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3D delineation of anatomical structures is a cardinal goal in medical imaginganalysis. Prior to deep learning, statistical shape models that imposedanatomical constraints and produced high quality surfaces were a coretechnology. Prior to deep learning, statistical shape models that imposedanatomical constraints and produced high quality surfaces were a coretechnology. Today fully-convolutional networks (FCNs), while dominant, do notoffer these capabilities. We present deep implicit statistical shape models(DISSMs), a new approach to delineation that marries the representation powerof convolutional neural networks (CNNs) with the robustness of SSMs. DISSMs usea deep implicit surface representation to produce a compact and descriptiveshape latent space that permits statistical models of anatomical variance. Toreliably fit anatomically plausible shapes to an image, we introduce a novelrigid and non-rigid pose estimation pipeline that is modelled as a Markovdecision process(MDP). We outline a training regime that includes invertedepisodic training and a deep realization of marginal space learning (MSL).Intra-dataset experiments on the task of pathological liver segmentationdemonstrate that DISSMs can perform more robustly than three leading FCNmodels, including nnU-Net: reducing the mean Hausdorff distance (HD) by7.7-14.3mm and improving the worst case Dice-Sorensen coefficient (DSC) by1.2-2.3%. More critically, cross-dataset experiments on a dataset directlyreflecting clinical deployment scenarios demonstrate that DISSMs improve themean DSC and HD by 3.5-5.9% and 12.3-24.5mm, respectively, and the worst-caseDSC by 5.4-7.3%. These improvements are over and above any benefits fromrepresenting delineations with high-quality surface.

Deep Implicit Statistical Shape Models for 3D Medical Image Delineation