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Standard losses for training deep segmentation networks could be seen asindividual classifications of pixels, instead of supervising the global shapeof the predicted segmentations. While effective, they require exact knowledgeof the label of each pixel in an image.  This study investigates how effective global geometric shape descriptorscould be, when used on their own as segmentation losses for training deepnetworks. Not only interesting theoretically, there exist deeper motivations toposing segmentation problems as a reconstruction of shape descriptors:Annotations to obtain approximations of low-order shape moments could be muchless cumbersome than their full-mask counterparts, and anatomical priors couldbe readily encoded into invariant shape descriptions, which might alleviate theannotation burden. Also, and most importantly, we hypothesize that, given atask, certain shape descriptions might be invariant across image acquisitionprotocols/modalities and subject populations, which might open interestingresearch avenues for generalization in medical image segmentation.  We introduce and formulate a few shape descriptors in the context of deepsegmentation, and evaluate their potential as standalone losses on twodifferent challenging tasks. Inspired by recent works in constrainedoptimization for deep networks, we propose a way to use those descriptors tosupervise segmentation, without any pixel-level label. Very surprisingly, aslittle as 4 descriptors values per class can approach the performance of asegmentation mask with 65k individual discrete labels. We also found that shapedescriptors can be a valid way to encode anatomical priors about the task,enabling to leverage expert knowledge without additional annotations. Ourimplementation is publicly available and can be easily extended to other tasksand descriptors: https://github.com/hkervadec/shape_descriptors

Beyond pixel-wise supervision for segmentation: A few global shape descriptors might be surprisingly good!