Differentiable minimin shape distance for incorporating topological priors in biomedical imaging

In the application of curve evolution and level set methods to biomedical image analysis, the incorporation of geometric priors for isolated shapes has been proved useful. On the other hand, the inclusion of a priori topological information concerning the relationship of multiple shapes remains a challenge. In this paper, we propose a differentiable minimin shape distance (DMSD) that is indicative of the topological relation between shapes. A curve evolution equation based on its first variation is derived and this enables us to incorporate this prior into a curve evolution framework. We demonstrate the application of the DMSD by proposing an extension to the Chan-Vese image segmentation model to incorporate topological prior information for challenging image segmentation tasks.