The contour depth methodology enables non-parametric summarization of contour ensembles by extracting their representatives, confidence bands, and outliers for visualization (via contour boxplots) and robust downstream procedures. We address two shortcomings of these methods. Firstly, we significantly expedite the computation and recomputation of Inclusion Depth (ID), introducing a linear-time algorithm for epsilon ID, a variant used for handling ensembles with contours with multiple intersections. We also present the inclusion matrix, which contains the pairwise inclusion relationships between contours, and leverage it to accelerate the recomputation of ID. Secondly, extending beyond the single distribution assumption, we present the Relative Depth (ReD), a generalization of contour depth for ensembles with multiple modes. Building upon the linear-time eID, we introduce CDclust, a clustering algorithm that untangles ensemble modes of variation by optimizing ReD. Synthetic and real datasets from medical image segmentation and meteorological forecasting showcase the speed advantages, illustrate the use case of progressive depth computation and enable non-parametric multimodal analysis. To promote research and adoption, we offer the contour-depth Python package.

Background and purpose: Retrospective dose evaluation for organ-at-risk auto-contours has previously used small cohorts due to additional manual effort required for treatment planning on auto-contours. We aimed to do this at large scale, by a) proposing and assessing an automated plan optimization workflow that used existing clinical plan parameters and b) using it for head-and-neck auto-contour dose evaluation. Materials and methods: Our automated workflow emulated our clinic's treatment planning protocol and reused existing clinical plan optimization parameters. This workflow recreated the original clinical plan (P_OG) with manual contours (P_MC) and evaluated the dose effect (P_OG-P_MC) on 70 photon and 30 proton plans of head-and-neck patients. As a use-case, the same workflow (and parameters) created a plan using auto-contours (P_AC) of eight head-and-neck organs-at-risk from a commercial tool and evaluated their dose effect (P_MC-P_AC). Results: For plan recreation (P_OG-P_MC), our workflow had a median impact of 1.0% and 1.5% across dose metrics of auto-contours, for photon and proton respectively. Computer time of automated planning was 25% (photon) and 42% (proton) of manual planning time. For auto-contour evaluation (P_MC-P_AC), we noticed an impact of 2.0% and 2.6% for photon and proton radiotherapy. All evaluations had a median ΔNTCP (Normal Tissue Complication Probability) less than 0.3%. Conclusions: The plan replication capability of our automated program provides a blueprint for other clinics to perform auto-contour dose evaluation with large patient cohorts. Finally, despite geometric differences, auto-contours had a minimal median dose impact, hence inspiring confidence in their utility and facilitating their clinical adoption.

Ensembles of contours arise in various applications like simulation, computer-Aided design, and semantic segmentation. Uncovering ensemble patterns and analyzing individual members is a challenging task that suffers from clutter. Ensemble statistical summarization can alleviate this issue by permitting analyzing ensembles' distributional components like the mean and median, confidence intervals, and outliers. Contour boxplots, powered by Contour Band Depth (CBD), are a popular non-parametric ensemble summarization method that benefits from CBD's generality, robustness, and theoretical properties. In this work, we introduce Inclusion Depth (ID), a new notion of contour depth with three defining characteristics. First, ID is a generalization of functional Half-Region Depth, which offers several theoretical guarantees. Second, ID relies on a simple principle: The inside/outside relationships between contours. This facilitates implementing ID and understanding its results. Third, the computational complexity of ID scales quadratically in the number of members of the ensemble, improving CBD's cubic complexity. This also in practice speeds up the computation enabling the use of ID for exploring large contour ensembles or in contexts requiring multiple depth evaluations like clustering. In a series of experiments on synthetic data and case studies with meteorological and segmentation data, we evaluate ID's performance and demonstrate its capabilities for the visual analysis of contour ensembles.

Literature on medical imaging segmentation claims that hybrid UNet models containing both Transformer and convolutional blocks perform better than purely convolutional UNet models. This recently touted success of hybrid Transformers warrants an investigation into which of its components contribute to its performance. Also, previous work has a limitation of analysis only at fixed dataset scales as well as unfair comparisons with other models where parameter counts are not equivalent. Here, we investigate the performance of a hybrid Transformer network i.e. the nnFormer for organ segmentation in prostate CT scans. We do this in context of replacing its various components and by constructing learning curves by plotting model performance at different dataset scales. To compare with literature, the first experiment replaces all the shifted-window(swin) Transformer blocks of the nnFormer with convolutions. Results show that the convolution prevails as the data scale increases. In the second experiment, to reduce complexity, the self-attention mechanism within the swin-Transformer block is replaced with an similar albeit simpler spatial mixing operation i.e. max-pooling. We observe improved performance for max-pooling in smaller dataset scales, indicating that the window-based Transformer may not be the best choice in both small and larger dataset scales. Finally, since convolution has an inherent local inductive bias of positional information, we conduct a third experiment to imbibe such a property to the Transformer by exploring two kinds of positional encodings. The results show that there are insignificant improvements after adding positional encoding, indicating the hybrid swin-Transformers deficiency in capturing positional information given our dataset at its various scales. Through this work, we hope to motivate the community to use learning curves under fair experimental settings to evaluate the efficacy of newer architectures like Transformers for their medical imaging tasks. Code is available on https://github.com/prerakmody/ window-transformer-prostate-segmentation.