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检索条件"任意字段=10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025"

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Appropriate Order of Regularization in 3D/2D Image Registration 10th

Appropriate Order of Regularization in 3D/2D Image Registr...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Schulz, Pia F. Mannel, Florian Modersitzki, Jan Institute of Mathematics and Image Computing University of Lübeck Lübeck23562 Germany Fraunhofer Institute for Digital Medicine MEVIS Lübeck23562 Germany

ISBN: (纸本)9783031923685

this paper pertains to the order of regularization in variational 3D/2D image registration. Such registration problems often occur in image-guided interventions, e.g. in ardiology, neurology, or orthopedics. In order to align 3D pre-operative data with 2D data acquired during the intervention, a 3D deformation is calculated. A common approach is to minimize an energy that consists of a data fitting and a regularization term. While the first is evaluated on a 2D set, the regularization acts on a 3D domain. thus, the regularizer has to ensure that the information given on the 2D set is transferred to the 3D domain. therefore, the regularization should be chosen such that the resulting 3D deformation is sufficiently smooth, e.g. continuously differentiable. this work addresses the question which regularization order is required to guarantee continuously differentiable deformations. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： variational techniques

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A Novel Interpretation of the Radon Transform’s Ray and Pixel-Driven Discretizations Under Balanced Resolutions 10th

A Novel Interpretation of the Radon Transform’s Ray and ...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Huber, Richard Technical University of Denmark Department of Applied Mathematics and Computer Science Kongens Lyngby2800 Denmark

ISBN: (纸本)9783031923654

Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. the corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the tomographic problem requires discretization of the Radon transform and its adjoint (called the backprojection). there are various discretization schemes;often structured around three discretization parameters: spatial-, detector-, and angular resolutions. the most widespread approach uses the ray-driven Radon transform and the pixel-driven backprojection in a balanced resolution setting, i.e., the spatial resolution roughly equals the detector resolution. the use of these particular discretization approaches is based on anecdotal reports of their approximation performance, but there is little rigorous analysis of these methods’ approximation errors. this paper presents a novel interpretation of ray-driven and pixel-driven methods as convolutional discretizations, illustrating that from an abstract perspective these methods are similar. Moreover, we announce statements concerning the convergence of the ray-driven Radon transform and the pixel-driven backprojection under balanced resolutions. Our considerations are supported by numerical experiments highlighting certain aspects of the discussed methods. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Error analysis

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Bundle scale spaces and Local Gauge Symmetries for Graph Networks 10th

Bundle Scale Spaces and Local Gauge Symmetries for Graph N...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Cassel, Jonas Schlindwein, Fabio Albers, Peter Schnörr, Christoph Institute for Mathematics Heidelberg University Heidelberg Germany Research Station Geometry and Dynamics Heidelberg University Heidelberg Germany

ISBN: (纸本)9783031923685

We introduce a class of processing architectures for node features on a graph, that are equivariant with respect to local actions of a general symmetry group G, i.e. G may act on each feature φv at some node v by an individual transformation gv∈G. Our method is based on modelling node feature data in terms of sections Γ(E) of associated vector bundles, which ensures preservation of local symmetries by construction. Processing architectures are then derived from mappings of bundle sections F:Γ(E)→Γ(E). We focus on mappings F induced by diffusion PDEs on vector bundles associated to a generalized Laplacian. We define a bundle scale space, which contains non-trivial fixed points corresponding to harmonic sections of the associated vector bundle, in contrast to the basic Gaussian scale space. We utilize vector diffusion maps and lattice gauge theory in order to discretize the geometric PDEs such that local symmetries are still respected. We outline parametrizations suited for supervised machine learning scenarios and provide a proof-of-concept numerical experiment. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Supervised learning

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Diffusion-Shock Filtering on the space of Positions and Orientations 10th

Diffusion-Shock Filtering on the Space of Positions and ...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Sherry, Finn M. Schaefer, Kristina Duits, Remco CASA & EAISI Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Mathematical Image Analysis Group Department of Mathematics and Computer Science Saarland University E1.7 Saarbrücken66123 Germany

