A Differentiable Convolutional Distance Transform Layer for Improved Image Segmentation

Pham, Duc Duy; Dovletov, Gurbandurdy; Pauli, Josef

In this paper we propose using a novel differentiable convolutional distance transform layer for segmentation networks such as U-Net to regularize the training process. In contrast to related work, we do not need to learn the distance transform, but use an approximation, which can be achieved by means of the convolutional operation. Therefore, the distance transform is directly applicable without previous training and it is also differentiable to ensure the gradient flow during backpropagation. First, we present the derivation of the convolutional distance transform by Karam et al. [6]. Then we address the problem of numerical instability for large images by presenting a cascaded procedure with locally restricted convolutional distance transforms. Afterwards, we discuss the issue of non-binary segmentation outputs for the convolutional distance transform and present our solution attempt for the incorporation into deep segmentation networks. We then demonstrate the feasibility of our proposal in an ablation study on the publicly available SegTHOR data set.