiate and preserve details at various
  scales or resolutions.

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Haar Wavelet
Resolution
4 2 1
Original image
9 7 3 5
8 4
1 -1
Averages
Details
6
2
1 -1
6 2 1 -1
Wavelet coefficients
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Haar Wavelet

• Calculate one resolution of wavelet coefficients
  horizontally
• Calculate one resolution of wavelet coefficients
  vertically

A D


A D
A
D
A
D
AD
DA DD
AA AD
DA DD
Repeat process on averages (AA) until desired
resolution level is reached
AA AD
DA DD
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Haar Wavelet
Averages Horizontal Activity
Vertical Activity Diagonal Activity
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Texture Descriptors
Calculate one resolution level of wavelet
coefficients Results horizontal, vertical, and
diagonal details
Calculate four co-occurrence matrices for each
wavelet detail based on the four directions 0,
45, 90, 135
Calculate histograms for each wavelet detail
Calculate Energy, Entropy, Contrast, Homogeneity,
Summean, Variance, Maximum Probability, Inverse
Difference Moment, Cluster Tendency for each
co-occurrence matrix
Calculate mean and standard deviation of each
histogram
Repeat the process for each resolution level
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Texture Descriptors
Total Descriptors Per Resolution Level 114
3 Levels of Resolution 342
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Feature Reduction
342 Descriptors Total
Average over co-occurrence directions 99
Descriptors total
Average over wavelet details 33 Descriptors
Total
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Decision Trees (Classification and Regression
Tree)

• A decision tree predicts the class of an object
  from values of predictor variables
• Depth the depth of the decision tree
• Parent Nodes the of possible roots per node
• Child Nodes the number of possible stems per
  root node

Parent Node 20
Child Node 1
Depth 10
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Decision Trees Haar Wavelets
Sample Decision Tree
Training Data Testing Data
Resulting Tree Total nodes 49 Total
levels 10 Total terminal nodes
25 Optimal Parameters Depth of Decision
Tree 10 Parent Node 20 Child Node
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Misclassification Matrix (Haar 33)
Actual Category Backbone Heart Liver K
idney Spleen Total Predicted Backbone 182
6 1 6 0 195 Category Heart
3 18 4 0 0 25 Liver
0 3 30 1 7 41 Kidney 10
4 0 49 1 64 Spleen 0
0 4 0 8 12 Total 195 31
39 56 16 337
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Results (Haar)
Organ Sensitivity Specificity Precision Accuracy
Backbone 93.3333 90.8451 93.3333 92.2849
Heart 58.0645 97.7124 72 94.0653
Liver 76.9231 96.3087 73.1707 94.0653
Kidney 87.5 94.6619 76.5625 93.4718
Spleen 50 98.7539 66.6667 96.4392
Depth 10 Parent Node 20 Child Node 4
Actual Category Backbone Heart Liver K
idney Spleen Total Predicted Backbone 182
6 1 6 0 195 Category Heart
3 18 4 0 0 25 Liver
0 3 30 1 7 41 Kidney 10
4 0 49 1 64 Spleen 0
0 4 0 8 12 Total 195 31
39 56 16 337
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References

• Mallat, Stephane G.. A Theory for
  Multiresolution Signal Decomposition. IEEE
• Transactions on Pattern Analysis and Machine
  Intelligence, VOL 11. NO. 7. July 1989.
• Mulcahy, Colm. Image Compression using the Haar
  Wavelet Transform. Spleman Science and Math
  Journal
• Mulcahy, Colm. Plotting and Scheming with
  Wavelets. Mathematics Magazine 69, 5, (1996),
  323-343.
• Stollnitz, Eric J., Tony D. DeRose, David H.
  Salesin. Wavelets for Computer Graphics A
• Primer 1. IEEE Computer Graphics and
  Applications, 15(4)75-85, July 1995.
• Stollnitz, Eric J., Tony D. DeRose, David H.
  Salesin. Wavelets for Computer Graphics A
• Primer 2. IEEE Computer Graphics and
  Applications, 15(4)75-85, July 1995.
• Tomita, Fumiaki, and Saburo Tsuji. Computer
  Analysis of Visual Textures. Kluwer
• Academic Publishers Norwell, Massachusetts,
  1990.
• Tuceryan, Mihran and Anil K. Jain. Texture
  Analysis. The Handbook of Pattern
• Recognition and Computer Vision (2nd Edition).
  World Scientific Publishing Co, 1998.
• Van de Wouwer, G., P. Scheunders, and D. Van
  Dyck. Statistical Texture
• Characterization from Discrete Wavelet
  Representations. University of Antwerp
  Antwerpen, Belgium.
• Weeks, Arthur R. Jr., Fundamentals of Electronic
  Image Processing. The Society for Optical
  Engineering Bellingham, Washington, 1996.
• D. Xu, J. Lee, D.S. Raicu, J.D. Furst, D.
  Channin. "Texture Classification of Normal
  Tissues in Computed Tomography", The 2005 Annual
  Meeting of the Society for Computer Applications
  in Radiology, Orlando, Florida, June 2-5,2005.
• A. Kurani, D. H. Xu, J. D. Furst, D. S. Raicu,
  "Co-occurrence matrices for volumetric data", The
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  Digital Image Processing. Pearson Education
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Texture Descriptors
Feature Definition Interpretation
Entropy Entropy - ? ? P i, j log P i, j i j Measures the randomness of a gray-level distribution The Entropy is expected high if the gray levels are distributed randomly through out the image
Energy Energy ? ? P² i, j i j Measures the number of repeated pairs The Energy is expected high if the occurrence of repeated pixel pairs are high.
Contrast Contrast ? ? (i -j)²P i, j i j Measures the local contrast of an image (how different the gray-level values in the pixel pair are) The Contrast is expect low if the gray levels of each pixel pair are similar.
Homogeneity Homogeneity ? ? (P i, j / (1 i j )) i j Measures the local homogeneity of a pixel pair (how similar the gray-level values in the pixel pair are) The Homogeneity is expect large if the gray levels of each pixel pair are similar
SumMean SumMean (1/2) ? ? iP i, j ? ? jP i, j i j i j Provides the mean of the gray levels in the image The SumMean is expected large if the sum of the gray levels of the image is high
Variance Variance (1/2) ? ? (i-µ)²P i, j ? ? (j-µ)² P i, j i j i j Variance tells us how spread out the distribution of gray-levels is The Variance is expect large if the gray levels of the image are spread out greatly.
Maximum Probability Max P i, j i,j Provides the pixel pair that is most predominant in the image The MP is expected high if the occurrence of the most predominant pixel pair is high.
InversDifference Moment Inverse Difference Moment ? (P i, j ) l i,j i-jk i?j Provides the smoothness of the image, just like homogeneity The IDM is expected high if the gray levels of the pixel pairs are similar
Cluster Tendency Cluster Tendency ? (i j - 2µ ) k P i, j i,j Measures the grouping of pixels that have similar gray-level values (an image of a black and white cow would result in a higher value for cluster tendency)