57 research outputs found
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 crossattention’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
CFD to Quantify Idealized Intra-Aneurysmal Blood Flow in Response to Regular and Flow Diverter Stent Treatment
Cerebral aneurysms are pathological dilatations of the vessels supplying the brain. They carry a certain risk of rupture, which in turn, results in a high risk of mortality and morbidity. Flow diverters (FDs) are high-density meshed stents which are implanted in the vessel segment harboring an intracranial aneurysm to cover the entrance of the aneurysm, thus reducing the blood flow into the aneurysm, promoting thrombosis formation and stable occlusion, which prevents rupture or growth of the aneurysm. In the present study, the blood flow in an idealized aneurysm, treated with an FD stent and a regular stent (RS), were modeled and analyzed considering their design, surface area porosity, and flow reduction to investigate the quantitative and qualitative effect of the stent on intra-aneurysmal hemodynamics. CFD simulations were conducted before and after treatment. Significant reductions were observed for most hemodynamic variables with the use of stents, during both the peak systolic and late diastolic cardiac cycles. FD reduces the intra-aneurysmal wall shear stress (WSS), inflow, and aneurysmal flow velocity, and increases the turnover time when compared to the RS;therefore, the possibility of aneurysm thrombotic occlusion is likely to increase, reducing the risk of rupture in cerebral aneurysms
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
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