Marcus Nordström

Marcus Nordström, Henrik Hult, Atsuto Maki et al.

This paper presents a study on the soft-Dice loss, one of the most popular loss functions in medical image segmentation, for situations where noise is present in target labels. In particular, the set of optimal solutions are characterized and sharp bounds on the volume bias of these solutions are provided. It is further shown that a sequence of soft segmentations converging to optimal soft-Dice also converges to optimal Dice when converted to hard segmentations using thresholding. This is an important result because soft-Dice is often used as a proxy for maximizing the Dice metric. Finally, experiments confirming the theoretical results are provided.

Marcus Nordström, Henrik Hult, Jonas Söderberg et al.

We study two of the most popular performance metrics in medical image segmentation, Accuracy and Dice, when the target labels are noisy. For both metrics, several statements related to characterization and volume properties of the set of optimal segmentations are proved, and associated experiments are provided. Our main insights are: (i) the volume of the solutions to both metrics may deviate significantly from the expected volume of the target, (ii) the volume of a solution to Accuracy is always less than or equal to the volume of a solution to Dice and (iii) the optimal solutions to both of these metrics coincide when the set of feasible segmentations is constrained to the set of segmentations with the volume equal to the expected volume of the target.

Marcus Nordström, Henrik Hult, Atsuto Maki

This work presents a study on label noise in medical image segmentation by considering a noise model based on Gaussian field deformations. Such noise is of interest because it yields realistic looking segmentations and because it is unbiased in the sense that the expected deformation is the identity mapping. Efficient methods for sampling and closed form solutions for the marginal probabilities are provided. Moreover, theoretically optimal solutions to the loss functions cross-entropy and soft-Dice are studied and it is shown how they diverge as the level of noise increases. Based on recent work on loss function characterization, it is shown that optimal solutions to soft-Dice can be recovered by thresholding solutions to cross-entropy with a particular a priori unknown threshold that efficiently can be computed. This raises the question whether the decrease in performance seen when using cross-entropy as compared to soft-Dice is caused by using the wrong threshold. The hypothesis is validated in 5-fold studies on three organ segmentation problems from the TotalSegmentor data set, using 4 different strengths of noise. The results show that changing the threshold leads the performance of cross-entropy to go from systematically worse than soft-Dice to similar or better results than soft-Dice.

Ture Hassler, Ida Åkerholm, Marcus Nordström et al.

Unet and its variations have been standard in semantic image segmentation, especially for computer assisted radiology. Current Unet architectures iteratively downsample spatial resolution while increasing channel dimensions to preserve information content. Such a structure demands a large memory footprint, limiting training batch sizes and increasing inference latency. Channel pruning compresses Unet architecture without accuracy loss, but requires lengthy optimization and may not generalize across tasks and datasets. By investigating Unet pruning, we hypothesize that the final structure is the crucial factor, not the channel selection strategy of pruning. Based on our observations, we propose a lean Unet architecture (LUnet) with a compact, flat hierarchy where channels are not doubled as resolution is halved. We evaluate on a public MRI dataset allowing comparable reporting, as well as on two internal CT datasets. We show that a state-of-the-art pruning solution (STAMP) mainly prunes from the layers with the highest number of channels. Comparatively, simply eliminating a random channel at the pruning-identified layer or at the largest layer achieves similar or better performance. Our proposed LUnet with fixed architectures and over 30 times fewer parameters achieves performance comparable to both conventional Unet counterparts and data-adaptively pruned networks. The proposed lean Unet with constant channel count across layers requires far fewer parameters while achieving performance superior to standard Unet for the same total number of parameters. Skip connections allow Unet bottleneck channels to be largely reduced, unlike standard encoder-decoder architectures requiring increased bottleneck channels for information propagation.