The stationary velocity field (SVF) approach allows to build parametrizations of invertible deformation fields, which is often a desirable property in image registration. Its expressiveness is particularly attractive when used as a block following a machine learning-inspired network. However, it can struggle with large deformations. We extend the SVF approach to matrix groups, in particular SE (3) . This moves Euclidean transformations into the low-frequency part, toward which network architectures are often naturally biased, so that larger motions can be recovered more easily. This requires an extension of the flow equation, for which we provide sufficient conditions for existence. We further prove a decomposition condition that allows us to apply a scaling-and-squaring approach for efficient numerical integration of the flow equation. We numerically validate the approach on inter-patient registration of 3D MRI images of the human brain

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and averaging-based methods, focus on compact, finite, or low-dimensional groups with linear actions, this work explores how equivariance can be extended to infinite-dimensional groups. We propose a strategy designed to induce diffeomorphism equivariance in pre-trained neural networks via energy-based canonicalisation. Formulating equivariance as an optimisation problem allows us to access the rich toolbox of already established differentiable image registration methods. Empirical results on segmentation and classification tasks confirm that our approach achieves approximate equivariance and generalises to unseen transformations without relying on extensive data augmentation or retraining.

Energy-based formulations of problems in computer vision and in particular the image registration problem are notoriously non-convex and traditionally require a combination of various techniques to obtain a good solution of the underlying optimization problem during the inference step. In this work, we explore how a recent result from quantum computing can help with this task. Specifically, we show how to employ Quantum Hamiltonian Descent for image registration. We demonstrate on a small-scale example that it is possible to implement the necessary phase oracle on a circuit-based quantum computer. Numerical simulations on real-world data show that the method allows to recover good global minima despite the strong non-convexity, without relying on any heuristics or meta-strategies for aiding the optimization.

We propose an image registration model for computing a dense, piecewise diffeomorphic deformation map between 3D thorax images which incorporates sliding motion as often occurring in the pleural cavity. Our approach is based on stationary velocity fields and neural implicit representations, with a particular focus on facilitating motion interpolation. This allows for generating a time-continuous model of the respiratory cycle based on end-inspiration and end-expiration images. We investigate the effect of composing deformations in motion interpolation, using a hybrid technique to enforce domain alignment. We experimentally validate our approach for registration and motion interpolation between thoracic end-inspiration and end-expiration images.

Head and neck squamous cell carcinoma (HNSCC) is often diagnosed at advanced stages. Due to pronounced intratumoral heterogeneity (ITH), reliable risk stratification and prediction of treatment response remain challenging. This study aimed to identify peptide signatures in HNSCC tissue that are associated with treatment outcomes in HPV-negative, advanced-stage HNSCC patients undergoing 5-fluorouracil/platinum-based chemoradiotherapy (CDDP-CRT). We integrated matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) of tryptic peptides with univariate statistics and machine learning approaches to uncover potential prognostic patterns. Formalin-fixed, paraffin-embedded whole tumor sections from 31 treatment-naive, HPV-negative HNSCC patients were digested in situ with trypsin, and the generated peptides were analyzed using MALDI-MSI. Clinical follow-up revealed recurrence or progression (RecPro) in 20 patients, while 11 patients showed no evidence of disease (NED). Classification models were developed based on the recorded peptide profiles using both unrestricted and feature-restricted approaches, employing either the full set of m/z features or a subset of the most discriminatory m/z features, respectively. The unrestricted model achieved a balanced accuracy of 71% at the patient level (75% sensitivity, 66% specificity), whereas the feature-restricted model reached a balanced accuracy of 72%, showing increased specificity (92%) but reduced sensitivity (52%) in the CDDP-CRT cohort. In order to assess treatment specificity, models trained on the CDDP-CRT cohort were tested on an independent patient cohort treated with mitomycin C-based CRT (MMC-CRT). Neither model demonstrated prognostic performance in the MMC-CRT patient cohort, suggesting specificity for platinum-based therapy. Presented findings highlight the potential of MALDI-MSI-based proteomic profiling to identify patients at elevated risk of recurrence following CDDP-CRT. This approach may support more personalized risk assessment and treatment planning, ultimately contributing to improved therapeutic outcomes in HPV-negative HNSCC.

