Robust Bayesian fusion of continuous segmentation maps

•Robust probabilistic framework to estimate a consensus from several continuous segmentation maps.•Replacement of the classical Gaussian model by heavy-tailed distributions allowing the raters performances to be locally estimated.•Definition of bias and spatial priors allowing the raters bias to be properly assessed and the smoothness of the consensus map to be controlled.•Introduction of the concept of mixture of consensuses allowing not only one but potentially several consensuses to be obtained.•Estimation of the model performances on several human expert and neural network segmentations of prostate and lung nodule images and comparison with state of the art algorithms. [Display omitted] The fusion of probability maps is required when trying to analyse a collection of image labels or probability maps produced by several segmentation algorithms or human raters. The challenge is to weight the combination of maps correctly, in order to reflect the agreement among raters, the presence of outliers and the spatial uncertainty in the consensus. In this paper, we address several shortcomings of prior work in continuous label fusion. We introduce a novel approach to jointly estimate a reliable consensus map and to assess the presence of outliers and the confidence in each rater. Our robust approach is based on heavy-tailed distributions allowing local estimates of raters performances. In particular, we investigate the Laplace, the Student’s t and the generalized double Pareto distributions, and compare them with respect to the classical Gaussian likelihood used in prior works. We unify these distributions into a common tractable inference scheme based on variational calculus and scale mixture representations. Moreover, the introduction of bias and spatial priors leads to proper rater bias estimates and control over the smoothness of the consensus map. Finally, we propose an approach that clusters raters based on variational boosting, and thus may produce several alternative consensus maps. Our approach was successfully tested on MR prostate delineations and on lung nodule segmentations from the LIDC-IDRI dataset.