In the field of delineation of 2D or 3D regions of interest (ROI) in medical imaging, and especially due to the development of multimodal and multiparametric image acquisition devices, the combination of segmentations of anatomical structures from different sources is interesting. It is also essential to accurately assess the variability between delineation experts or algorithms with different parameters. In this work, we propose to estimate a mutual shape defined as the optimum of a statistical criterion based on information theory. The mutual shape is computed using shape optimization tools through the computation of shape gradients. Compared to our previous work, we propose to interpret the mutual shape as a sum of distances of the Fréchet family. Moreover, we extend our framework to 3D shape fusion and provide a synthetic example to demonstrate the difference between mutual shape, average shape and shape union.