Medical Image Analysis

1
Medical Image Analysis

• Image Representation and Analysis

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
2
Image Representation and Analysis

• A hierarchical framework of processing steps
  representing the image (data) and knowledge
  (model) domains
• Scenes of specific objects
• Surface regions (S-regions)
• Region
• Contours and edges
• Pixels

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
3
Figure 8.1. A hierarchical representation of
image features.
4
Figure 8.2. A hierarchical structure of medical
image analysis.
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Feature Extraction and Representation

• Statistical pixel-level (SPL) features
• Mean, variance, histogram, area, contrast of
  pixels within the region, edge gradient of
  boundary pixels
• Shape feature
• Circularity, compactness, moments, chain-codes
  and Hough transform, morphological processing
  methods

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
6
Feature Extraction and Representation

• Texture features
• Second-order histogram statistics or
  co-occurrence matrices, wavelet processing
  methods for spatio-frequency analysis
• Relational features
• Relational and hierarchical structure of the
  regions associated with a single or a group of
  objects

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
7
Statistical Pixel-Level (SPL) Features

• Histogram
• Mean
• Variance and central moments

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Statistical Pixel-Level (SPL) Features

• The third central moment is a measure of
  noncentrality
• The fourth central moment is a measure of
  flatness of the histogram
• Energy

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Statistical Pixel-Level (SPL) Features

• Entropy
• The entropy Ent is a measure of information
  represented by the distribution of gray-values in
  the region

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Statistical Pixel-Level (SPL) Features

• Local contrast
• Maximum, minimum
• The mean, variance, energy and entropy of
  contrast values
• Gradient information for the boundary pixels

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Shape Features

• Longest axis GE
• Shortest axis HF
• Perimeter and area of the minimum bounded
  rectangle ABCD
• Elongation ratio GE/HF
• Perimeter and the area of the segmented
  region
• Hough transform of the region using the gradient
  information of the boundary pixels of the region

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Shape Features

• Circularity ( 1 for a circle) of the region
  computed as
• Compactness of the region computed as

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Shape Features

• Chain code for boundary contour
• Obtained using a set of orientation primitives on
  the boundary segments derived from a piecewise
  linear approximation
• Fourier descriptor of boundary contours
• Obtained using the Fourier transform of the
  sequence of boundary segments derived from a
  piecewise linear approximation

14
Shape Features

• Central moments based shape features for the
  segmented region
• Morphological shape descriptors
• Obtained through the morphological processing on
  the segmented region

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Boundary Encoding Chain Code

• Orientation primitives
• 8-connected neighborhood
• Divide-and-conquer
• Curve approximation
• Maximum-deviation criterion
• Perpendicular distance between any point on the
  original curve segment between the selected
  vertices and the corresponding approximated
  straight-line segment

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Figure 8.4. The 8-connected neighborhood codes
(left) and the orientation directions (right)
with respect to the center pixel xc.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
17
Figure 8.5. A schematic example of developing
chain code for a region with boundary contour
ABCDE. From top left to bottom right the
original boundary contour, two points A and C
with maximum vertical distance parameter BF, two
segments AB and BC approximating the contour ABC,
five segments approximating the entire contour
ABCDE, contour approximation represented in terms
of orientation primitives, and the respective
chain code of the boundary contour.
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Boundary Encoding Fourier Descriptor

• Closed boundary of a region
• Discrete Fourier transform (DFT) of the sequence
• Rigid geometric transformation of a boundary
• Translation, rotation, scaling

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Moments for Shape Description

• Central moments of a segmented image
• Invariant moments
• Shape matching, pattern recognition

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Figure 8.6. A large region with square shape
representing the set A and a small region with
rectangular shape representing the structuring
element set B.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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A B
Figure 8.7 The dilation of set A by the
structuring element set B (top left), the erosion
of set A by the structuring element set B (top
right) and the result of two successive erosions
of set A by the structuring element set B
(bottom).
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Figure 8.8. Dilation and erosion of an arbitrary
shape region A (top left) by a circular
structuring element B (top right) dilation of A
by B (bottom left) and erosion of A by B (bottom
right).
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Dilation
Figure comes from the Wikipedia,
www.wikipedia.org.
24
Erosion
Figure comes from the Wikipedia,
www.wikipedia.org.
25
Morphological Processing for Shape Description

• Opening
• Closing

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Figure 8.9. The morphological opening and closing
of set A (top left) by the structuring element
set B (top right) opening of A by B (bottom
left) and closing of A by B (bottom right).
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Opening
Figure comes from the Wikipedia,
www.wikipedia.org.
28
Closing
Figure comes from the Wikipedia,
www.wikipedia.org.
29
Morphological Processing for Shape Description

