Shape and geometry preserving loss functions for computed tomography image segmentation

Segmentation networks are not explicitly imposed to learn global invariants of an image, such as the shape of an object and the geometry between multiple objects, when they are trained with a standard loss function. On the other hand, especially when there exists a limited amount of training data, incorporating such invariants into network training may help regularize the training, provided that these invariants are the intrinsic characteristics of the objects to be segmented. This thesis addresses this issue by introducing the topology-aware loss function, with alternative formulations, that penalizes shape and geometry dissimilarities between the ground truth and prediction through persistent homology. We use three different topological filtration functions, leading to alternative formulations of the topology-aware loss function. After obtaining the persistence diagrams of both the ground truth and prediction maps by a topological filtration function, the topological dissimilarity is calculated by the use of the Wasserstein distance between the corresponding persistence diagrams. Our experiments on two different datasets of CT images reveal that the increase in the network's performance is significant.