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Medical Image Analysis

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A schematic diagram of a rule-based system for image analysis. Feature and Image Classification Image and feature classification: ... – PowerPoint PPT presentation

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Title: 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.
5
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

8
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

9
Statistical Pixel-Level (SPL) Features
  • Entropy
  • The entropy Ent is a measure of information
    represented by the distribution of gray-values in
    the region

10
Statistical Pixel-Level (SPL) Features
  • Local contrast
  • Maximum, minimum
  • The mean, variance, energy and entropy of
    contrast values
  • Gradient information for the boundary pixels

11
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

12
Shape Features
  • Circularity ( 1 for a circle) of the region
    computed as
  • Compactness of the region computed as

13
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

15
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

16
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.
18
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

19
Moments for Shape Description
  • Central moments of a segmented image
  • Invariant moments
  • Shape matching, pattern recognition

20
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.
21
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).
22
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).
23
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

26
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).
27
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

30
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

31
(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.
32
(c)
(d)
(f)
(e)
33
(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

35
(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.
36
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

37
Second-Order Histogram Statistics
  • Entropy of
  • Angular second moment of

38
Second-Order Histogram Statistics
  • Contrast of
  • Inverse difference moment of

39
Second-Order Histogram Statistics
  • Correlation of

40
Second-Order Histogram Statistics
  • Mean of
  • Deviation of

41
Second-Order Histogram Statistics
  • Entropy of
  • Angular second moment of

42
Second-Order Histogram Statistics
  • Mean of

43
(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 .
44
(c)
45
(d)
46
Relational Features
  • Relational features
  • Information about adjacencies, repetitive
    patterns and geometrical relationships among
    regions of an object
  • Quad-tree representation
  • Tree and graph structures

47
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.
50
Feature and Image Classification
  • Statistical classification methods
  • Unsupervised k-means, fuzzy clustering
  • Supervised
  • Nearest neighbor classifier
  • Assigned to the class if

51
Feature and Image Classification
  • Bayes classifier
  • Risk of wrong classification for assigning the
    feature vector to the class
  • Assigned to the class if

52
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

53
Figure 8.15. A schematic diagram of a rule-based
system for image analysis.
54
Feature and Image Classification
  • Image and feature classification neural networks
  • Backpropagation
  • Radial basis function
  • Associative memories
  • Self-organizing
  • Neuro-fuzzy pattern classification

55
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.
60
(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.
62
Figure 8.22. Resulting decision surface Mblack(x)
for the black category membership function.
63
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
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