ISBN: (纸本)9783031923685

We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space R2 [26] to the space of positions and orientations M2:=R2×S1. this has numerous advantages, e.g. making it possible to enhance and inpaint crossing structures, since they become disentangled when lifted to M2. We create a version of the algorithm using gauge frames to mitigate issues caused by lifting to a finite number of orientations. this leads us to study generalisations of diffusion, since the gauge frame diffusion is not generated by the Laplace-Beltrami operator. RDS filtering compares favourably to existing techniques such as Total Roto-Translational Variation (TR-TV) flow [9, 29], NLM [8], and BM3D [13] when denoising images with crossing structures, particularly if they are segmented. Additionally, we see that M2 RDS inpainting is indeed able to restore crossing structures, unlike R2 RDS inpainting. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Crossing-Preserving Denoising Diffusion Shock Filter

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Convergence Analysis of a Proximal Stochastic Denoising Regularization Algorithm 10th

Convergence Analysis of a Proximal Stochastic Denoising Re...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Renaud, Marien Hermant, Julien Papadakis, Nicolas Univ. Bordeaux CNRS INRIA Bordeaux INP IMB UMR 5251 Talence33400 France

ISBN: (纸本)9783031923685

Plug-and-Play methods for image restoration are iterative algorithms that solve a variational problem to recover a clean image from a degraded observation. these algorithms are known to be flexible to changes of degradation and to perform state-of-the-art restoration. Recently, significant efforts have been made to explore new stochastic algorithms based on the Plug-and-Play or REgularization by Denoising (RED) frameworks, such as SNORE, which is a convergent stochastic gradient descent algorithm. A variant of this algorithm, named SNORE Prox, reaches state-of-the-art performances, especially for inpainting tasks. However, the convergence of SNORE Prox, that can be seen as a stochastic proximal gradient descent, has not been analyzed so far. In this paper, we prove the convergence of SNORE Prox under non convex assumptions. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： variational techniques

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Crossing-Preserving Geodesic Tracking on Spherical Images 10th

Crossing-Preserving Geodesic Tracking on Spherical Images

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： van den Berg, Nicky J. Sherry, Finn M. Berendschot, Tos T. J. M. Duits, Remco CASA Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands EAISI Eindhoven University of Technology Eindhoven Netherlands Ophthalmology Department Maastricht University Maastricht Netherlands

ISBN: (纸本)9783031923685

In image analysis one often encounters spherical images, for instance in retinal imaging. the behavior of the vessels in the retina is an indicator of several diseases. To automate disease diagnosis using retinal images, it is necessary to develop an algorithm that automatically identifies and tracks vessels. To deal with crossings due to projected blood vessels in the image it is common to lift retinal images to the space of planar positions and orientations M2:=R2×S1. this implicitly assumes that the flat image accurately represents the geometry of the retina. As the eyeball is a sphere (and not a plane), we propose to compute the cusp-free, crossing-preserving geodesics in the space of spherical positions and orientations W2 on wide-field images. We clarify how to relate both manifolds and compare the calculated geodesics. the results show clear advantages of crossing-preserving tracking in W2 over non-crossing-preserving tracking in W2 and are comparable to tracking results in M2. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Geometry

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Efficient Representations of the Diffusion Echo

Efficient Representations of the Diffusion Echo

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Gaa, Daniel Weickert, Joachim Farag, Iva Çiçek, Özgün Mathematical Image Analysis Group Faculty of Mathematics and Computer Science Saarland University Campus E1.7 Saarbrücken66041 Germany

ISBN: (纸本)9783031923685

Diffusion echoes are a fundamental concept for understanding the behaviour of nonlinear diffusion filters. they describe the accumulated data exchange during a diffusion process and are given by the columns or rows of the corresponding state transition matrix. Unfortunately, they involve a prohibitively large amount of data. therefore, we propose the first compression strategy to efficiently represent and reconstruct diffusion echoes. Using a truncated singular value decomposition (SVD) we can reduce the storage requirements substantially, while still obtaining very accurate reconstructions. the SVD works on all echoes jointly and captures the redundancy between them. To approximate the singular value decomposition, we use a powerful probabilistic approach: the randomised subspace iteration. We show on a test case with a difficult, rapidly decaying diffusivity that we can reduce the storage requirements by a factor of 20, without creating visually noticeable errors. Furthermore, our compressed data representation enables an efficient reconstruction, which allows a fast and detailed echo investigation. this paves the way for various future applications of the diffusion echo that have been prevented by its huge amount of data so far. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Compression Diffusion Echoes Impulse Response Singular Value Decomposition

