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.
Bottom-Up
Scenario
Scene-1
Scene-I
Object-1
Object-J
S-Region-1
S-Region-K
Region-1
Region-L
Pixel (i,j)
Edge-M
Edge-1
Pixel (k,l)
Top-Down
Figure 8.1. A hierarchical representation of image features.

4. Figure 8.2. A hierarchical structure of medical image analysis.
Image Reconstruction
Image
Segmentation
(Edge and Region)
Feature Extraction
and
Representation
Classification
Object Identification
Analysis
of Classified Objects
Multi-Modality/Multi-Subject/Multi-Dimensional Registration, Visualization and Analysis
Raw Data from Imaging System
Single Image
Understanding
Multi-Modality/ Multi-Subject/Multi-Dimensional
Image Understanding
Scene
Models
Object
Feature
Edge/Region Representation
Physical Property/
Constraint
Knowledge Domain
Data
Domain
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. 4 2 3 1 5 6 7 xc 4 2 3 1 5 6 7
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. F A D C E B
Chain Code:
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. Set A
Set B
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 A B A B: Erosion of A by B : Dilation of A by B ( A B) 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. A B
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,

24. Erosion
Figure comes from the Wikipedia,

25. Morphological Processing for Shape Description
Opening
Closing

26. A B
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,

28. Closing
Figure comes from the Wikipedia,

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. (a)
(b)
Figure 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)
(e)
(f)

33. (g)
(h)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

34. Texture Features Texture Gray-level co-occurrence matrix (GLCM)
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 (a) A matrix representation of a 5x5 pixel image with three gray values; (b) the GLCM P(i,j) for d=[1,1].

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

47. R1
R21
R22
R23
R41
R43
R24
R42
R44 R3
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. R R4 R3 R2 R1
R24
R23
R22
R21
R44
R43
R42
R41
R14
R13
R12
R11
R34
R33
R32
R31
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

49. A C B D F I E B C A I E D F
Figure 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. Focus of Attention Rules
Strategy Rules
A priori knowledge
or models
Focus of Attention Rules
Knowledge Rules
Activity
Center
Input
Database
Output
Figure 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 (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