RoughFuzzy 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)

• Infarction is on the left side..
• The left side is compressing the right side
• Dilation of the blood ventricles
• Severe edema
• Division of brain into gray matter, white matter
  and the cerebrospinal fluid (CSF)
• The third ventricle is not visible here due to
  severe edema from the right ventricle side
• 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)

• Patient suffering from vascular insult
• Right and left should have been symmetric (the
  most definite metric for comparison)
• Right side is dark because it has not received
  blood supply for a very long time
• Due to this the blood ventricles have dilated and
  have undergone liquefaction (water)
• Parenchyma is infarcted
• Arteries were blocked due to high cholesterol
  levels
• 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)

• The third ventricle has dilated
• Edema from below
• Blockage of arteries, no blood supply from a long
  time
• Dilation of left and right ventricles due to this
  as passage from below is blocked
• Problem modeling same. although the infarction
  here is petty difficult to locate
• Tough problem of segmentation for infarction
• 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 ?