Rough-Fuzzy Clustering: An Application to Medical Imagery

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Rough-Fuzzy Clustering An Application to Medical
Imagery

• Sushmita Mitra
• Center for Soft Computing Research
• Indian Statistical Institute, Kolkata, INDIA
• Bishal Barman
• Electrical Engineering Department
• S. V. National Institute of Technology, Surat,
  INDIA

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Rough and Rough-Fuzzy Sets

• Rough Set Theory Z. Pawlak (1990 91)
• Idea of Approximation Spaces
• Handles vagueness, uncertainty and incompleteness
  in information systems
• Rough-Fuzzy and Fuzzy-Rough Sets Dubois and
  Prade (1990)
• Uncertainty modeling through Upper and Lower
  Approximations
• Hybridized Rough-Fuzzy modeling through
  Upper-Lower Approximations and membership values

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Brief Overview

• Novel Application of Rough-Fuzzy (RF) Clustering
  (For Synthetic as well as CT scan images of the
  brain)
• RF Clustering simultaneously handles overlap of
  clusters (Fuzzy) and uncertainty involved in
  class boundary (Rough)
• Number of clusters was optimized via cluster
  validity indices
• Main objective was the diagnosis of the extent of
  brain infarction in CT scan images

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Rough Clustering Algorithms

• Rough and Fuzzy sets incorporated in c-means
  framework to give Rough c-means (RCM) and Fuzzy
  c-means (FCM)
• RCM views each cluster as an interval or rough
  set U
• Cluster prototypes in the RCM algorithm defined
  as

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Rough-Fuzzy c-means (RFCM)

• Rough-Fuzzy c-means (RFCM) Mitra, S., Banka, H.,
  Pedrycz, W. Rough-fuzzy collaborative
  clustering. IEEE Transactions on Systems, Man,
  and Cybernetics, Part-B, 36, (2006), 795 805
• Algorithm outlined as

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RFCM Continued
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Salient Features of the hybridized algorithm
(RFCM)

• Fuzzy membership enables efficient handling of
  overlapping partitions while Rough set deals with
  uncertainty, vagueness and incompleteness in data
  in terms of upper and lower approximation
• Incorporation of membership in the RCM framework
  enhances the robustness of the algorithm
• Previously, in RCM, one never had the idea of how
  similar a sample was to the given cluster in the
  absence of any similarity index. RFCM solves this
  problem with the help of membership values
• Maximizes the use of both Fuzzy and Rough sets
  for effective approach in Knowledge Discovery

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Cluster Validation

• Partitive clustering requires pre-specification
  of the number of clusters
• To evaluate the goodness of clustering, we
  employed three cluster validity indices
• Davies-Bouldin Index
• Xie-Beni Index
• Silhouette Statistic

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Davies-Bouldin Index
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Xie-Beni Index
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Silhouette Statistic

• Silhouette Index, S, computes for each point a
  width depending on its membership in any cluster
• ai is the average distance between point i and
  all other points in its own cluster and bi is the
  minimum of the average dissimilarities between i
  and points in other clusters

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RESULTS

• Synthetic Data
• 32 points with 2 clusters
• 3 outliers to test the ability of the algorithms
  to resist a bias in the estimation of cluster
  prototypes
• Results obtained for the Hard c-means (HCM) or
  the k-means, Fuzzy c-means (FCM), Rough c-means
  (RCM) and Rough-Fuzzy c-means (RFCM)

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Original Scatter Plot of X-32
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Hard c-means (HCM) or k-means
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Fuzzy c-means (FCM)
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Rough c-means (RCM)
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Rough-Fuzzy c-means (RFCM)
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Scatter Plot and RFCM result for another
synthetic data with 45 points (X-45)
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Scatter Plot and RFCM result for another
synthetic data with 70 points (X-70)
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Cluster Validity Indices for X-32 ( 2 Clusters)
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CT Scan Image Segmentation

• Segmentation Process of partitioning an image
  into some non-overlapping meaningful regions
• Segmentation here via Pixel Clustering
• Study consists of cases of Vascular Infarction of
  the Human Brain
• Partitioning into five regions Gray matter
  (GM), White matter (WM), Infarcted region, Skull
  and the backround

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Fresh case of Vascular Insult (Original Image)

1. Infarction is on the left side..
2. The left side is compressing the right side
3. Dilation of the blood ventricles
4. Severe edema
5. Division of brain into gray matter, white matter
   and the cerebrospinal fluid (CSF)
6. The third ventricle is not visible here due to
   severe edema from the right ventricle side
7. Cause Cholesterol Deposit, Blockage

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Segmentation Result (HCM)
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Segmentation Result (FCM)
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Segmentation Result (RCM)
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Segmentation Result (RFCM)
White Matter
Infarcted Region
Cerebrospinal Fluid
Gray Matter
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Comparative Analysis (HCM, FCM, RCM RFCM
respectively)
HCM (Noisy)
FCM (Noisy)
RFCM Much Crisper segmentation of White matter,
Gray matter and CSF.
RCM (Noisy)
GM
WM
Skull
CSF
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Chronic Infarction (Original Image)

1. Patient suffering from vascular insult
2. Right and left should have been symmetric (the
   most definite metric for comparison)
3. Right side is dark because it has not received
   blood supply for a very long time
4. Due to this the blood ventricles have dilated and
   have undergone liquefaction (water)
5. Parenchyma is infarcted
6. Arteries were blocked due to high cholesterol
   levels
7. Happens due to normal old age

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Chronic Infarction (RFCM Segmentation result)
Skull
Gray Matter
Infarcted Region
White Matter
Cerebrospinal Fluid
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Subtle Case of Infarction (Original Image)

1. The third ventricle has dilated
2. Edema from below
3. Blockage of arteries, no blood supply from a long
   time
4. Dilation of left and right ventricles due to this
   as passage from below is blocked
5. Problem modeling same. although the infarction
   here is petty difficult to locate
6. Tough problem of segmentation for infarction
7. Cause Cholesterol deposit, Blockage

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Subtle Case of Infarction (RFCM Segmentation
result)
White Matter
Uniform merging of Gray Matter and the Infarcted
region
Cerebrospinal Fluid
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Conclusion

• In the absence of an accurate index to test the
  accuracy of segmentation results in CT scan
  imagery, we resorted to expert domain knowledge
• 36 frames of each case of infarction was studied
  and results verified by an experienced
  radiologist
• RFCM produced the best result as verified by
  expert radiologist
• Results promise to provide a helpful second
  opinion to radiologists in case of Computer-Aided
  Diagnostic (CAD)

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QUESTIONS ?