Deep Elastica For Image Segmentation

Image segmentation is a fundamental topic in image processing and has been studied for many decades. Deep learning-based supervised segmentation models have achieved state-of-the-art performance, but most of them are limited by using pixel-wise loss functions for training without geometrical constraints. Inspired by the Euler's Elastica model and recent active contour models introduced into deep learning, we propose a novel active contour with an elastic (ACE) loss function. The ACE loss function incorporates Elastica knowledge as geometrically-natural constraints for the image segmentation tasks. In the ACE loss function, we introduce the mean curvature, i.e. the average of all principal curvatures, as a more compelling image prior to represent the curvature. Furthermore, based on the mean curvature definition, we propose a fast solution (Fast-ACE) to approximate our ACE loss with Laplace operators for three-dimensional (3D) image segmentation. We evaluate our ACE loss and Fast-ACE loss functions on one two-dimensional (2D) dataset and one 3D biomedical image dataset. Our results show that the proposed loss function outperforms other mainstream loss functions when different segmentation networks are used. Our source code is available at https://github.com/HiLab-git/ACELoss.