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检索条件"任意字段=7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019"

共 46 条记录，以下是21-30 订阅

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Iterative Sampled methods for Massive and Separable Nonlinear Inverse Problems 7th

Iterative Sampled Methods for Massive and Separable Nonlinea...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Chung, Julianne Chung, Matthias Slagel, J. Tanner Virginia Tech Dept Math Blacksburg VA 24060 USA

ISBN: (纸本)9783030223687;9783030223670

In this paper, we consider iterative methods based on sampling for computing solutions to separable nonlinear inverse problems where the entire dataset cannot be accessed or is not available all-at-once. In such scenarios (e.g., when massive amounts of data exceed memory capabilities or when data is being streamed), solving inverse problems, especially nonlinear ones, can be very challenging. We focus on separable nonlinear problems, where the objective function is nonlinear in one (typically small) set of parameters and linear in another (larger) set of parameters. For the linear problem, we describe a limited-memory sampled Tikhonov method, and for the nonlinear problem, we describe an approach to integrate the limited-memory sampled Tikhonov method within a nonlinear optimization framework. the proposed method is computationally efficient in that it only uses available data at any iteration to update both sets of parameters. Numerical experiments applied to massive super-resolution image reconstruction problems show the power of these methods.

关键词： Tikhonov regularization Sampled methods Variable projection Kaczmarz methods Super-resolution Medical imaging and other applications

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A Connection Between Image Processing and Artificial Neural Networks Layers through a Geometric Model of Visual Perception 7th

A Connection Between Image Processing and Artificial Neural ...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Batard, thomas Ramon Maldonado, Eduard Steidl, Gabriele Bertalmio, Marcelo Crisalix Barcelona Spain Univ Politecn Cataluna Barcelona Spain TU Kaiserslautern Kaiserslautern Germany Univ Pompeu Fabra Barcelona Spain

ISBN: (纸本)9783030223687;9783030223670

In this paper, we establish a connection between image processing, visual perception, and deep learning by introducing a mathematical model inspired by visual perception from which neural network layers and image processing models for color correction can be derived. Our model is inspired by the geometry of visual perception and couples a geometric model for the organization of some neurons in the visual cortex with a geometric model of color perception. More precisely, the model is a combination of a Wilson-Cowan equation describing the activity of neurons responding to edges and textures in the area V1 of the visual cortex and a Retinex model of color vision. For some particular activation functions, this yields a color correction model which processes simultaneously edges/textures, encoded into a Riemannian metric, and the color contrast, encoded into a nonlocal covariant derivative. then, we show that the proposed model can be assimilated to a residual layer provided that the activation function is nonlinear and to a convolutional layer for a linear activation function. Finally, we show the accuracy of the model for deep learning by testing it on the MNIST dataset for digit classification.

关键词： Differential geometry variational model Image processing vision Neural network

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Macrocanonical Models for Texture Synthesis 7th

Macrocanonical Models for Texture Synthesis

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： De Bortoli, Valentin Desolneux, Agnes Galerne, Bruno Leclaire, Arthur Univ Paris Saclay ENS Paris Saclay Ctr Math & Leurs Applicat CNRS F-94235 Cachan France Univ Tours Univ Orleans Inst Denis Poisson CNRS Tours France Univ Bordeaux Bordeaux INP CNRS IMBUMR 5251 F-33400 Talence France

ISBN: (纸本)9783030223687;9783030223670

In this article we consider macrocanonical models for texture synthesis. In these models samples are generated given an input texture image and a set of features which should be matched in expectation. It is known that if the images are quantized, macrocanonical models are given by Gibbs measures, using the maximum entropy principle. We study conditions under which this result extends to real-valued images. If these conditions hold, finding a macrocanonical model amounts to minimizing a convex function and sampling from an associated Gibbs measure. We analyze an algorithm which alternates between sampling and minimizing. We present experiments with neural network features and study the drawbacks and advantages of using this sampling scheme.

关键词： Texture synthesis Gibbs measure Monte carlo methods Langevin algorithms Neural networks

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A variational Convex Hull Algorithm 7th

A Variational Convex Hull Algorithm

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Li, Lingfeng Luo, Shousheng Tai, Xue-Cheng Yang, Jiang Southern Univ Sci & Technol Dept Math Shenzhen Guangdong Peoples R China Hong Kong Baptist Univ Dept Math Kowlong Tong Hong Kong Peoples R China Beijing Computat Sci Res Ctr Beijing Peoples R China Henan Univ Data Anal Technol Lab Sch Math & Stat Kaifeng Peoples R China

ISBN: (纸本)9783030223687;9783030223670

Finding the convex hull of a given object or a point set is a very important problem. In this paper, we propose a variational convex hull model and numerical algorithms to solve it. Our model is based on level set representation. Efficient numerical algorithms and implementations based on splitting ideas are given. To test our proposed model, we conduct many experiments for objects represented by binary images, and the results suggest that our model can identify the convex hull accurately. Even more, our model can be easily modified to handle the outliers, and this is also demonstrated by numerical examples.

