  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.