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Bi-level Optimization and Implicit Differentiation as a Framework for Optimal Experimental Design in Tomography

Bi-level Optimization and Implicit Differentiation as a F...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Fathi, Hamid Skorikov, Alexander van Leeuwen, Tristan Science Park 123 Amsterdam1098 XG Netherlands Mathematical Institute Utrecht University Budapestlaan 6 Utrecht3584 CD Netherlands

ISBN: (纸本)9783031923685

Total Variation (TV) regularized reconstruction is one of the most relevant methods to improve the quality of limited-angle tomographic reconstructions. Nevertheless, the accuracy of computed tomography (CT) reconstructions with a limited number of measurements can be further improved by selecting the most informative acquisition angles. this optimal experimental design (OED) task can be formulated as a bi-level optimization problem, with selecting optimal angle combinations (experimental design parameter) on the upper-level and tomographic reconstruction on the lower-level. However, integrating TV regularized reconstruction into the bi-level optimization approach is non-trivial because of the large number of iterations required for the algorithm convergence, which impedes naive computation of gradients of the upper-level objective with respect to the experimental design parameter. In this work, we address this problem by employing implicit differentiation approach to calculate the upper-level objective gradient. Moreover, we utilize inexact methods to dynamically adjust the accuracy of the lower-level solver, refining the gradient calculation as needed. We demonstrate that this approach makes OED with TV regularized reconstruction applicable to realistic 3D data. Our numerical results demonstrate that the angles selected by our bi-level optimization framework significantly outperform the standard equidistant angular selection. the proposed approach is therefore effective in minimizing experimental time and radiation dose requirements for CT reconstruction of objects benefiting from TV regularization, and can be readily extended to other types of computationally demanding iterative reconstruction algorithms. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Gradient methods

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Fast Inexact Bilevel Optimization for Analytical Deep Image Priors 10th

Fast Inexact Bilevel Optimization for Analytical Deep Image...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Salehi, Mohammad Sadegh Bubba, Tatiana A. Korolev, Yury Department of Mathematical Sciences University of Bath BathBA27AY United Kingdom Department of Mathematics and Computer Science University of Ferrara Ferrara Italy

ISBN: (纸本)9783031923654

the analytical deep image prior (ADP) introduced by Dittmer et al. (2020) establishes a link between deep image priors and classical regularization theory via bilevel optimization. While this is an elegant construction, it involves expensive computations if the lower-level problem is to be solved accurately. To overcome this issue, we propose to use adaptive inexact bilevel optimization to solve ADP problems. We discuss an extension of a recent inexact bilevel method called the method of adaptive inexact descent of Salehi et al. (2024) to an infinite-dimensional setting required by the ADP framework. In our numerical experiments we demonstrate that the computational speed-up achieved by adaptive inexact bilevel optimization allows one to use ADP on larger-scale problems than in the previous literature, e.g. in deblurring of 2D color images. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Data-driven regularization inexact bilevel optimization regularization by architecture semi-blind deblurring

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TomoSelfDEQ: Self-supervised Deep Equilibrium Learning for Sparse-Angle CT Reconstruction

TomoSelfDEQ: Self-supervised Deep Equilibrium Learning for ...

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10th international conference on scale space and variational methods in computer vision, ssvm 2025

作者： Bubba, Tatiana A. Santacesaria, Matteo Sebastiani, Andrea Department of Mathematics and Computer Science University of Ferrara Ferrara Italy MaLGa Center Department of Mathematics University of Genoa Genoa Italy Department of Physics Computer Science and Mathematics University of Modena and Reggio Emilia Modena Italy

ISBN: (纸本)9783031923654

Deep learning has emerged as a powerful tool for solving inverse problems in imaging, including computed tomography (CT). However, most approaches require paired training data with ground truth images, which can be difficult to obtain, e.g., in medical applications. We present TomoSelfDEQ, a self-supervised Deep Equilibrium (DEQ) framework for sparse-angle CT reconstruction that trains directly on undersampled measurements. We establish theoretical guarantees showing that, under suitable assumptions, our self-supervised updates match those of fully-supervised training with a loss including the (possibly non-unitary) forward operator like the CT forward map. Numerical experiments on sparse-angle CT data confirm this finding, also demonstrating that TomoSelfDEQ outperforms existing self-supervised methods, achieving state-of-the-art results with as few as 16 projection angles. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Inverse problems

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