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共 291 条记录，以下是61-70 订阅

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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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GMM Based Simultaneous Reconstruction and Segmentation in X-Ray CT Application 8th

GMM Based Simultaneous Reconstruction and Segmentation in X-...

引用

8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Yan, Shi Dong, Yiqiu School of Mathematical Science Nankai University Tianjin300071 China Department of Applied Mathematics and Computer Science Technical University of Denmark 2800 Kgs. Lyngby Denmark

ISBN: (纸本)9783030755485

In this paper, we propose a new simultaneous reconstruction and segmentation (SRS) model in X-ray computed tomography (CT). The new SRS model is based on the Gaussian mixture model (GMM). In order to transform non-separable log-sum term in GMM into a form that can be easy solved, we introduce an auxiliary variable, which in fact plays a segmentation role. The new SRS model is much simpler comparing with the models derived from the hidden Markov measure field model (HMMFM). Numerical results show that the proposed model achieves improved results than other methods, and the CPU time is greatly reduced. © 2021, Springer Nature Switzerland AG.

关键词： Inverse problems

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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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First Order Locally Orderless Registration 8th

First Order Locally Orderless Registration

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8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Darkner, Sune Vidarte, José D. T. Lauze, François Department of Computer Science University of Copenhagen Copenhagen Denmark

ISBN: (纸本)9783030755485

First Order Locally Orderless Registration (FLOR) is a scale-space framework for image density estimation used for defining image similarity, mainly for Image Registration. The Locally Orderless Registration framework was designed in principle to use zeroth-order information, providing image density estimates over three scales: image scale, intensity scale, and integration scale. We extend it to take first-order information into account and hint at higher-order information. We show how standard similarity measures extend into the framework. We study especially Sum of Squared Differences (SSD) and Normalized Cross-Correlation (NCC) but present the theory of how Normalised Mutual Information (NMI) can be included. © 2021, Springer Nature Switzerland AG.

关键词： Image registration

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Inpainting-Based Video Compression in FullHD 8th

Inpainting-Based Video Compression in FullHD

引用

8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Andris, Sarah Peter, Pascal Mohideen Kaja Mohideen, Rahul Weickert, Joachim Hoffmann, Sebastian Mathematical Image Analysis Group Faculty of Mathematics and Computer Science Saarland University Campus E1.7 Saarbrücken66041 Germany

ISBN: (纸本)9783030755485

Compression methods based on inpainting are an evolving alternative to classical transform-based codecs for still images. Attempts to apply these ideas to video compression are rare, since reaching real-time performance is very challenging. Therefore, current approaches focus on simplified frame-by-frame reconstructions that ignore temporal redundancies. As a remedy, we propose a highly efficient, real-time capable prediction and correction approach that fully relies on partial differential equations (PDEs) in all steps of the codec: Dense variational optic flow fields yield accurate motion-compensated predictions, while homogeneous diffusion inpainting is applied for intra prediction. To compress residuals, we introduce a new highly efficient block-based variant of pseudodifferential inpainting. Our novel architecture outperforms other inpainting-based video codecs in terms of both quality and speed. For the first time in inpainting-based video compression, we can decompress FullHD (1080p) videos in real-time with a fully CPU-based implementation, outperforming previous approaches by roughly one order of magnitude. © 2021, Springer Nature Switzerland AG.

关键词： Optical flows

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Fast Morphological Dilation and Erosion for Grey scale Images Using the Fourier Transform 8th

Fast Morphological Dilation and Erosion for Grey Scale Image...

引用

8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Kahra, Marvin Sridhar, Vivek Breuß, Michael Institute for Mathematics Brandenburg Technical University Cottbus-Senftenberg Cottbus03046 Germany

ISBN: (纸本)9783030755485

The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. Existing fast algorithms that realise dilation and erosion for grey value images are often limited with respect to size or shape of the structuring element. Usually their algorithmic complexity depends on these aspects. Many fast methods only address flat morphology. In this paper we propose a novel way to make use of the fast Fourier transform for the computation of dilation and erosion. Our method is by design highly flexible, as it can be used with flat and non-flat structuring elements of any size and shape. Moreover, its complexity does not depend on size or shape of the structuring element, but only on the number of pixels in the filtered images. We show experimentally that we obtain results of very reasonable quality with the proposed method. © 2021, Springer Nature Switzerland AG.

