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Active contours for multi-region image segmentation with a single level set function

4th international conference on scale space and variational methods in computer vision, ssvm 2013

作者： Dubrovina, Anastasia Rosman, Guy Kimmel, Ron Computer Science Department Technion - IIT Haifa Israel

ISBN: (纸本)9783642382666

Segmenting the image into an arbitrary number of parts is at the core of image understanding. Many formulations of the task have been suggested over the years. Among these are axiomatic functionals, which are hard to implement and analyze, while graph-based alternatives impose a non-geometric metric on the problem. We propose a novel approach to tackle the problem of multiple-region segmentation for an arbitrary number of regions. the proposed framework allows generic region appearance models while avoiding metrication errors. Updating the segmentation in this framework is done by level set evolution. Yet, unlike most existing methods, evolution is executed using a single non-negative level set function, through the Voronoi Implicit Interface Method for a multi-phase interface evolution. We apply the proposed framework to synthetic and real images, with various number of regions, and compare it to state-of-the-art image segmentation algorithms. © 2013 Springer-Verlag.

关键词： Phase interfaces

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Weighted patch-based reconstruction: Linking (multi-view) stereo to scale space

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4th international conference on scale space and variational methods in computer vision, ssvm 2013

作者： Klowsky, Ronny Kuijper, Arjan Goesele, Michael Technische Universität Darmstadt Germany

ISBN: (纸本)9783642382666

Surface reconstruction using patch-based multi-view stereo commonly assumes that the underlying surface is locally planar. this is typically not true so that least-squares fitting of a planar patch leads to systematic errors which are of particular importance for multi-scale surface reconstruction. In a recent paper [12], we determined the modulation transfer function of a classical patch-based stereo system. Our key insight was that the reconstructed surface is a box-filtered version of the original surface. Since the box filter is not a true low-pass filter this causes high-frequency artifacts. In this paper, we propose an extended reconstruction model by weighting the least-squares fit of the 3D patch. We show that if the weighting function meets specified criteria the reconstructed surface is the convolution of the original surface with that weighting function. A choice of particular interest is the Gaussian which is commonly used in image and signal processing but left unexploited by many multi-view stereo algorithms. Finally, we demonstrate the effects of our theoretic findings using experiments on synthetic and real-world data sets. © 2013 Springer-Verlag.

关键词： Surface reconstruction

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A fully discrete theory for linear osmosis filtering

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4th international conference on scale space and variational methods in computer vision, ssvm 2013

作者： Vogel, Oliver Hagenburg, Kai Weickert, Joachim Setzer, Simon Dept. of Mathematics and Computer Science Campus E1.7 Saarland University 66041 Saarbrücken Germany

ISBN: (纸本)9783642382666

Osmosis filters are based on drift-diffusion processes. they offer nontrivial steady states with a number of interesting applications. In this paper we present a fully discrete theory for linear osmosis filtering that follows the structure of Weickert's discrete framework for diffusion filters. It regards the positive initial image as a vector and expresses its evolution in terms of iterative matrix-vector multiplications. the matrix differs from its diffusion counterpart by the fact that it is unsymmetric. We assume that it satisfies four properties: vanishing column sums, nonnegativity, irreducibility, and positive diagonal elements. then the resulting filter class preserves the average grey value and the positivity of the solution. Using the Perron-Frobenius theory we prove that the process converges to the unique eigenvector of the iteration matrix that is positive and has the same average grey value as the initial image. We show that our theory is directly applicable to explicit and implicit finite difference discretisations. We establish a stability condition for the explicit scheme, and we prove that the implicit scheme is absolutely stable. Both schemes converge to a steady state that solves the discrete elliptic equation. this steady state can be reached efficiently when the implicit scheme is equipped with a BiCGStab solver. © 2013 Springer-Verlag.

