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