关键词： Convex hull Level set method Image processing Outliers detection

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Dahl, Vedrana Andersen Dahl, Anders Bjorholm Tech Univ Denmark Dept Appl Math & Comp Sci Lyngby Denmark

ISBN: (纸本)9783030223687;9783030223670

Faithful representation of pairwise pixel affinities is crucial for the outcome of spectral segmentation methods. In conventional affinity models only close-range pixels interact, and a variety of subsequent techniques aims at faster propagation of local grouping cues across long-range connections. In this paper we propose a general framework for constructing a full-range affinity matrix. Our affinity matrix consists of a global similarity matrix and an additive proximity matrix. the similarity in appearance, including intensity and texture, is encoded for each pair of image pixels. Despite being full-range, our similarity matrix has a simple decomposition, which exploits an assignment of image pixels to dictionary elements. the additive proximity enforces smoothness to the segmentation by imposing interactions between near-by pixels. Our approach allows us to assess the advantages of using a full-range affinity for various spectral segmentation problems. Within our general framework we develop a few variants of full affinity for experimental validation. the performance we accomplish on composite textured images is excellent, and the results on natural images are promising.

关键词： Image segmentation Spectral methods Affinity matrix

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Pseudodifferential Inpainting: the Missing Link Between PDE- and RBF-Based Interpolation 7th

Pseudodifferential Inpainting: The Missing Link Between PDE-...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Augustin, Matthias Weickert, Joachim Andris, Sarah Saarland Univ Math Image Anal Grp Fac Math & Comp Sci Campus E1-7 D-66041 Saarbrucken Germany

ISBN: (纸本)9783030223687;9783030223670

Inpainting with partial differential equations (PDEs) has been used successfully to reconstruct missing parts of an image, even for sparse data. On the other hand, sparse data interpolation is a rich field of its own with different methods such as scattered data interpolation with radial basis functions (RBFs). the goal of this paper is to establish connections between inpainting with linear shift- and rotation-invariant differential operators and interpolation with radial basis functions. the bridge between these two worlds is built by generalising inpainting methods to handle pseudo-differential operators and by considering their Green's functions. In this way, we find novel relations of various multiquadrics to pseudodifferential operators. Moreover, we show that many popular radial basis functions are related to processes from the diffusion and scale-space literature. We present a single numerical algorithm for all methods. It combines conjugate gradients with pseudodifferential operator evaluations in the Fourier domain. Our experiments show that the linear PDE- and the RBF-based communities have developed concepts of comparable quality.

关键词： Inpainting Sparse data Partial differential equations Pseudodifferential operators Scattered data interpolation Radial basis functions Green's functions

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A Cortical-Inspired Model for Orientation-Dependent Contrast Perception: A Link with Wilson-Cowan Equations 7th

A Cortical-Inspired Model for Orientation-Dependent Contrast...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Bertalmio, Marcelo Calatroni, Luca Franceschi, Valentina Franceschiello, Benedetta Prandi, Dario Univ Pompeu Fabra DTIC Barcelona Spain Ecole Polytech CNRS CMAP Palaiseau France Univ Paris Sud IMO Orsay France Fdn Asile Aveugles Lausanne Switzerland Lab Invest Neurophysiol Lausanne Switzerland Cent Supelec CNRS L2S Gif Sur Yvette France

ISBN: (纸本)9783030223687;9783030223670

We consider a differential model describing neuro-physiological contrast perception phenomena induced by surrounding orientations. the mathematical formulation relies on a cortical-inspired modelling [11] largely used over the last years to describe neuron interactions in the primary visual cortex (V1) and applied to several image processing problems [14,15,21]. Our model connects to Wilson-Cowan-type equations [26] and it is analogous to the one used in [3,4,16] to describe assimilation and contrast phenomena, the main novelty being its explicit dependence on local image orientation. To confirm the validity of the model, we report some numerical tests showing its ability to explain orientation-dependent phenomena (such as grating induction) and geometric-optical illusions [18,24] classically explained only by filtering-based techniques [7,20].

