The extraction of consensus segmentations from several binary or probabilistic masks is important to solve various tasks such as the analysis of inter-rater variability or the fusion of several neural network outputs. One of the most widely used methods to obtain such a consensus segmentation is the STAPLE algorithm. In this paper, we first demonstrate that the output of that algorithm is heavily impacted by the background size of images and the choice of the prior. We then propose a new method to construct a binary or a probabilistic consensus segmentation based on the Fréchet means of carefully chosen distances which makes it totally independent of the image background size. We provide a heuristic approach to optimize this criterion such that a voxel’s class is fully determined by its voxel-wise distance to the different masks, the connected component it belongs to and the group of raters who segmented it. We compared extensively our method on several datasets with the STAPLE method and the naive segmentation averaging method, showing that it leads to binary consensus masks of intermediate size between Majority Voting and STAPLE and to different posterior probabilities than Mask Averaging and STAPLE methods. Our code is available at https://gitlab.inria.fr/dhamzaou/jaccardmap