Respiratory surface electromyography measures the electrical muscle activity during breathing non-invasively. Electrophysiological modeling of the respiratory cycle is a valuable tool for analysis of the signals. A promising approach for dynamic simulations is based on knowing the deformation of the torso at a finite number of time steps between expiration and inspiration. In order to provide a foundation for such models, we present a new image registration method that determines the torso transformation during the respiratory cycle. For this purpose, we extend a ResNet-LDDMM based 3D/3D registration approach. We modify the network structure and add 2D data taken during respiration into the registration to include information about the breathing motion. Our experiments show that these modifications improve the registration quality, thereby providing a step towards a more realistic model of electrical transfer behavior over the respiratory cycle. The code is publicly available at https://github.com/schulz-p/Image-Registration-for-a-Dynamic-Breathing-Model.

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The Riemannian geometry setting can be suitable for a variety of reasons. First, it comes with a rich structure to account for a wide range of geometries that can be modelled after an energy landscape. Second, many standard data analysis tools initially developed for data in Euclidean space can also be generalised to data on a Riemannian manifold. In the context of protein dynamics, a conceptual challenge comes from the lack of a suitable smooth manifold and the lack of guidelines for constructing a smooth Riemannian structure based on an energy landscape. In addition, computational feasibility in computing geodesics and related mappings poses a major challenge. This work considers these challenges. The first part of the paper develops a novel local approximation technique for computing geodesics and related mappings on Riemannian manifolds in a computationally feasible manner. The second part constructs a smooth manifold of point clouds modulo rigid body group actions and a Riemannian structure that is based on an energy landscape for protein conformations. The resulting Riemannian geometry is tested on several data analysis tasks relevant for protein dynamics data. It performs exceptionally well on coarse-grained molecular dynamics simulated data. In particular, the geodesics with given start- and end-points approximately recover corresponding molecular dynamics trajectories for proteins that undergo relatively ordered transitions with medium sized deformations. The Riemannian protein geometry also gives physically realistic summary statistics and retrieves the underlying dimension even for large-sized deformations within seconds on a laptop.

Intuitive visualization of relevant changes between radiological image pairs in the form of change maps has the potential to not only increase efficiency in diagnostic reading, but also to decrease the number of missed abnormalities. Classically, change maps are created from difference images after an image registration step, which requires a careful balance in order to neither generate artifacts nor disguise relevant changes.We propose jointly learning registration and change map in order to address these limitations. As a proof of concept, the method was tested on NLST lung CT images and synthetically generated data, and shows comparable results to the conventional approach. In a reader study, the use of change maps resulted in a 23% reduction in reading time while maintaining similar recall.

We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system. The system is enforced to evolve toward the ground state of the problem Hamiltonian by optimizing a set of angles using normalized gradient descent. Experimentally, our algorithm outperforms the state-of-the-art quantum approximate optimization algorithm on random fully connected graphs and challenges D-Wave quantum annealers by producing good approximate solutions. Source code and data files are publicly available ( https://github.com/nkuetemeli/UQMaxCutAndIsing ).

Motivated by the trade-off between noise robustness and data consistency for joint three-imensional (3D) map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularizing and approximating the global minimizer of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimizer we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimizer. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimization problems have to be solved and where regularization is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularizing effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimization would.

Despite numerous diagnostic and therapeutic advances, pancreatic ductal adenocarcinoma (PDAC) has a high mortality rate, and is the fourth leading cause of cancer death in developing countries. Besides its increasing prevalence, pancreatic malignancies are characterized by poor prognosis. Omics technologies have potential relevance for PDAC assessment but are time-intensive and relatively cost-intensive and limited by tissue heterogeneity. Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) can obtain spatially distinct peptide-signatures and enables tumor classification within a feasible time with relatively low cost. While MALDI-MSI data sets are inherently large, machine learning methods have the potential to greatly decrease processing time. We present a pilot study investigating the potential of MALDI-MSI in combination with neural networks, for classification of pancreatic ductal adenocarcinoma. Neural-network models were trained to distinguish between pancreatic ductal adenocarcinoma and other pancreatic cancer types. The proposed methods are able to correctly classify the PDAC types with an accuracy of up to 86% and a sensitivity of 82%. This study demonstrates that machine learning tools are able to identify different pancreatic carcinoma from complex MALDI data, enabling fast prediction of large data sets. Our results encourage a more frequent use of MALDI-MSI and machine learning in histopathological studies in the future.

