Real-world problems are often multi-objective, with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail providing multiple predictions that span and uniformly cover the Pareto front of all optimal trade-off solutions. We propose a novel approach for multi-objective training of neural networks to approximate the Pareto front during inference. In our approach, we train the neural networks multi-objectively using a dynamic loss function, wherein each network’s losses (corresponding to multiple objectives) are weighted by their hypervolume maximizing gradients. Experiments on different multi-objective problems show that our approach returns well-spread outputs across different trade-offs on the approximated Pareto front without requiring the trade-off vectors to be specified a priori. Further, results of comparisons with the state-of-the-art approaches highlight the added value of our proposed approach, especially in cases where the Pareto front is asymmetric.

Manual or automatic delineation of the esophageal tumor in CT images is known to be very challenging. This is due to the low contrast between the tumor and adjacent tissues, the anatomical variation of the esophagus, as well as the occasional presence of foreign bodies (e.g. feeding tubes). Physicians therefore usually exploit additional knowledge such as endoscopic findings, clinical history, additional imaging modalities like PET scans. Achieving his additional information is time-consuming, while the results are error-prone and might lead to non-deterministic results. In this paper we aim to investigate if and to what extent a simplified clinical workflow based on CT alone, allows one to automatically segment the esophageal tumor with sufficient quality. For this purpose, we present a fully automatic end-to-end esophageal tumor segmentation method based on convolutional neural networks (CNNs). The proposed network, called Dilated Dense Attention Unet (DDAUnet), leverages spatial and channel attention gates in each dense block to selectively concentrate on determinant feature maps and regions. Dilated convolutional layers are used to manage GPU memory and increase the network receptive field. We collected a dataset of 792 scans from 288 distinct patients including varying anatomies with air pockets, feeding tubes and proximal tumors. Repeatability and reproducibility studies were conducted for three distinct splits of training and validation sets. The proposed network achieved a DSC value of 0.79 ± 0.20, a mean surface distance of 5.4 ± 20.2mm and 95% Hausdorff distance of 14.7 ± 25.0mm for 287 test scans, demonstrating promising results with a simplified clinical workflow based on CT alone. Our code is publicly available via https://github.com/yousefis/DenseUnet_Esophagus_Segmentation.