FourierLoss: Shape-aware loss function with Fourier descriptors

Abstract

Encoder–decoder networks are commonly used for medical image segmentation tasks. When they are trained with a standard loss function, these networks are not explicitly enforced to preserve the shape integrity of an object in an image. However, this ability of the network is important to obtain more accurate results, especially when there is a low-contrast difference between the object and its surroundings. To respond this issue, this work introduces a new shape-aware loss function, which we name FourierLoss. This loss function relies on quantifying the shape dissimilarity between the ground truth and the predicted segmentation maps through the Fourier descriptors calculated on the objects of these maps, and penalizing this dissimilarity in network training. Different than the previous studies, FourierLoss offers an adaptive loss function with trainable hyperparameters that control the importance of the level of the shape details that the network is enforced to learn in the training process. This control is achieved by the proposed adaptive loss update mechanism, which end-to-end learns the hyperparameters simultaneously with the network weights by backpropagation. As a result of using this mechanism, the network can dynamically change its attention from learning the general outline of an object to learning the details of its contour points, or vice versa, in different training epochs. Working on two different datasets, our experiments revealed that the proposed adaptive shape-aware loss function led to statistically significantly better results for liver segmentation, compared to its counterparts. © 2025 Elsevier B.V.