Abdominal aortic aneurysms (AAAs) are progressive focal dilatations of the abdominal aorta. AAAs may rupture, with fatal consequences in >80% of cases. Current clinical guidelines recommend elective surgical repair when the maximum AAA diameter exceeds 55 mm in men or 50 mm in women. Patients that do not meet these criteria are periodically monitored, with surveillance intervals based on the maximum AAA diameter. However, this diameter does not take into account the complex relation between the 3D AAA shape and its growth, making standardized intervals potentially unfit. Personalized AAA growth predictions could improve monitoring strategies. We propose to use an SE(3)-symmetric transformer model to predict AAA growth directly on the vascular model surface enriched with local, multi-physical features. In contrast to other works which have parameterized the AAA shape, this representation preserves the vascular surface's anatomical structure and geometric fidelity. We train our model using a longitudinal dataset of 113 computed tomography angiography (CTA) scans of 24 AAA patients at irregularly sampled intervals. After training, our model predicts AAA growth to the next scan moment with a median diameter error of 1.18 mm. We further demonstrate our model's utility to identify whether a patient will become eligible for elective repair within two years (acc = 0.93). Finally, we evaluate our model's generalization on an external validation set consisting of 25 CTAs from 7 AAA patients from a different hospital. Our results show that local directional AAA growth prediction from the vascular surface is feasible and may contribute to personalized surveillance strategies.

Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not widely available, such as 4D flow magnetic resonance imaging (MRI). In this work, we create a surrogate model for hemodynamic flow field estimation, powered by machine learning. We train graph neural networks that include priors about the underlying symmetries and physics, limiting the amount of data required for training. This allows us to train the model using moderately-sized, in-vivo 4D flow MRI datasets, instead of large in-silico datasets obtained by computational fluid dynamics (CFD), as is the current standard. We create an efficient, equivariant neural network by combining the popular PointNet++ architecture with group-steerable layers. To incorporate the physics-informed priors, we derive an efficient discretisation scheme for the involved differential operators. We perform extensive experiments in carotid arteries and show that our model can accurately estimate low-noise hemodynamic flow fields in the carotid artery. Moreover, we show how the learned relation between geometry and hemodynamic quantities transfers to 3D vascular models obtained using a different imaging modality than the training data. This shows that physics-informed graph neural networks can be trained using 4D flow MRI data to estimate blood flow in unseen carotid artery geometries.

The orientation of a blood vessel as visualized in 3D medical images is an important descriptor of its geometry that can be used for centerline extraction and subsequent segmentation, labeling, and visualization. Blood vessels appear at multiple scales and levels of tortuosity, and determining the exact orientation of a vessel is a challenging problem. Recent works have used 3D convolutional neural networks (CNNs) for this purpose, but CNNs are sensitive to variations in vessel size and orientation. We present SIRE: a scale-invariant rotation-equivariant estimator for local vessel orientation. SIRE is modular and has strongly generalizing properties due to symmetry preservations. SIRE consists of a gauge equivariant mesh CNN (GEM-CNN) that operates in parallel on multiple nested spherical meshes with different sizes. The features on each mesh are a projection of image intensities within the corresponding sphere. These features are intrinsic to the sphere and, in combination with the gauge equivariant properties of GEM-CNN, lead to SO(3) rotation equivariance. Approximate scale invariance is achieved by weight sharing and use of a symmetric maximum aggregation function to combine predictions at multiple scales. Hence, SIRE can be trained with arbitrarily oriented vessels with varying radii to generalize to vessels with a wide range of calibres and tortuosity. We demonstrate the efficacy of SIRE using three datasets containing vessels of varying scales; the vascular model repository (VMR), the ASOCA coronary artery set, and an in-house set of abdominal aortic aneurysms (AAAs). We embed SIRE in a centerline tracker which accurately tracks large calibre AAAs, regardless of the data SIRE is trained with. Moreover, a tracker can use SIRE to track small-calibre tortuous coronary arteries, even when trained only with large-calibre, non-tortuous AAAs. Additional experiments are performed to verify the rotational equivariant and scale invariant properties of SIRE. In conclusion, by incorporating SO(3) and scale symmetries, SIRE can be used to determine orientations of vessels outside of the training domain, offering a robust and data-efficient solution to geometric analysis of blood vessels in 3D medical images.