• Skeleton
• Image processing
• Erosion can reduce the background noise
• Opening can remove the speckle noise and provide
  smooth contours

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Morphological Processing for Shape Description

• Image processing
• Closing preserves the peaks and reduces the sharp
  variations in the signal such as dark artifacts
• Opening followed by closing can reduce the bright
  and dark artifacts and noise
• The morphological gradient image can be obtained
  by subtracting the eroded image from the dilated
  image
• Edges can also be detected by subtracting the
  eroded image from the original image

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(b)
(a)
Figure 8.10. Example of morphological operations
on MR brain image using a structuring element of


(a) the original MR brain
image (b) the thresholded MR brain image for
morphological operations (c) dilation of the
thesholded MR brain image (d) resultant image
after 5 successive dilations of the thresholded
brain image (e) erosion of the thresholded MR
brain image (f) closing of the thesholded MR
brain image (g) opening of the thresholded MR
brain image and (h) morphological boundary
detection on the thresholded MR brain image.
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(c)
(d)
(f)
(e)
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(h)
(g)
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
34
Texture Features

• Texture
• Statistical
• Structural
• A repetitive arrangement of square and triangular
  shapes
• Spectral
• Fourier and wavelet transforms
• Gray-level co-occurrence matrix (GLCM)
• is the distribution of the number of
  occurrences of a pair of gray values and
  separated by a distance vector

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(a)
(b)
Figure 8.11. (a) A matrix representation of a 5x5
pixel image with three gray values (b) the GLCM
P(i,j) for d1,1.
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Texture Features

• The probability of occurrence of a pair of gray
  values and separated by a distance
  vector
• ,
• The probability that a difference in gray-levels
  exists between two distinct pixels

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Second-Order Histogram Statistics

• Entropy of
• Angular second moment of

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Second-Order Histogram Statistics

• Contrast of
• Inverse difference moment of

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Second-Order Histogram Statistics

• Correlation of

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Second-Order Histogram Statistics

• Mean of
• Deviation of

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Second-Order Histogram Statistics

• Entropy of
• Angular second moment of

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Second-Order Histogram Statistics

• Mean of

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(b)
(a)
Figures 8.12 (a) A part of a digitized X-ray
mammogram showing a region of benign lesion (b) a
part of a digitized X-ray mammogram showing a
region of malignant cancer of the breast (c). A
second-order histograms of (a) computed from the
gray-level co-occurrence matrices with a distance
vector of 1,1 and (d) A second-order histogram
of (b) computed from the gray-level co-occurrence
matrices with a distance vector of 1,1 .
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(c)
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(d)
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Relational Features

• Relational features
• Information about adjacencies, repetitive
  patterns and geometrical relationships among
  regions of an object
• Quad-tree representation
• Tree and graph structures

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Figure 8.13 A block representation of an image
with major quad partitions (top) and its
quad-tree representation.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
48
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
49
Figure 8.14. A 2-D brain ventricles and skull
model (top) and region-based tree representation.
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Feature and Image Classification

• Statistical classification methods
• Unsupervised k-means, fuzzy clustering
• Supervised
• Nearest neighbor classifier
• Assigned to the class if

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Feature and Image Classification

• Bayes classifier
• Risk of wrong classification for assigning the
  feature vector to the class
• Assigned to the class if

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Feature and Image Classification

• Rule-based systems
• Analyze the feature vector using multiple sets of
  rules that are designed to check specific
  conditions in the database of feature vectors to
  initiate an action

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Figure 8.15. A schematic diagram of a rule-based
system for image analysis.
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Feature and Image Classification

• Image and feature classification neural networks
• Backpropagation
• Radial basis function
• Associative memories
• Self-organizing
• Neuro-fuzzy pattern classification

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Figure 8.16. A computational neuron model with
linear synapses.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
56
Figure 8.17. The architecture of the Neuro-Fuzzy
Pattern Classifier.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
57
Figure 8.18. The structure of the fuzzy
membership function.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
58
Figure 8.19. Convex set-based separation of two
categories.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
59
(a)
Figure 8.20. (a). Fuzzy membership function M1(x)
for the subset 1 of the black category. (b).
Fuzzy membership function M2(x) for the subset 2
of the black category.
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(b)
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
61
Figure 8.21. Fuzzy membership function M3(x)
(decision surface) for the white category
membership.
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Figure 8.22. Resulting decision surface Mblack(x)
for the black category membership function.
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Image Analysis Example Analysis of
Difficult-to-Diagnose Mammographic
Microcalcification

• Features
• Number of microcalcification
• Average number of pixels per microcalcification
• Entropy of
• Energy fro the wavelet packet at Level 0