关键词： Orientation-dependent modelling Wilson-Cowan equations Primary visual cortex Contrast perception variational modelling

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Time Discrete Geodesics in Deep Feature spaces for Image Morphing 7th

Time Discrete Geodesics in Deep Feature Spaces for Image Mor...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Effland, Alexander Kobler, Erich Pock, thomas Rumpf, Martin Graz Univ Technol Inst Comp Graph & Vis Graz Austria Univ Bonn Inst Numer Simulat Bonn Germany

ISBN: (纸本)9783030223687;9783030223670

Image morphing in computer vision amounts to computing a visually appealing transition of two images. A prominent model for image morphing originally proposed by Trouve, Younes and coworkers is image metamorphosis. Here, the space of images is endowed with a Riemannian metric that separately quantifies the contributions due to transport and image intensity variations along a transport path. Geodesic curves in this Riemannian space of images give rise to morphing transitions. the classical metamorphosis model considers images as square-integrable functions on some image domain and thus is non-sensitive to image features such as sharp interfaces or fine texture patterns. To resolve this drawback, we treat images not as intensity maps, but rather as maps into some feature space that encode local structure information. In the simplest case, color intensities are such feature vectors. To appropriately treat local structures and semantic information, deep convolutional neural network features are investigated. the resulting model is formulated directly in terms of a variational time discretization developed for the classical metamorphosis model by Berkels, Effland and Rumpf. the key ingredient is a mismatch energy that locally approximates the squared Riemannian distance and consists of a regularization energy of the time discrete flow and a dissimilarity energy that measures the feature vector modulation along discrete transport paths. the spatial discretization is based on a finite difference and a stable spline interpolation. A variety of numerical examples demonstrates the robustness and versatility of the proposed method for real images using a variant of the iPALM algorithm for the minimization of the fully discrete energy functional.

关键词： Image metamorphosis Image morphing Image registration Feature space Convolutional neural network iPALM algorithm

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Total Variation and Mean Curvature PDEs on the space of Positions and Orientations 7th

Total Variation and Mean Curvature PDEs on the Space of Posi...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Duits, Remco St-Onge, Etienne Portegies, Jim Smets, Bart Eindhoven Univ Technol CASA Eindhoven Netherlands Sherbrooke Connect Imaging Lab SCIL Sherbrooke PQ Canada

ISBN: (纸本)9783030223687;9783030223670

Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space M = R-d x Sd-1 of positions and orientations as a Lie group quotient in SE(d). For d = 2 this is called 'total roto-translation variation' by Chambolle & Pock. We extend this to d = 3, by a PDE-approach with a limiting procedure for which we prove convergence. We also include a Mean Curvature Flow (MCF) in our PDE model on M. this was first proposed for d = 2 by Citti et al. and we extend this to d = 3. Furthermore, for d = 2 we take advantage of locally optimal differential frames in invertible orientation scores (OS). We apply our TVF and MCF in the denoising/enhancement of crossing fiber bundles in DW-MRI. In comparison to data-driven diffusions, we see a better preservation of bundle boundaries and angular sharpness in fiber orientation densities at crossings. We support this by error comparisons on a noisy DW-MRI phantom. We also apply our TVF and MCF in enhancement of crossing elongated structures in 2D images via OS, and compare the results to nonlinear diffusions (CED-OS) via OS.

关键词： Total variation Mean Curvature Sub-Riemannian Geometry Roto-translations Denoising Fiber enhancement

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PDE Evolutions for M-Smoothers: From Common Myths to Robust Numerics 7th

PDE Evolutions for M-Smoothers: From Common Myths to Robust ...

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7th international conference on scale space and variational methods in computer vision (ssvm)

作者： Welk, Martin Weickert, Joachim Private Univ Hlth Sci Med Informat & Technol Inst Biomed Image Anal Eduard Wallnofer Zentrum 1 A-6060 Hall Tyrol Austria Saarland Univ Math Image Anal Grp Campus E1-7 D-66041 Saarbrucken Germany

ISBN: (纸本)9783030223687;9783030223670

Local M-smoothers constitute an interesting and important class of image processing techniques with many connections to other methods. In our paper we derive a family of partial differential equations (PDEs) that result as limiting processes from M-smoothers which are based on local order-p means within a disc the radius of which tends to zero. the order p may take any nonzero value > -1. thus, we also allow negative values which have never been considered before. In contrast to results from the literature, we show in the space-continuous case that mode filtering does not arise for p -> 0, but for p -> -1. Extending our filter class to p-values smaller than - 1 allows to include e.g. the classical image sharpening flow of Gabor. Since our PDE class is highly anisotropic and may contain backward parabolic operators, designing adequate numerical methods is difficult. We present an L-infinity-stable explicit finite difference scheme that satisfies a discrete maximum-minimum principle, is fairly efficient, and offers excellent rotation invariance. Although it solves parabolic PDEs, it makes consequent use of stabilisation concepts from the numerics of hyperbolic PDEs. Our experiments show that the PDEs forp < 1 are of specific interest: their backward parabolic term creates favourable sharpening properties, while they appear to maintain the strong shape simplification properties of mean curvature motion.

关键词： M-smoother Partial differential equation Mode filter Backward parabolic operator Anisotropy Finite difference methods Shape analysis

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