Medical Image Analysis

1
Medical Image Analysis

• Image Segmentation

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
2
Edge-Based Image Segmentation

• Useful links
• The Berkeley Segmentation Dataset and Benchmark
• TurtleSeg

3
Edge-Based Image Segmentation

• Edge-based approach
• Spatial filtering to compute the first-order or
  second-order gradient information of the image
  Sobel, Laplacian masks
• Edges need to be linked to form closed regions
• Uncertainties in the gradient information due to
  noise and artifacts in the image

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
4
Edge Detection Operations

• Gradient magnitude and directional information
  from the Sobel horizontal and vertical direction
  masks

5
Edge Detection Operations

• The second-order gradient operator Laplacian can
  be computed by convolving one pf the following
  masks

6
Edge Detection Operations

• A smoothing filter first before taking a
  Laplacian of the image
• Combined into a single Laplacian of Gaussian
  function as

7
Edge Detection Operations
8
Edge Detection Operations

• A Laplacian of Gaussian (LOG) mask of
  pixels,

9
Boundary Tracking

• Edge-linking
• Pixel-by-pixel search to find connectivity among
  the edge segments
• Connectivity can be defined using a similarity
  criterion among edge pixels
• Geometrical proximity or topographical properties

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
10
Boundary Tracking

• The neighborhood search method
• edge magnitude
• edge orientation
• a boundary pixel
• a successor boundary pixel
• , , pre-determined thresholds

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Boundary Tracking

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Boundary Tracking

• A graph-based search method
• Find paths between the start and end nodes
  minimizing a cost function that may be
  established based on the distance and transition
  probabilities
• The start and end nodes are determined from
  scanning the edge pixels based on some heuristic
  criterion

13







End Node
Figure 7.1. Top An edge map with magnitude and
direction information Bottom A graph derived
from the edge map with a minimum cost path
(darker arrows) between the start and end nodes.
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Boundary Tracking

• A search algorithm
• 1. Select an edge pixel as the start node of the
  boundary and put all of the successor boundary
  pixels in a list, OPEN
• 2. If there is no node in the OPEN list, stop
  otherwise continue
• 3. For all nodes in the OPEN list, compute the
  cost function and select the node
  with the smallest cost . Remove the node
  from the OPEN list and label it as CLOSED.
  The cost function may be computed as

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Boundary Tracking

• A search algorithm
• 4. If is the end node, exit with the
  solution path by backtracking the pointers
  otherwise continue
• 5. Expand the node by finding all
  successors of . If there is no successor,
  go to Step 2 otherwise continue

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Boundary Tracking

• A search algorithm
• 6. If a successor is not labeled yet in any
  list, put it in the list OPEN with updated cost
  as
  and a pointer to its predecessor
• 7. If a successor is already labeled as
  CLOSED or OPEN, update its value by
• 
  . Put those CLOSED successors
  whose cost functions were lowered,
  in the OPEN list and redirect to the
  pointers from all nodes whose costs were lowered.
  Go to Step 2

17
Hough Transform

• Hough transform
• Similar to the Radon transform
• Detect straight lines and other parametric curves
  such as circles, ellipses
• A line in the image space forms a point
  in the parameter space

18
Hough Transform
Figure comes from the Wikipedia,
www.wikipedia.org.
19
Gradient e
O
r
p
Figure 7.2. A model of the object shape to be
detected in the image using Hough transform. The
vector r connects the Centroid and a tangent
point p. The magnitude and angle of the vector r
are stored in the R-table at a location indexed
by the gradient of the tangent point p.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
20
Pixel-Based Direct Classification Methods

• Example the histogram for bimodal distribution
• Find the deepest valley point between the two
  consecutive major peaks

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
21
Figure 7.3. The original MR brain image (top),
its gray-level histogram (middle) and the
segmented image (bottom) using a gray value
threshold T12 at the first major valley point in
the histogram.
22
Figure 7.3. The original MR brain image (top),
its gray-level histogram (middle) and the
segmented image (bottom) using a gray value
threshold T12 at the first major valley point in
the histogram.
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Figure 7.4. Two segmented MR brain images using a
gray value threshold T166 (top) and T225
(bottom).
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Optimal Global Thresholding