Abstract. Diffeomorphic registration frameworks such as large deformation diffeomorphic metric mapping (LDDMM) are used in computer graphics and the medical domain for atlas building, statistical latent modeling, and pairwise and groupwise registration. In recent years, researchers have developed neural network–based approaches regarding diffeomorphic registration to improve the accuracy and computational efficiency of traditional methods. In this work, we focus on a limitation of neural network–based atlas building and statistical latent modeling methods, namely that they either (i) are resolution dependent or (ii) disregard any data- or problem-specific geometry needed for proper mean-variance analysis. In particular, we overcome this limitation by designing a novel encoder based on resolution-independent implicit neural representations. The encoder achieves resolution invariance for LDDMM-based statistical latent modeling. Additionally, the encoder adds LDDMM Riemannian geometry to resolution-independent deep learning models for statistical latent modeling. We investigate how the Riemannian geometry improves latent modeling and is required for a proper mean-variance analysis. To highlight the benefit of resolution independence for LDDMM-based data variability modeling, we show that our approach outperforms current neural network–based LDDMM latent code models. Our work paves the way for more research into how Riemannian geometry; shape, respectively, image analysis; and deep learning can be combined.

Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification. This study empirically investigates the latter and expands the understanding of frequency shortcuts. First, we perform experiments on synthetic datasets, designed to have a bias in different frequency bands. Our results demonstrate that NNs tend to find simple solutions for classification, and what they learn first during training depends on the most distinctive frequency characteristics, which can be either low- or high-frequencies. Second, we confirm this phenomenon on natural images. We propose a metric to measure class-wise frequency characteristics and a method to identify frequency shortcuts. The results show that frequency shortcuts can be texture-based or shape-based, depending on what best simplifies the objective. Third, we validate the transferability of frequency shortcuts on out-of-distribution (OOD) test sets. Our results suggest that frequency shortcuts can be transferred across datasets and cannot be fully avoided by larger model capacity and data augmentation. We recommend that future research should focus on effective training schemes mitigating frequency shortcut learning. Codes and data are available at https://github.com/nis-research/nn-frequency-shortcuts.

Recently, super-resolution ultrasound imaging with ultrasound localization microscopy (ULM) has received much attention. However, ULM relies on low concentrations of microbubbles in the blood vessels, ultimately resulting in long acquisition times. Here, we present an alternative super-resolution approach, based on direct deconvolution of single-channel ultrasound radio-frequency (RF) signals with a one-dimensional dilated convolutional neural network (CNN). This work focuses on low-frequency ultrasound (1.7 MHz) for deep imaging (10 cm) of a dense cloud of monodisperse microbubbles (up to 1000 microbubbles in the measurement volume, corresponding to an average echo overlap of 94%). Data are generated with a simulator that uses a large range of acoustic pressures (5-250 kPa) and captures the full, nonlinear response of resonant, lipid-coated microbubbles. The network is trained with a novel dual-loss function, which features elements of both a classification loss and a regression loss and improves the detection-localization characteristics of the output. Whereas imposing a localization tolerance of 0 yields poor detection metrics, imposing a localization tolerance corresponding to 4% of the wavelength yields a precision and recall of both 0.90. Furthermore, the detection improves with increasing acoustic pressure and deteriorates with increasing microbubble density. The potential of the presented approach to super-resolution ultrasound imaging is demonstrated with a delay-and-sum reconstruction with deconvolved element data. The resulting image shows an order-of-magnitude gain in axial resolution compared to a delay-and-sum reconstruction with unprocessed element data.

Reinforcement learning algorithms have proven to be capable of solving complicated robotics tasks in an end-to-end fashion without any need for hand-crafted features or policies. Especially in the context of robotics, in which the cost of real-world data is usually extremely high, Reinforcement Learning solutions achieving high sample efficiency are needed. In this paper, we propose a framework combining the learning of a low-dimensional state representation, from high-dimensional observations coming from the robot’s raw sensory readings, with the learning of the optimal policy, given the learned state representation. We evaluate our framework in the context of mobile robot navigation in the case of continuous state and action spaces. Moreover, we study the problem of transferring what learned in the simulated virtual environment to the real robot without further retraining using real-world data in the presence of visual and depth distractors, such as lighting changes and moving obstacles. A video of our experiments can be found at: https://youtu.be/rUdGPKr2Wuo.

