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Medical Image AnalysisMedical Image AnalysisImage Representation and Analysis
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Image Representation and Image Representation and AnalysisAnalysis
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
A hierarchical framework of processing steps representing the image (data) and knowledge (model) domains
Scenes of specific objectsSurface regions (S-regions)RegionContours and edgesPixels
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-MEdge-1
Pixel (k,l)
Top-Down
Figure 8.1. A hierarchical representation of image features.
Image Reconstruction
ImageSegmentation
(Edge and Region)
Feature Extractionand
Representation
Classificationand
Object Identification
Analysisof Classified Objects
Multi-Modality/Multi-Subject/Multi-Dimensional
Registration, Visualization and Analysis
Raw Data from Imaging System
Single ImageUnderstanding
Multi-Modality/ Multi-Subject/Multi-Dimensional
Image Understanding
Scene Representation
Models
Object Representation
Models
Feature Representation
Models
Edge/Region Representation
Models
Physical Property/Constraint
Models
Knowledge Domain
DataDomain
Figure 8.2. A hierarchical structure of medical image analysis.
Feature Extraction and Feature Extraction and RepresentationRepresentation
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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
Feature Extraction and Feature Extraction and RepresentationRepresentation
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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
Statistical Pixel-Level (SPL) Statistical Pixel-Level (SPL) FeaturesFeaturesHistogram
Mean
Variance and central moments
n
rnrp ii
)()(
1
0
)(1 L
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))((L
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Statistical Pixel-Level (SPL) Statistical Pixel-Level (SPL) FeaturesFeatures
◦The third central moment is a measure of noncentrality
◦The fourth central moment is a measure of flatness of the histogram
Energy
1
0
2)]([L
iirpE
Statistical Pixel-Level (SPL) Statistical Pixel-Level (SPL) FeaturesFeaturesEntropy
◦The entropy Ent is a measure of information represented by the distribution of gray-values in the region
1
02 )(log)(
L
iii rrpEnt
Statistical Pixel-Level (SPL) Statistical Pixel-Level (SPL) FeaturesFeaturesLocal contrast
Maximum, minimumThe mean, variance, energy and
entropy of contrast valuesGradient information for the
boundary pixels
),(),,(max
),(),(),(
yxPyxP
yxPyxPyxC
sc
sc
Shape FeaturesShape FeaturesLongest axis GEShortest axis HFPerimeter and area of the minimum
bounded rectangle ABCDElongation ratio: GE/HFPerimeter and the area of the
segmented regionHough transform of the region using
the gradient information of the boundary pixels of the region
p A
Shape FeaturesShape FeaturesCircularity ( = 1 for a circle) of
the region computed as
Compactness of the region computed as
C
2
4
p
AC
pC
A
pC p
2
Shape FeaturesShape FeaturesChain 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
Shape FeaturesShape FeaturesCentral moments based shape
features for the segmented region
Morphological shape descriptors◦Obtained through the morphological
processing on the segmented region
Boundary Encoding: Chain Boundary Encoding: Chain CodeCodeOrientation primitives
◦8-connected neighborhoodDivide-and-conquer
◦Curve approximationMaximum-deviation criterion
◦Perpendicular distance between any point on the original curve segment between the selected vertices and the corresponding approximated straight-line segment
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
04
23 1
5 6 7
xc 04
23 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.
FA D
C
E
B
A D
C
E
B
A D
C
E
B
A D
C
E
B
A
B C
D Chain Code: 110000554455533
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.
Boundary Encoding: Fourier Boundary Encoding: Fourier DescriptorDescriptorClosed boundary of a region
Discrete Fourier transform (DFT) of the sequence
Rigid geometric transformation of a boundary◦Translation, rotation, scaling
)()()( niynxnu 1,...,2,1,0 Nn
1
0
/ 2)(1
][N
n
Nind enu
Nn F
Moments for Shape Moments for Shape DescriptionDescriptionCentral moments of a segmented
image
Invariant moments◦Shape matching, pattern recognition
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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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.
: Dilation of A by B
A B: Erosion of A by B
( A B) B
A A
BA BA
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).
A
B
BA
BAFigure 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).
Figure comes from the Wikipedia, www.wikipedia.org.
Dilation
Figure comes from the Wikipedia, www.wikipedia.org.
Erosion
Morphological Processing for Morphological Processing for Shape DescriptionShape DescriptionOpening
Closing
BBABA )(
BBABA )(
AB
BA BA 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).
Figure comes from the Wikipedia, www.wikipedia.org.
Opening
Figure comes from the Wikipedia, www.wikipedia.org.
