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检索条件"任意字段=8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021"

共 22 条记录，以下是11-20 订阅

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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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Extension of Mathematical Morphology in Riemannian spaces 8th

Extension of Mathematical Morphology in Riemannian Spaces

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

作者： Diop, El Hadji S. Mbengue, Alioune Manga, Bakary Seck, Diaraf Department of Mathematics University Iba Der Thiam Thies Senegal Department of Mathematics and Computer Science University Cheikh Anta Diop Dakar Senegal LMDAN NLAGA University Cheikh Anta Diop Dakar Senegal

ISBN: (纸本)9783030755485

Mathematical morphology remains an efficient image analysis tool due to its morphological scale-spaces capability. It can be formulated using partial differential equations that are in fact a particular case of the first order Hamilton-Jacobi equations for which viscosity solutions exist and are given by Hopf-Lax-Oleinik (HLO) formulas. In this study, we propose an extension of HLO formulas in Riemannian manifolds by considering a general Cauchy problem, and prove the existence of a unique viscosity solution. Some properties are derived, and example on the hyperbolic ball is also provided. © 2021, Springer Nature Switzerland AG.

关键词： Mathematical morphology

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variational Models for Signal Processing with Graph Neural Networks 8th

Variational Models for Signal Processing with Graph Neural N...

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

作者： Azad, Amitoz Rabin, Julien Elmoataz, Abderrahim Normandie Univ UNICAEN ENSICAEN CNRS GREYC Caen14000 France

ISBN: (纸本)9783030755485

this paper is devoted to signal processing on point-clouds by means of neural networks. Nowadays, state-of-the-art in image processing and computer vision is mostly based on training deep convolutional neural networks on large datasets. While it is also the case for the processing of point-clouds with Graph Neural Networks (GNN), the focus has been largely given to high-level tasks such as classification and segmentation using supervised learning on labeled datasets such as ShapeNet. Yet, such datasets are scarce and time-consuming to build depending on the target application. In this work, we investigate the use of variational models for such GNN to process signals on graphs for unsupervised learning. Our contributions are two-fold. We first show that some existing variational - based algorithms for signals on graphs can be formulated as Message Passing Networks (MPN), a particular instance of GNN, making them computationally efficient in practice when compared to standard gradient-based machine learning algorithms. Secondly, we investigate the unsupervised learning of feed-forward GNN, either by direct optimization of an inverse problem or by model distillation from variational-based MPN. © 2021, Springer Nature Switzerland AG.

关键词： Graph neural networks

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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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Equivariant Deep Learning via Morphological and Linear scale space PDEs on the space of Positions and Orientations 8th

Equivariant Deep Learning via Morphological and Linear Scale...

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

作者： Duits, Remco Smets, Bart Bekkers, Erik Portegies, Jim Department Mathematics and Computer Science TU/e Eindhoven Netherlands Informatics Institute UvA Amsterdam Netherlands

ISBN: (纸本)9783030755485

We present PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) that generalize Group equivariant Convolutional Neural Networks (G-CNNs). In PDE-G-CNNs a network layer is a set of PDE-solvers where geometrically meaningful PDE-coefficients become trainable weights. the underlying PDEs are morphological and linear scale space PDEs on the homogeneous space Md of positions and orientations. they provide an equivariant, geometrical PDE-design and model interpretability of the network. the network is implemented by morphological convolutions with approximations to kernels solving morphological α -scale-space PDEs, and to linear convolutions solving linear α -scale-space PDEs. In the morphological setting, the parameter α regulates soft max-pooling over balls, whereas in the linear setting the cases α= 1 / 2 and α= 1 correspond to Poisson and Gaussian scale spaces respectively. We show that our analytic approximation kernels are accurate and practical. We build on techniques introduced by Weickert and Burgeth who revealed a key isomorphism between linear and morphological scale spaces via the Fourier-Cramér transform. It maps linear α -stable Lévy processes to Bellman processes. We generalize this to Md and exploit this relation between linear and morphological scale-space kernels. We present blood vessel segmentation experiments that show the benefits of PDE-G-CNNs compared to state-of-the-art G-CNNs: increase of performance along with a huge reduction in network parameters. © 2021, Springer Nature Switzerland AG.

关键词： Convolution

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Multi-frame Super-Resolution from Noisy Data 8th

Multi-frame Super-Resolution from Noisy Data

引用

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

作者： Bodduna, Kireeti Weickert, Joachim Cárdenas, Marcelo Mathematical Image Analysis Group Faculty of Mathematics and Computer Science Saarland University Saarbrücken66041 Germany

ISBN: (纸本)9783030755485

Obtaining high resolution images from low resolution data with clipped noise is algorithmically challenging due to the ill-posed nature of the problem. So far such problems have hardly been tackled, and the few existing approaches use simplistic regularisers. We show the usefulness of two adaptive regularisers based on anisotropic diffusion ideas: Apart from evaluating the classical edge-enhancing anisotropic diffusion regulariser, we introduce a novel non-local one with one-sided differences and superior performance. It is termed sector diffusion. We combine it with all six variants of the classical super-resolution observational model that arise from permutations of its three operators for warping, blurring, and downsampling. Surprisingly, the evaluation in a practically relevant noisy scenario produces a different ranking than the one in the noise-free setting in our previous work (ssvm 2017). © 2021, Springer Nature Switzerland AG.

关键词： Diffusion

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Inpainting-Based Video Compression in FullHD 8th

Inpainting-Based Video Compression in FullHD

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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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First Order Locally Orderless Registration 8th

First Order Locally Orderless Registration

引用

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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Translating Numerical Concepts for PDEs into Neural Architectures 8th

Translating Numerical Concepts for PDEs into Neural Architec...

引用

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

An Anisotropic Selection Scheme for Variational Optical Flow...

引用

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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