关键词： Mathematical morphology

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An Anisotropic Selection Scheme for variational Optical Flow methods with Order-Adaptive Regularisation 8th

An Anisotropic Selection Scheme for Variational Optical Flow...

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8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Mehl, Lukas Beschle, Cedric Barth, Andrea Bruhn, Andrés Institute for Visualization and Interactive Systems University of Stuttgart Stuttgart Germany Institute for Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany

ISBN: (纸本)9783030755485

Approaches based on order-adaptive regularisation belong to the most accurate variational methods for computing the optical flow. By locally deciding between first- and second-order regularisation, they are applicable to scenes with both fronto-parallel and ego-motion. So far, however, existing order-adaptive methods have a decisive drawback. While the involved first- and second-order smoothness terms already make use of anisotropic concepts, the underlying selection process itself is still isotropic in that sense that it locally chooses the same regularisation order for all directions. In our paper, we address this shortcoming. We propose a generalised order-adaptive approach that allows to select the local regularisation order for each direction individually. To this end, we split the order-adaptive regularisation across and along the locally dominant direction and perform an energy competition for each direction separately. This in turn offers another advantage. Since the parameters can be chosen differently for both directions, the approach allows for a better adaption to the underlying scene. Experiments for MPI Sintel and KITTI 2015 demonstrate the usefulness of our approach. They not only show improvements compared to an isotropic selection scheme. They also make explicit that our approach is able to improve the results from state-of-the-art learning-based approaches, if applied as a final refinement step – thereby achieving top results in both benchmarks. © 2021, Springer Nature Switzerland AG.

关键词： Optical flows

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

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

引用

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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Lossless PDE-based Compression of 3D Medical Images 8th

Lossless PDE-based Compression of 3D Medical Images

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8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Jumakulyyev, Ikram Schultz, Thomas University of Bonn Bonn Germany

ISBN: (纸本)9783030755485

Inpainting with Partial Differential Equations (PDEs) has previously been used as a basis for lossy image compression. For medical images, lossless compression is often considered to be safer, given that even subtle details could be diagnostically relevant. In this work, we introduce a PDE-based codec that achieves competitive compression rates for lossless image compression. It is based on coding the differences between the original image and its PDE-based reconstruction. These differences often have lower entropy than the original image, and can therefore be coded more efficiently. We optimize this idea via an iterative reconstruction scheme, and a separate coding of empty space, which takes up a considerable fraction of the field of view in many 3D medical images. We demonstrate that our PDE-based codec compares favorably to previously established lossless codecs. We also investigate the individual benefit from each ingredient of our codec on multiple examples, explore the effect of using homogeneous, edge enhancing, and fourth-order anisotropic diffusion, and discuss the choice of contrast parameters. © 2021, Springer Nature Switzerland AG.

关键词： Image compression

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Translating Numerical Concepts for PDEs into Neural Architectures 8th

Translating Numerical Concepts for PDEs into Neural Architec...

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8th international conference on scale space and variational methods in computer vision, SSVM 2021

作者： Alt, Tobias Peter, Pascal Weickert, Joachim Schrader, Karl Mathematical Image Analysis Group Faculty of Mathematics and Computer Science Campus E1.7 Saarland University Saarbrücken66041 Germany

ISBN: (纸本)9783030755485

We investigate what can be learned from translating numerical algorithms into neural networks. On the numerical side, we consider explicit, accelerated explicit, and implicit schemes for a general higher order nonlinear diffusion equation in 1D, as well as linear multigrid methods. On the neural network side, we identify corresponding concepts in terms of residual networks (ResNets), recurrent networks, and U-nets. These connections guarantee Euclidean stability of specific ResNets with a transposed convolution layer structure in each block. We present three numerical justifications for skip connections: as time discretisations in explicit schemes, as extrapolation mechanisms for accelerating those methods, and as recurrent connections in fixed point solvers for implicit schemes. Last but not least, we also motivate uncommon design choices such as nonmonotone activation functions. Our findings give a numerical perspective on the success of modern neural network architectures, and they provide design criteria for stable networks. © 2021, Springer Nature Switzerland AG.

关键词： Partial differential equations

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