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Macrocanonical Models for Texture Synthesis 1

引用

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: (数字)9783030223687

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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Iterative Sampled methods for Massive and Separable Nonlinear Inverse Problems 1

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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: (数字)9783030223687

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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Direct MRI Segmentation from k-space Data by Iterative Potts Minimization 1

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

作者： Kiefer, Lukas Petra, Stefania Storath, Martin Weinmann, Andreas Heidelberg Univ Math Imaging Grp Heidelberg Germany Hsch Darmstadt Dept Math & Nat Sci Darmstadt Germany Hsch Wurzburg Schweinfurt Dept Appl Nat Sci & Humanities Wurzburg Germany Helmholtz Zentrum Munchen Inst Computat Biol Munich Germany

ISBN: (数字)9783030223687

ISBN: (纸本)9783030223687;9783030223670

We consider the problem of image segmentation in magnetic resonance imaging (MRI) directly from k-space measurements as opposed to more standard approaches that first reconstruct the image before segmenting it. The model we employ is the piecewise-constant Mumford-Shah model (the Potts model) in connection with the MRI reconstruction problem. The output of our proposed scheme is a piecewise-constant function which yields a segmentation of the image domain. To solve the involved non-convex and non-smooth optimization problem, we adopt an iterative minimization strategy based on surrogate functionals. Numerical experiments illustrate the potential of the approach when applied on undersampled MRI data.

关键词： MRI segmentation Joint reconstruction and segmentation Potts model Piecewise-constant Mumford-Shah model Regularization of inverse problems

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7th international conference on scale space and variational methods in computer vision, SSVM 2019

7th International Conference on Scale Space and Variational ...

引用

7th international conference on scale space and variational methods in computer vision, SSVM 2019

ISBN: (纸本)9783030223670

The proceedings contain 44 papers. The special focus in this conference is on scale space and variational methods in computer vision. The topics include: Iterative Sampled methods for Massive and Separable Nonlinear Inverse Problems;Refitting Solutions Promoted by $$\ell _variational$$ Sparse Analysis Regularizations with Block Penalties;An Iteration Method for X-Ray CT Reconstruction from Variable-Truncation Projection Data;A New Iterative Method for CT Reconstruction with Uncertain View Angles;time Discrete Geodesics in Deep Feature spaces for Image Morphing;minimal Lipschitz Extensions for Vector-Valued Functions on Finite Graphs;the Convex-Hull-Stripping Median Approximates Affine Curvature Motion;Total Variation and Mean Curvature PDEs on the space of Positions and Orientations;a variational Convex Hull Algorithm;PDE Evolutions for M-Smoothers: From Common Myths to Robust Numerics;macrocanonical Models for Texture Synthesis;variational Registration of Multiple Images with the SVD Based $$\mathrm {S}q\mathrm {N}$$ Distance Measure;Multi-tasking to Correct: Motion-Compensated MRI via Joint Reconstruction and Registration;variational Image Registration for Inhomogeneous-Resolution Pairs;computing Nonlinear Eigenfunctions via Gradient Flow Extinction;sparsification scale-spaces;stable Explicit p-Laplacian Flows Based on Nonlinear Eigenvalue Analysis;provably scale-Covariant Networks from Oriented Quasi Quadrature Measures in Cascade;a Fast Multi-layer Approximation to Semi-discrete Optimal Transport;global Similarity with Additive Smoothness for Spectral Segmentation;segmentation of 2D and 3D Objects with Intrinsically Similarity Invariant Shape Regularisers;finding Structure in Point Cloud Data with the Robust Isoperimetric Loss;lattice Metric space Application to Grain Defect Detection;learning Adaptive Regularization for Image Labeling Using Geometric Assignment;a Balanced Phase Field Model for Active Contours.

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Time Discrete Geodesics in Deep Feature spaces for Image Morphing 1

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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: (数字)9783030223687

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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A Cortical-Inspired Model for Orientation-Dependent Contrast Perception: A Link with Wilson-Cowan Equations 1

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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: (数字)9783030223687

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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引用

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: (数字)9783030223687

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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scale-space Autoencoders for Unsupervised Anomaly Segmentation in Brain MRI 23rd

Scale-Space Autoencoders for Unsupervised Anomaly Segmentati...

引用

23rd international conference on Medical Image Computing and computer-Assisted Intervention, MICCAI 2020

作者： Baur, Christoph Wiestler, Benedikt Albarqouni, Shadi Navab, Nassir TU Munich Munich Germany Computer Vision Laboratory ETH Zurich Zurich Switzerland Whiting School of Engineering Johns Hopkins University Baltimore United States Department of Diagnostic and Interventional Neuroradiology Klinikum rechts der Isar TU Munich Munich Germany

ISBN: (纸本)9783030597184

Brain pathologies can vary greatly in size and shape, ranging from few pixels (i.e. MS lesions) to large, space-occupying tumors. Recently proposed Autoencoder-based methods for unsupervised anomaly segmentation in brain MRI have shown promising performance, but face difficulties in modeling distributions with high fidelity, which is crucial for accurate delineation of particularly small lesions. Here, similar to these previous works, we model the distribution of healthy brain MRI to localize pathologies from erroneous reconstructions. However, to achieve improved reconstruction fidelity at higher resolutions, we learn to compress and reconstruct different frequency bands of healthy brain MRI using the laplacian pyramid. In a range of experiments comparing our method to different State-of-the-Art approaches on three different brain MR datasets with MS lesions and tumors, we show improved anomaly segmentation performance and the general capability to obtain much more crisp reconstructions of input data at native resolution. The modeling of the laplacian pyramid further enables the delineation and aggregation of lesions at multiple scales, which allows to effectively cope with different pathologies and lesion sizes using a single model. © 2020, Springer Nature Switzerland AG.

关键词： Pathology

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Total Variation and Mean Curvature PDEs on the space of Positions and Orientations 1

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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: (数字)9783030223687

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 1

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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: (数字)9783030223687

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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