FourierLoss: Shape-Aware Loss Function with Fourier Descriptors

Encoder-decoder networks become a popular choice for various 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. In response to 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 their objects, 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 2879 computed tomography images of 93 subjects, our experiments revealed that the proposed adaptive shape-aware loss function led to statistically significantly better results for liver segmentation, compared to its counterparts.

FourierNet: Shape-Preserving Network for Henle's Fiber Layer Segmentation in Optical Coherence Tomography Images

The Henle's fiber layer (HFL) in the retina carries valuable information on the macular condition of an eye. However, in the common practice, this layer is not separately segmented but rather included in the outer nuclear layer since it is difficult to perceive HFL contours on standard optical coherence tomography (OCT) imaging. Due to its variable reflectivity under an imaging beam, delineating the HFL contours necessitates directional OCT, which requires additional imaging. This paper addresses this issue by introducing a shape-preserving network, FourierNet, that achieves HFL segmentation in standard OCT scans with the target performance obtained when directional OCT scans are used. FourierNet is a new cascaded network design that puts forward the idea of benefiting the shape prior of HFL in the network training. This design proposes to represent the shape prior by extracting Fourier descriptors on the HFL contours and defining an additional regression task of learning these descriptors. It then formulates HFL segmentation as concurrent learning of regression and classification tasks, in which Fourier descriptors are estimated from an input image to encode the shape prior and used together with the input image to construct the HFL segmentation map. Our experiments on 1470 images of 30 OCT scans reveal that quantifying the HFL shape with Fourier descriptors and concurrently learning them with the main task of HFL segmentation lead to better results. This indicates the effectiveness of designing a shape-preserving network to improve HFL segmentation by reducing the need to perform directional OCT imaging.