Optimization of a Shape Metric Based on Information Theory Applied to Segmentation Fusion and Evaluation in Multimodal MRI for DIPG Tumor Analysis

In medical imaging, the construction of a reference shape from a set of segmentation results from different algorithms or image modalities is an important issue when dealing with the evaluation of segmentation without knowing the gold standard or when an evaluation of the inter or intra expert variability is needed. It is also interesting to build this consensus shape to merge the results obtained for the same target object from automatic or semi-automatic segmentation methods. In this paper, to deal with both segmentation fusion and evaluation, we propose to define such a “mutual shape” as the optimum of a criterion using both the mutual information and the joint entropy of the segmentation methods. This energy criterion is justified using the similarities between quantities of information theory and area measures and is presented in a continuous variational framework. We investigate the applicability of our framework for the fusion and evaluation of segmentation methods in multimodal MR images of diffuse intrinsic pontine glioma (DIPG).