Variable Variance Adaptive Mean-Shift and possibilistic fuzzy C-means based recursive framework for brain MR image segmentation

Segmentation of brain MR image tissues has been a challenge because of the embedded nonlinear bias field acquired during the image acquisition process. This problem is further compounded due to the presence of noise. In order to deal with such issues, we have proposed a Variable Variance Adaptive Mean-Shift (VVAMS) algorithm which not only removes noise but also reinforces the clustering attribute by its mode seeking ability. We have formulated the problem for jointly estimating the bias field, tissue class labels and noise free pixels. Since, all the parameters are unknown and interdependent it is hard to obtain optimal estimates. In this regard, we have proposed a recursive framework to obtain the estimates of the parameters, which are partial optimal ones. In the first step of the recursion, the possibilistic fuzzy clustering algorithms has been applied to determine different clusters and bias field. These clusters are noisy and hence in the second step of the recursion, VVAMS algorithm has been applied on each cluster to eliminate noise and reinforce the modes of the clusters. These two steps constitute one combined iteration. Theoretically, the recursive framework is supposed to converge after large number of recursions but in practice it converges after a few iterations. This proposed scheme has successfully been tested with 50 biased noisy slices from Brainweb database and some real brain MR image data from IBSR database. The results have been quantitatively evaluated by percentage of misclassification, Rand Index, t-test, fuzzy partition coefficient (Vpc), fuzzy partition entropy (Vpe) and Tanimoto index. The quantitative evaluations of the tissue class labels demonstrate the superiority of proposed scheme over the existing methods.