International audienceConvolutional neural networks (CNN) have had unprecedented success in medical imaging and, in particular, in medical image segmentation. However, despite the fact that segmentation results are closer than ever to the inter-expert variability, CNNs are not immune to producing anatomically inaccurate segmentations, even when built upon a shape prior. In this paper, we present a framework for producing cardiac image segmentation maps that are guaranteed to respect pre-defined anatomical criteria, while remaining within the inter-expert variability. The idea behind our method is to use a well-trained CNN, have it process cardiac images, identify the anatomically implausible results and warp these results toward the closest...