A Quantitative Comparison of Epistemic Uncertainty Maps Applied to Multi-Class Segmentation.

Uncertainty assessment has gained rapid interest in medical image analysis. A popular technique to compute epistemic uncertainty is the Monte-Carlo (MC) dropout technique. From a network with MC dropout and a single input, multiple output can be sampled. Various methods can be used to obtain epistemic uncertainty maps from those multiple outputs. In the case, of multi-class segmentation the number of methods is even larger as epistemic uncertainty can be computed voxelwise per class or voxelwise per image. This paper highlights a systematic approach to define and quantitatively compare those methods in those two different contexts: class specific epistemic uncertainty maps (one value per image, voxel and class) and combined epistemic uncertainty maps (one value per image and voxel). We applied this quantitative analysis to a multi-class segmentation of the carotid artery lumen and vessel wall, on a multi-center, multi-scanner, multi-sequence dataset of Magnetic Resonance (MR) images. We validated our analysis over 144 sets of hyperparameters of a model. Our main analysis consider the relationship between the order of the voxels of an epistemic uncertainty map and the misclassification of the prediction. Under this consideration, the comparison of combined uncertainty maps reveals that the multi-class entropy and the multi-class mutual information statistically out-perform the other combined uncertainty maps under study (the averaged entropy, the averaged variance, the similarity Bhattacharya coefficient and the similarity Kullback-Leibler divergence). In a class specific scenario, the one versus all entropy statistically out-performs the class-wise entropy, the class-wise variance and the one versus all mutual information. The class-wise entropy statistically out-performs the other class specific uncertainty maps in term of calibration. We made a python package available at to reproduce our analysis on different data and tasks.