Medical Image Segmentation Using the Equivariance Under Diffeomorphisms Framework

Medical image segmentation plays a crucial role in medical image analysis, computer-aided detection and diagnosis, treatment planning, and etc. However, it is still challenging to obtain an accurate segmentation result due to irregularity of organ contours or lack of labeled dataset. In this work, we formulate an important property for image segmentation: equivariance under diffeomorphisms, that is, the segmentation results are independent of the small diffeomorphic deformations. Based on this property, we propose a novel Equivariance under Diffeomorphism (ED) framework for medical image segmentation using the optimal transport maps. Experiments are carried out to evaluate the proposed method on two publicly available datasets, including a colon dataset and a hepatic vessels dataset. Results show that the proposed method outperforms the existing method in terms of two metrics Jaccard and Dice, respectively.