Segmentation of 2D and 3D Objects with Intrinsically Similarity Invariant Shape Regularisers

This paper presents a 2D and 3D variational segmentation approach based on a similarity invariant, i.e., translation, scaling, and rotation invariant shape regulariser. Indeed, shape moments of order up to 2 for shapes with limited symmetries can be combined to provide a shape normalisation for the group of similarities. In order to obtain a segmentation objective function, a two-means or two-local-means data term is added to it. Segmentation is then obtained by standard gradient descent on it. We demonstrate the capabilities of the approach on a series of experiments, of different complexity levels. We specifically target rat brain shapes in MR scans, where the setting is complex, because of bias field and complex anatomical structures. Our last experiments show that our approach is indeed capable of recovering brain shapes automatically.