In this paper, we propose to consider the estimation of a reference shape from a set of different segmentation results using both active contours and information theory. The reference shape is then defined as the minimum of a criterion that benefits from both the mutual information and the joint entropy of the input segmentations. This energy criterion is here justified using similarities between information theory quantities and area measures, and presented in a continuous variational framework. This framework brings out some interesting evaluation measures such as the specificity and sensitivity. In order to solve this shape optimization problem, shape derivatives are computed for each term of the criterion and interpreted as an evolution equation of an active contour. A mutual shape is then estimated together with the sensitivity and specificity. Some synthetical examples allow us to cast the light on the difference between our mutual shape and an average shape. The applicability and robustness of our framework has also been tested for the evaluation of different segmentation methods of the left ventricular cavity from cardiac MRI.
