arXiv subjects

David Bernstein

Publications and source records attributed to David Bernstein.

5 recordsLinked to original sources

arXiv2026

Latent-to-Latent Flow for Volumetric Stochastic Segmentation

Uncertainty arising from inter-observer variability in medical image segmentation plays an important role in developing treatment plans. Research in this area is inhibited by the lack of multiple annotations for large-scale medical datasets, especially for volumetric data, which suffers from additional scaling and computational complexity challenges. Flow matching has emerged as a powerful framework for generative modelling and has also been demonstrated to maintain strong performance when working with latent representations of images. In this work, we introduce a latent-to-latent flow technique for stochastic segmentation of medical volumes via encoded representations of both the image and label space. We evaluate our method on two challenging applications covering delineation uncertainty for radiotherapy planning and multiple organ structure segmentation, improving efficiency up to 14x compared with full resolution models while maintaining clinically relevant performance.

cs.CV↗

arXiv2021

Learning from Partially Overlapping Labels: Image Segmentation under Annotation Shift

Scarcity of high quality annotated images remains a limiting factor for training accurate image segmentation models. While more and more annotated datasets become publicly available, the number of samples in each individual database is often small. Combining different databases to create larger amounts of training data is appealing yet challenging due to the heterogeneity as a result of differences in data acquisition and annotation processes, often yielding incompatible or even conflicting information. In this paper, we investigate and propose several strategies for learning from partially overlapping labels in the context of abdominal organ segmentation. We find that combining a semi-supervised approach with an adaptive cross entropy loss can successfully exploit heterogeneously annotated data and substantially improve segmentation accuracy compared to baseline and alternative approaches.

cs.CV↗

arXiv2008

Generating Initial Data in General Relativity using Adaptive Finite Element Methods

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear elliptic system. We derive weak formulations of the coupled constraints, and review some new developments in the solution theory for the constraints in the cases of constant mean extrinsic curvature (CMC) data, near-CMC data, and arbitrarily prescribed mean extrinsic curvature data. We then outline some recent results on a priori and a posteriori error estimates for a broad class of Galerkin-type approximation methods for this system which includes techniques such as finite element, wavelet, and spectral methods. We then use these estimates to construct an adaptive finite element method (AFEM) for solving this system numerically, and outline some new convergence and optimality results. We then describe in some detail an implementation of the methods using the FETK software package, which is an adaptive multilevel finite element code designed to solve nonlinear elliptic and parabolic systems on Riemannian manifolds. We finish by describing a simplex mesh generation algorithm for compact binary objects, and then look at a detailed example showing the use of FETK for numerical solution of the constraints.

gr-qc↗

arXiv1994

Event Horizons of Numerical Black Holes

We have developed a powerful and efficient method for locating the event horizon of a black hole spacetime, making possible the study of the dynamics of event horizons in numerical relativity. We describe the method and apply it to a colliding black hole spacetime.

gr-qc↗

arXiv1994

Dynamics of Apparent and Event Horizons

The dynamics of apparent and event horizons of various black hole spacetimes, including those containing distorted, rotating and colliding black holes, are studied. We have developed a powerful and efficient new method for locating the event horizon, making possible the study of both types of horizons in numerical relativity. We show that both the event and apparent horizons, in all dynamical black hole spacetimes studied, oscillate with the quasinormal frequency.

gr-qc↗