Reinforcement Learning has been able to solve many complicated robotics tasks without any need for feature engineering in an end-to-end fashion. However, learning the optimal policy directly from the sensory inputs, i.e the observations, often requires processing and storage of a huge amount of data. In the context of robotics, the cost of data from real robotics hardware is usually very high, thus solutions that achieve high sample-efficiency are needed. We propose a method that aims at learning a mapping from the observations into a lower-dimensional state space. This mapping is learned with unsupervised learning using loss functions shaped to incorporate prior knowledge of the environment and the task. Using the samples from the state space, the optimal policy is quickly and efficiently learned. We test the method on several mobile robot navigation tasks in a simulation environment and also on a real robot. A video of our experiments can be found at: https://youtu.be/dgWxmfSv95U.

In an inhomogeneously illuminated photoacoustic image, important information like vascular geometry is not readily available, when only the initial pressure is reconstructed. To obtain the desired information, algorithms for image segmentation are often applied as a post-processing step. In this article, we propose to jointly acquire the photoacoustic reconstruction and segmentation, by modifying a recently developed partially learned algorithm based on a convolutional neural network. We investigate the stability of the algorithm against changes in initial pressures and photoacoustic system settings. These insights are used to develop an algorithm that is robust to input and system settings. Our approach can easily be applied to other imaging modalities and can be modified to perform other high-level tasks different from segmentation. The method is validated on challenging synthetic and experimental photoacoustic tomography data in limited angle and limited view scenarios. It is computationally less expensive than classical iterative methods and enables higher quality reconstructions and segmentations than the state-of-the-art learned and non-learned methods.

In biomedical imaging reliable segmentation of objects (e.g., from small cells up to large organs) is of fundamental importance for automated medical diagnosis. New approaches for multiscale segmentation can considerably improve performance in case of natural variations in intensity, size, and shape. This paper aims at segmenting objects of interest based on shape contours and automatically finding multiple objects with different scales. The overall strategy of this work is to combine nonlinear segmentation with scales spaces and spectral decompositions. We generalize a variational segmentation model based on total variation using Bregman distances to construct an inverse scale space. This offers the new model to be accomplished by a scale analysis approach based on a spectral decomposition of the total variation. As a result we obtain a very efficient, (nearly) parameter-free multiscale segmentation method that comes with an adaptive regularization parameter choice. To address the variety of shapes and scales present in biomedical imaging we analyze synthetic cases clarifying the role of scale and the relationship of Wulff shapes and eigenfunctions. To underline the potential of our approach and to show its wide applicability we address three different experimental biomedical applications. In particular, we demonstrate the added benefit for identifying and classifying circulating tumor cells and present interesting results for network analysis in retina imaging. Due to the nature of underlying nonlinear diffusion, the mathematical concepts in this work offer promising extensions to nonlocal classification problems.

Given a graph where vertices represent alternatives and pairwise comparison data, y_ij, is given on the edges, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with pairwise comparisons. We study the dependence of the statistical ranking problem on the available pairwise data, i.e., pairs (i,j) for which the pairwise comparison data y_ij is known, and propose a framework to identify data which, when augmented with the current dataset, maximally increases the Fisher information of the ranking. Under certain assumptions, the data collection problem decouples, reducing to a problem of finding an edge set on the graph (with a fixed number of edges) such that the second eigenvalue of the graph Laplacian is maximal. This reduction of the data collection problem to a spectral graph-theoretic question is one of the primary contributions of this work. As an application, we study the Yahoo! Movie user rating dataset and demonstrate that the addition of a small number of well-chosen pairwise comparisons can significantly increase the Fisher informativeness of the ranking.

In this paper, we propose a new optimization approach for the simultaneous computation of optical flow and edge detection therein. Instead of using an Ambrosio–Tortorelli type energy functional, we reformulate the optical flow problem as a multidimensional control problem. The optimal control problem is solved by discretization methods and large-scale optimization techniques. The edge detector can be immediately built from the control variables. We provide three series of numerical examples. The first shows that the mere presence of a gradient restriction has a regularizing effect, while the second demonstrates how to balance the regularizing effects of a term within the objective and the control restriction. The third series of numerical results is concerned with the direct evaluation of a TV-regularization term by introduction of control variables with sign restrictions.