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 Fr\'{e}chet 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 .

翻译：从多个二值或概率掩模中提取共识分割对于解决诸如分析评分者间变异性或融合多个神经网络输出等任务至关重要。获取此类共识分割最广泛使用的方法之一是STAPLE算法。本文首先证明，该算法的输出严重受图像背景尺寸和先验选择的影响。随后，我们提出了一种新方法，基于精心选择的距离的Fr\'{e}chet均值构建二值或概率共识分割，使其完全独立于图像背景尺寸。我们提供了一种启发式方法来优化该准则，使得体素的类别完全由该体素到不同掩模的体素级距离、其所属连通分量以及对其分割的评分者组决定。我们在多个数据集上将我们的方法与STAPLE方法和朴素分割平均方法进行了广泛比较，结果表明，该方法生成的二值共识掩模尺寸介于多数投票与STAPLE之间，且后验概率不同于掩模平均和STAPLE方法。我们的代码可在 https://gitlab.inria.fr/dhamzaou/jaccardmap 获取。