Tumor segmentation by fusion of MRI images using copula based Statistical methods.
In this paper, we propose a statistical fusion approach to fuse three different cerebral MRI sequences (T1, T2 and FLAIR) in order to segment tumoral volume. As T1, T2 and FLAIR provide complementary information, we propose a new fusion method based on copula which is capable to represent statistical dependency between different modalities. Indeed, the copula is a functional dependency measure which is able to identify complementary information in case of independence and to eliminate redundant information in case of dependance. To take into account the dependency, our segmentation is based on a Hidden Markov Field (HMF) statistical model in which the observation distribution is a multivariate distribution whose margins represent intensity distributions for the individual modalities and the copula represents dependency between the modalities. In this paper, we present a tumor segmentation based on HMF using no-standardized Gamma distributions for the margins to model tumor tissue distributions, and a Gaussian copula for describing the dependency between T1, T2 and FLAIR. Real MRI images for different patients are used to evaluate quantitatively and qualitatively our method. A comparison between individual and multi-tracer segmentations shows advantages of the proposed fusion method.