We propose a model-driven neural fields approach for solving variational problems. The approach can be applied to a variety of problems with convex, 1-homogeneous regularizer and arbitrary, possibly non-convex, data term. Our strategy is to embed the non-convex energy into a higher-dimensional space, reaching a convex primal-dual formulation. Instead of using classical gradient-descent based optimization algorithms, we propose training multiple fields representing the primal and dual variables in order to solve the problem.

Motivated by the trade-off between noise-robustness and data-consistency for joint 3D map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularising and approximating the global minimiser of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimiser we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimiser. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimisation problems have to be solved and where regularisation is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularising effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimisation would.

Groupwise image registration describes the problem of simultaneously aligning a series of more than two images through individual spatial deformations and it is a common task in the processing of medical image sequences. Variational methods with data fidelity terms based on robust PCA (RPCA) have proven successful in accounting for structural changes in image intensity stemming, e.g., from the uptake of a contrast agent in functional imaging. In this article, we investigate the drawbacks of the most commonly used RPCA data term and derive an improved replacement that employs explicit constraints instead of penalties. We further present a multilevel scheme with theoretically justified scaling to solve the underlying fully deformable registration model. Our numerical experiments on synthetic and real-life medical data confirm the advanced adaptability of RPCA-based data terms and showcase an improved registration accuracy of our algorithm when compared to related groupwise approaches.

We propose an iterative method for estimating rigid transformations from point sets using adiabatic quantum computation. Compared to existing quantum approaches, our method relies on an adaptive scheme to solve the problem to high precision, and does not suffer from inconsistent rotation matrices. Experimentally, our method performs robustly on several 2D and 3D datasets even with high outlier ratio.

We propose a trainable architecture for affine image registration to produce robust starting points for conventional image registration methods. Learning-based methods for image registration often require networks with many parameters and heavily engineered cost func-tions and thus are complex and computationally expensive. Despite their success in recent years, these methods often lack the accuracy of classical iterative image registration and struggle with large deformations. On the other hand, iterative methods depend on good initial estimates and tuned hyperparameters. We tackle this problem by combining ef-fective shallow networks and classical optimization algorithms using strategies from the field of meta-learning. The architecture presented in this work incorporates only first-order gradient information of the given registration problems, making it highly flexible and particularly well-suited as an initialization step for classical image registration.

Nonlinear filtering approaches allow to obtain decomposition of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can be obtained using the classical Bregman iteration with quadratic data term. We apply the Bregman iteration to lifted, i.e., higher-dimensional and convex, functionals in order to extend the scope of these approaches to functionals with arbitrary data term. We provide conditions for the subgradients of the regularizer – in the continuous and discrete setting– under which this lifted iteration reduces to the standard Bregman iteration. We show experimental results for the convex and non-convex case.

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale. The associated inverse scale space flow can be obtained using the classical Bregman iteration applied to a convex, absolutely one-homogeneous regularizer. In order to extend these approaches to general energies with non-convex data term, we apply the Bregman iteration to a lifted version of the functional with sublabel-accurate discretization. We provide a condition for the subgradients of the regularizer under which this lifted iteration reduces to the standard Bregman iteration. We show experimental results for the convex and non-convex case.

We propose a method for solving non-smooth optimization problems on manifolds. In order to obtain superlinear convergence, we apply a Riemannian Semi-smooth Newton method to a non-smooth non-linear primal-dual optimality system based on a recent extension of Fenchel duality theory to Riemannian manifolds. We also propose an inexact version of the Riemannian Semi-smooth Newton method and prove conditions for local linear and superlinear convergence. Numerical experiments on l2-TV-like problems confirm superlinear convergence on manifolds with positive and negative curvature.