Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis
arXiv:2606. 17022v1 Announce Type: cross Abstract: A central objective of machine learning is to identify structure and patterns in data.
arXiv:2602. 11467v2 Announce Type: replace Abstract: Understanding how anatomical shapes evolve in response to developmental covariates - and quantifying their spatially varying uncertainties - is critical in healthcare research.
arXiv:2606. 17022v1 Announce Type: cross Abstract: A central objective of machine learning is to identify structure and patterns in data.
arXiv:2606. 15837v1 Announce Type: cross Abstract: Deep neural networks (DNNs) frequently fail to generalize to out-of-distribution (OOD) medical images because of variations in scanners and acquisition protocols.
arXiv:2603. 04024v2 Announce Type: replace-cross Abstract: Ambiguous 3D medical image segmentation often involves boundaries where different expert delineations are non-identical yet clinically plausible.
arXiv:2607. 19600v1 Announce Type: cross Abstract: 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.
arXiv:2608. 02306v1 Announce Type: cross Abstract: We introduce a mathematical framework for shape comparison based on mapping functions from the shape domain to a common reference domain.
arXiv:2608. 09182v1 Announce Type: cross Abstract: Accurate landmark localization in medical images is a fundamental step for quantitative clinical measurement and downstream analysis.
arXiv:2608. 14766v1 Announce Type: cross Abstract: Uncertainty estimation is critical for the safe clinical deployment of deep learning in medical image segmentation, with aleatoric uncertainty theoretically designed to capture irreducible data ambiguity.
arXiv:2603.18792v3 Announce Type: replace Abstract: Uncertainty quantification (UQ) is crucial in safety-critical applications such as medical image segmentation. Total uncertainty is typically decom...
arXiv:2608. 09938v1 Announce Type: cross Abstract: Hyperelastic deformations are highly sensitive to domain geometry and boundary conditions, making generalization across both a critical capability for neural operators applied to these problems.
arXiv:2608. 00187v1 Announce Type: cross Abstract: Correspondence-based statistical shape modeling (SSM) is vital for population-level morphometric analysis, but conventional pipelines assume clean, fully registered surfaces.
We introduce SMART, a framework for learning a flexible, interpretable, and scalable spatio-temporal brain atlas from longitudinal high-resolution 3D medical images. Existing approaches to spatio-temporal atlas construction rely on black-box generative models that lack flexibility, limit interpretability, and struggle to scale to high-dimensional data.
The paper investigates how pre‑training strategy, dataset size, and domain affect uncertainty estimation in vision medical foundation models. It compares point‑prediction calibration with conformal (region) prediction across retinal, histopathological, and chest X‑ray models, finding that domain‑specific, self‑supervised pre‑training yields better calibration and more efficient conformal sets. The study shows that standard recalibration alone cannot fully reconcile uncertainty differences between models trained on different data sources.