• Assume
• The histogram of an image to be segmented has two
  Gaussian distributions belonging to two
  respective classes such as background and object
• The histogram

25
Optimal Global Thresholding

• The error probabilities of misclassifying a pixel

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Optimal Global Thresholding

• Assume the Gaussian probability density functions

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Optimal Global Thresholding

• The optimal global threshold

28
Pixel Classification Through Clustering

• Feature vector of pixels
• Gray value, contrast, local texture measure, red,
  green, or blue components
• Clusters in the multi-dimensional feature space
• Group data points with similar feature vectors
  together in a single cluster
• Distance measure Euclidean or Mahalanobis
  distance
• Post-processing
• Region growing, pixel connectivity

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K-Means Clustering

• 1. Select the number of clusters with
  initial cluster centroids
• 2. Partition the input data points into
  clusters by assigning each data point to
  the closest cluster centroid using the
  selected distance measure
• 3. Compute a cluster assignment matrix
  representing the partition of the data points
  with the binary membership value of the th data
  point to the th cluster such that

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K-Means Clustering

• 4. Re-compute the centroids using the membership
  values as
• 5. If cluster centroids or the assignment matrix
  does not change from the previous iteration,
  stop otherwise go to Step 2.

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K-Means Clustering

• Objective function

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Fuzzy c-Means Clustering

• The objective function

33
Region-Based Segmentation

• Region-growing based segmentation
• Examine pixels in the neighborhood based on a
  pre-defined similarity criterion
• The neighborhood pixels with similar properties
  are merged to form closed regions
• Region splitting
• The entire image or large regions are split into
  two or more regions based on a heterogeneity or
  dissimilarity criterion

34
Region-Growing

• Two criteria
• A similarity criterion that defines the basis for
  inclusion of pixels in the growth of the region
• A stopping criterion that stops the growth of the
  region

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Figure 7.5. A pixel map of an image (top) with
the region-growing process (middle) and the
segmented region (bottom).
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Figure 7.6. A T-2 weighted MR brain image (top)
and the segmented ventricles (bottom) using the
region-growing method.
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Region-Splitting

• The following conditions are met
• 1. Each region,
  is connected
• 2.
• 3. for all ,
• 4. TRUE for
• 5. FALSE for
  , where is a logical predicate
  for the homogeneity criterion on the region

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Figure 7.7. An image with quad region-splitting
process (top) and the corresponding quad-tree
structure (bottom).
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Recent Advances in Segmentation

• Model-based estimation methods
• Rule-based systems
• Automatic segmentation

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Estimation-Model Based Adaptive Segmentation

• A multi-level adaptive segmentation (MAS) method

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
41
Figure 7.8 The overall approach of the MAS
method.
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Figure 7.9 (a) Proton Density MR and (b)
perfusion image of a patient 48 hours after
stroke.
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Figure 7.10. Results of MAS method with 4x4 pixel
probability cell size and 4 pixel wide averaging.
(a) pixel classification as obtained on the
basis of maximum probability, (b) as obtained
with pgt0.9.
44
Image Segmentation Using Neural Networks

• Backpropagation neural network for classification
• Radial basis function (RBF) network
• Segmentation of arterial structure in digital
  subtraction angiograms

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
45
Figure 7.11. A basic computational neural element
or Perceptron for classification.
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Figure 7.12. A feedforward Backpropagation neural
network with one hidden layer.
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Figure 7.13. An RBF network classifier for image
segmentation.
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Figure 7.14. RBF Segmentation of Angiogram Data
of Pig-cast Phantom image (top left) with using a
set of 10 clusters (top right) and 12 clusters
(bottom) respectively.
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Figure 7.14. RBF Segmentation of Angiogram Data
of Pig-cast Phantom image (top left) with using a
set of 10 clusters (top right) and 12 clusters
(bottom) respectively.