In this paper, we investigate the eect of using an optimum number of clusters with Fuzzy C-Means clustering, for Liver CT image segmentation. The optimum number of clusters to be used was measured using the average silhouette value. The evaluation was carried out using the Jaccard index, in which we concluded that using the optimum number of clusters may not necessarily lead to the best segmentation results.

1. Fuzzy C-Means Based Liver CT Image
Segmentation with Optimum Number of Clusters
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
Abder-Rahman Ali
The 5th International Conference on Innovations in Bio-
Inspired Computing and Applications, June 23-25, 2014

2. Scientific Research Group in Egypt
www.egyptscience.net

3. Overview
 Motivation
 Proposed Approach
 Optimal number of clusters
 Average Generalized Silhoeutte
 Results
 Conclusion
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014

4. Motivation
We investigate the effect of using an optimum
number of clusters with Fuzzy C-Means
clustering, for Liver CT image segmentation
Is the optimum always the better?
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014

5. Proposed Approach
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014

6. Optimal Number of Clusters
 Generalized Intra-Inter Silhouettes
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014

7. Optimal Number of Clusters
(cont…)
 Generalized Intra-Inter Silhouettes
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014

8. Optimal Number of Clusters
(cont...)
 Generalized Intra-Inter Silhouettes
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
Compactnes
s distance

9. Optimal Number of Clusters
(cont...)
 Generalized Intra-Inter Silhouettes
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
Separation
distance

10. Optimal Number of Clusters
(cont...)
 Generalized Intra-Inter Silhouettes
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
silhouette
[-1, +1]
If bi-aj  +: good clustering
If bi-aj  - : poor clustering

11. Average Generalized Silhouette
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
• Average Generalized is considered in this work, since we are interested in
the overall clustering quality of the entire dataset
• Average Generalized Silhouette returns a vector of silhouette values, one
value for each data point (pixel)
• If one point has a silhouette value near 1, then its clustering is very good

12. Average Generalized Silhouette
(cont…)
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
• If the silhouette is near -1, then the clustering of the point is very bad
• A silhouette value of 0 indicates an intermediate case
• Each silhouette is considered a measure of the clustering quality of the
associated point

13. Results
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
The first and second images, the best number of clusters to be used is 3. For
the third image, the best number of clusters to be used is 4. And, for the fourth
and fifth images, the best number of clusters to be used is 2

14. Results (cont…)
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
where the optimal number of clusters to be used are larger than 2-clusters,
based on Table (1) in the previous slide, they gave the best Jaccard index
values. And, where the optimal number of clusters to be used are 2-clusters,
choosing a random number of clusters in the range 3-5 gave better Jaccard
index values

15. Results (cont…)
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
• The figure represents image (1) from the table
• Using 3-clusters, as recommended by the average silhouette value, shows
more clearly the groundtruth than using 2-clusters

16. Conclusions
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
 Choosing the correct number of clusters is
very important in Fuzzy C-Means clustering
 it was noticed that it is not always necessary
that using the optimum number of clusters
with FCM, as measured by the average
silhouette value, always gives the best results
in terms of Jaccard index

17. Thanks and Acknowledgement
The 5th International Conference on Innovations in Bio-Inspired Computing and Applications. June 23-25, 2014
http://www.egyptscience.net
Authors: Abder-Rahman Ali, Micael Couceiro, Aboul Ella
Hassenian, Mohamed F. Tolba5, and Vaclav Snasel