A Mutual Reference Shape for Segmentation Fusion and Evaluation

This paper proposes the estimation of a mutual shape from a set of different segmentation results using both active contours and information theory. The mutual shape is here defined as a consensus shape estimated from a set of different segmentations of the same object. In an original manner, such a shape is 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 justified using similarities between information theory quantities and area measures, and presented in a continuous variational framework. 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 of each segmentation. Some synthetic examples allow us to cast the light on the difference between the mutual shape and an average shape. The applicability of our framework has also been tested for segmentation evaluation and fusion of different types of real images (natural color images, old manuscripts, medical images).