Conditional Entropy as a Supervised Primitive Segmentation Loss Function

Abstract: Supervised image segmentation assigns image voxels to a set of labels, as defined by a specific labeling protocol. In this paper, we decompose segmentation into two steps. The first step is what we call "primitive segmentation", where voxels that form sub-parts (primitives) of the various segmentation labels available in the training data, are grouped together. The second step involves computing a protocol-specific label map based on the primitive segmentation. Our core contribution is a novel loss function for the first step, where a primitive segmentation model is trained. The proposed loss function is the entropy of the (protocol-specific) "ground truth" label map conditioned on the primitive segmentation. The conditional entropy loss enables combining training datasets that have been manually labeled with different protocols. Furthermore, as we show empirically, it facilitates an efficient strategy for transfer learning via a lightweight protocol adaptation model that can be trained with little manually labeled data. We apply the proposed approach to the volumetric segmentation of brain MRI scans, where we achieve promising results.