Semi-Implicit Neural Solver for Time-dependent Partial Differential Equations

Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over explicit ones to improve stability and correctness. However, existing semi-implicit methods are usually iterative and employ a general-purpose solver, which may be sub-optimal for a specific class of PDEs. In this paper, we propose a neural solver to learn an optimal iterative scheme in a data-driven fashion for any class of PDEs. Specifically, we modify a single iteration of a semi-implicit solver using a deep neural network. We provide theoretical guarantees for the correctness and convergence of neural solvers analogous to conventional iterative solvers. In addition to the commonly used Dirichlet boundary condition, we adopt a diffuse domain approach to incorporate a diverse type of boundary conditions, e.g., Neumann. We show that the proposed neural solver can go beyond linear PDEs and applies to a class of non-linear PDEs, where the non-linear component is non-stiff. We demonstrate the efficacy of our method on 2D and 3D scenarios. To this end, we show how our model generalizes to parameter settings, which are different from training; and achieves faster convergence than semi-implicit schemes

Focused Decoding Enables 3D Anatomical Detection by Transformers

Detection Transformers represent end-to-end object detection approaches based on a Transformer encoder-decoder architecture, exploiting the attention mechanism for global relation modeling. Although Detection Transformers deliver results on par with or even superior to their highly optimized CNN-based counterparts operating on 2D natural images, their success is closely coupled to access to a vast amount of training data. This, however, restricts the feasibility of employing Detection Transformers in the medical domain, as access to annotated data is typically limited. To tackle this issue and facilitate the advent of medical Detection Transformers, we propose a novel Detection Transformer for 3D anatomical structure detection, dubbed Focused Decoder. Focused Decoder leverages information from an anatomical region atlas to simultaneously deploy query anchors and restrict the cross-attention's field of view to regions of interest, which allows for a precise focus on relevant anatomical structures. We evaluate our proposed approach on two publicly available CT datasets and demonstrate that Focused Decoder not only provides strong detection results and thus alleviates the need for a vast amount of annotated data but also exhibits exceptional and highly intuitive explainability of results via attention weights. Our code is available at https://github.com/bwittmann/transoar.Comment: Accepted for publication at the Journal of Machine Learning for Biomedical Imaging (MELBA) https://melba-journal.org/2023:00

Focused Decoding Enables 3D Anatomical Detection by Transformers

Detection Transformers represent end-to-end object detection approaches based on a Transformer encoder-decoder architecture, exploiting the attention mechanism for global relation modeling. Although Detection Transformers deliver results on par with or even superior to their highly optimized CNN-based counterparts operating on 2D natural images, their success is closely coupled to access to a vast amount of training data. This, however, restricts the feasibility of employing Detection Transformers in the medical domain, as access to annotated data is typically limited. To tackle this issue and facilitate the advent of medical Detection Transformers, we propose a novel Detection Transformer for 3D anatomical structure detection, dubbed Focused Decoder. Focused Decoder leverages information from an anatomical region atlas to simultaneously deploy query anchors and restrict the cross-attention's field of view to regions of interest, which allows for a precise focus on relevant anatomical structures. We evaluate our proposed approach on two publicly available CT datasets and demonstrate that Focused Decoder not only provides strong detection results and thus alleviates the need for a vast amount of annotated data but also exhibits exceptional and highly intuitive explainability of results via attention weights. Code for Focused Decoder is available in our medical Vision Transformer library this http URL

Topologically faithful image segmentation via induced matching of persistence barcodes

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching

Evaluating the Robustness of Self-Supervised Learning in Medical Imaging

Self-supervision has demonstrated to be an effective learning strategy when training target tasks on small annotated data-sets. While current research focuses on creating novel pretext tasks to learn meaningful and reusable representations for the target task, these efforts obtain marginal performance gains compared to fully-supervised learning. Meanwhile, little attention has been given to study the robustness of networks trained in a self-supervised manner. In this work, we demonstrate that networks trained via self-supervised learning have superior robustness and generalizability compared to fully-supervised learning in the context of medical imaging. Our experiments on pneumonia detection in X-rays and multi-organ segmentation in CT yield consistent results exposing the hidden benefits of self-supervision for learning robust feature representations