Deep Shape Regression for Planar Curves with Multimodal Covariates

The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional covariance. To estimate this covariance surface, we propose a novel deep conditional covariance smoother with modality-specific encoders - e.g. splines for scalar covariates and convolutional networks for images, which classical spline smoothers cannot accommodate. Our model is by construction invariant to the translation, rotation and scaling of the input curves and handles sparsely and irregularly sampled curves. We further provide an algorithm for elastic mean estimation that also removes parametrisation by iterating covariance smoothing, rotational alignment and parametrisation alignment. We illustrate the method on simulated outlines with known conditional mean and multimodal covariates, and give a first application to hippocampal outlines from the ADNI cohort, recovering covariate effects consistent with the literature. Code is available at https://github.com/mpff/dnn-shapes.

Better than Average: Spatially-Aware Aggregation of Segmentation Uncertainty Improves Downstream Performance

Uncertainty Quantification (UQ) is crucial for ensuring the reliability of automated image segmentations in safety-critical domains like biomedical image analysis or autonomous driving. In segmentation, UQ generates pixel-wise uncertainty scores that must be aggregated into image-level scores for downstream tasks like Out-of-Distribution (OoD) or failure detection. Despite routine use of aggregation strategies, their properties and impact on downstream task performance have not yet been comprehensively studied. Global Average is the default choice, yet it does not account for spatial and structural features of segmentation uncertainty. Alternatives like patch-, class- and threshold-based strategies exist, but lack systematic comparison, leading to inconsistent reporting and unclear best practices. We address this gap by (1) formally analyzing properties, limitations, and pitfalls of common strategies; (2) proposing novel strategies that incorporate spatial uncertainty structure and (3) benchmarking their performance on OoD and failure detection across ten datasets that vary in image geometry and structure. We find that aggregators leveraging spatial structure yield stronger performance in both downstream tasks studied. However, the performance of individual aggregators depends heavily on dataset characteristics, so we (4) propose a meta-aggregator that integrates multiple aggregators and performs robustly across datasets.