Closing
Morphological Processing for Morphological Processing for Shape DescriptionShape DescriptionSkeleton
Image processing◦Erosion can reduce the background
noise◦Opening can remove the speckle noise
and provide smooth contours
N
nn AKAK
0
)()(
BnBAnBAAKn )()()(
Morphological Processing for Morphological Processing for Shape DescriptionShape DescriptionImage 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
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.
10
01
(b)(a)
(c) (d)
(f)(e)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
(g) (h)
Texture FeaturesTexture FeaturesTexture
◦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
),( jipi j
],[ dydxd
2 2 2 0 10 2 2 1 10 1 1 2 01 2 2 0 12 1 0 1 1
0 3 1 02 1 0 11 4 3 2 i0 1 2
j
(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 d=[1,1].
Texture FeaturesTexture 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
),,( drq yyH
qy ryd),( dsd yH
rqs yyy
Second-Order Histogram Second-Order Histogram StatisticsStatisticsEntropy of
Angular second moment of
),,( drq yyH
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yy
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yyrqrqH yyHyyHS
1 1
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),,( drq yyH
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1 1
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Second-Order Histogram Second-Order Histogram StatisticsStatisticsContrast of
Inverse difference moment of
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1 11 1
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),,( drq yyH
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1 1),(1
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Second-Order Histogram Second-Order Histogram StatisticsStatisticsCorrelation of ),,( drq yyH
t
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t
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rq
rq
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y
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1 1
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yyrqrm yyHyH
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Second-Order Histogram Second-Order Histogram StatisticsStatisticsMean of
Deviation of
),,( drq yyH
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Second-Order Histogram Second-Order Histogram StatisticsStatisticsEntropy of
Angular second moment of
),( dsd yH
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sd
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yysdsdyH yHyHS
1
)],([log),( 10),( ddd
),( dsd yH
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sd
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2),( )],([ dd
Second-Order Histogram Second-Order Histogram StatisticsStatisticsMean of ),( dsd yH
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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] .
(a) (b)
(c)
(d)
Relational FeaturesRelational FeaturesRelational features
◦Information about adjacencies, repetitive patterns and geometrical relationships among regions of an object
Quad-tree representationTree and graph structures
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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.
R
R4
R3
R2
R1
R24
R23
R22
R21
R44
R43
R42
R41
R14
R13
R12
R11
R34
R33
R32
R31
A
C
B
D
F
I
EB
C
A
I
ED
F
Figure 8.14. A 2-D brain ventricles and skull model (top) and region-based tree representation.
Feature and Image Feature and Image ClassificationClassificationStatistical classification methods
◦Unsupervised: k-means, fuzzy clustering
◦SupervisedNearest neighbor classifier
◦Assigned to the class if
jjD uff )(
jcf
jj
j Nfu
1
Cj ,...,2,1ic
)(min)( 1 ff jCji DD
Feature and Image Feature and Image ClassificationClassificationBayes classifier
◦Risk of wrong classification for assigning the feature vector to the class
◦Assigned to the class if
C
kkkjj cpZr
1
)|()( ff
Cj ,...,2,1
jc
ic
C
kkkj
C
kkki cpZcpZ
11
)|()|( ff
Feature and Image Feature and Image ClassificationClassificationRule-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
Strategy RulesA priori
knowledgeor models
Focus of Attention Rules
Knowledge Rules
ActivityCenter
InputDatabase
OutputDatabase
Figure 8.15. A schematic diagram of a rule-based system for image analysis.
Feature and Image Feature and Image ClassificationClassificationImage and feature classification:
neural networks◦Backpropagation◦Radial basis function◦Associative memories◦Self-organizing
Neuro-fuzzy pattern classification
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
X f()
1
w2
w0
w1
wd
f():
Y
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.
M1
winner-take-alloutput layer
L
1
fuzzy membershipfunction layer
x1
xi
xd
hyperplanelayer
inputlayer
max
M2
MK
C
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.
L
input fromhyperplane
layer
2
1
scaling
1f
2f
Lf
f
multiplication
Mf
outputfuzzy
function
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.
1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
Figure 8.19. Convex set-based separation of two categories.
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.
(a)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
(b)
Figure 8.21. Fuzzy membership function M3(x) (decision surface) for the white category membership.
Figure 8.22. Resulting decision surface Mblack(x) for the black category membership function.
Image Analysis Example: Image Analysis Example: Analysis of Difficult-to-Analysis of Difficult-to-Diagnose Mammographic Diagnose Mammographic MicrocalcificationMicrocalcification
Features◦Number of microcalcification◦Average number of pixels per
microcalcification◦…◦Entropy of◦…◦Energy fro the wavelet packet at
Level 0◦…
),,( drq yyH
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