Topology-Aware Loss for Aorta and Great Vessel Segmentation in Computed Tomography Images

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, incorporating such invariants into network training may help improve performance for various segmentation tasks when they are the intrinsic characteristics of the objects to be segmented. One example is segmentation of aorta and great vessels in computed tomography (CT) images where vessels are found in a particular geometry in the body due to the human anatomy and they mostly seem as round objects on a 2D CT image. This paper addresses this issue by introducing a new topology-aware loss function that penalizes topology dissimilarities between the ground truth and prediction through persistent homology. Different from the previously suggested segmentation network designs, which apply the threshold filtration on a likelihood function of the prediction map and the Betti numbers of the ground truth, this paper proposes to apply the Vietoris-Rips filtration to obtain persistence diagrams of both ground truth and prediction maps and calculate the dissimilarity with the Wasserstein distance between the corresponding persistence diagrams. The use of this filtration has advantage of modeling shape and geometry at the same time, which may not happen when the threshold filtration is applied. Our experiments on 4327 CT images of 24 subjects reveal that the proposed topology-aware loss function leads to better results than its counterparts, indicating the effectiveness of this use.