Fuzzy classification of brain MRI using a priori knowledge: weighted fuzzy C-means

We report in this communication a new formulation for the cost function of the well-known fuzzy C-means classification technique whereby we introduce weights. We derive the equations of this new weighted fuzzy C-means algorithm (WFCM) in the presence of additive and multiplicative bias field. We show that the weights can be designed in the same manner as prior probabilities commonly used in maximum a posteriori classifier (MAP) to introduce prior knowledge (e.g. using atlas), and increase robustness to noise (e.g. using Markov random field). Using prior probabilities of three popular MAP algorithms, we compare the performances of our proposed WFCM scheme using the simulated MRI T1W BrainWeb datasets, as well as five T1W MR patient scans. Our results show that WFCM achieves superior performances for low SNR conditions, whereas a Gaussian mixture model is desirable for high noise levels. WFCM allows rigorous comparison of fuzzy and probabilistic classifiers, and offers a framework where improvements can be shared between those two types of classifier.