  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).