关键词： Finite difference method

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Lecture Notes in computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

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Lecture Notes in computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2013年 7893 LNCS卷 VI页

作者： Kuijper, Arjan Bredies, Kristian Pock, thomas Bischof, Horst Fraunhofer Gesellschaft Institut für Graphische Datenverarbeitung Fraunhoferstrasse 5 64283 Darmstadt Germany University of Graz Institute for Mathematics and Scientific Computing Heinrichstrasse 36 8010 Graz Austria Graz University of Technology Institute for Computer Graphics and Vision Inffeldgasse 16 8010 Graz Austria

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Analysis of Bayesian blind deconvolution

Analysis of Bayesian blind deconvolution

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9th international conference on Energy Minimization methods in computer vision and Pattern Recognition, EMMCVPR 2013

作者： Wipf, David Zhang, Haichao Visual Computing Group Microsoft Research Beijing China School of Computer Science Northwestern Polytechnical University Xi'an China

ISBN: (纸本)9783642403941

Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the solution space. While this naturally leads to a standard MAP estimation framework, performance is compromised by unknown trade-off parameter settings, optimization heuristics, and convergence issues stemming from non-convexity and/or poor prior selections. To mitigate these problems, several authors have recently proposed substituting a variational Bayesian (VB) strategy that marginalizes over the high-dimensional image space leading to better estimates of the blur kernel. However, the underlying cost function now involves both integrals with no closed-form solution and complex, function-valued arguments, thus losing the transparency of MAP. To elucidate these issues, we demonstrate that the VB methodology can be recast as an unconventional MAP problem with a very particular penalty/prior that couples the image, blur kernel, and noise level in a principled way. this unique penalty has a number of useful characteristics pertaining to relative concavity, local minima avoidance, and scale-invariance that allow us to rigorously explain the success of VB including its existing implementational heuristics and approximations. It also provides strict criteria for choosing the optimal image prior that, perhaps counter-intuitively, need not reflect the statistics of natural scenes. In so doing we challenge the prevailing notion of why VB is successful for blind deconvolution while providing a transparent platform for introducing enhancements and extensions. © 2013 Springer-Verlag.

关键词： Cost functions

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Analysis of iterative methods for solving a Ginzburg-Landau equation

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international JOURNAL OF computer vision 2005年第2-3期64卷 203-219页

作者： Borzi, A Grossauer, H Scherzer, O Graz Univ Math Inst A-8010 Graz Austria Univ Innsbruck Dept Comp Sci A-6020 Innsbruck Austria

Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed.

关键词： Ginzburg-Landau equation inpainting diffusion filtering non-linear partial differential equations variational problems

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Analysis of iterative methods for solving a Ginzburg-Landau equation

Analysis of iterative methods for solving a Ginzburg-Landau ...

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4th international conference on scale space methods in computer vision

作者： Borzi, A Grossauer, H Scherzer, O Graz Univ Math Inst A-8010 Graz Austria Univ Innsbruck Dept Comp Sci A-6020 Innsbruck Austria

关键词： Ginzburg-Landau equation inpainting diffusion filtering non-linear partial differential equations variational problems

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Towards recognition-based variational segmentation using shape priors and dynamic labeling

Towards recognition-based variational segmentation using sha...

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4th international conference on scale space methods in computer vision

作者： Cremers, D Sochen, N Schnörr, C Univ Calif Los Angeles Dept Comp Sci Los Angeles CA 90024 USA Tel Aviv Univ Dept Appl Math Tel Aviv Israel Univ Mannheim Dept Math & Comp Sci D-6800 Mannheim Germany

ISBN: (纸本)354040368X

We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both the level set function and the labeling function, the algorithm selects image regions where it is favorable to enforce the shape prior. By this, the approach permits to segment multiple independent objects in an image, and to discriminate familiar objects from unfamiliar ones by means of the labeling function. Numerical results demonstrate the performance of our approach.

关键词： Image segmentation

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variational dense motion estimation using the Helmholtz Decomposition

Variational dense motion estimation using the Helmholtz Deco...

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4th international conference on scale space methods in computer vision

作者： Kohlberger, T Mémin, É Schnörr, C Univ Mannheim Dept Math & Comp Sci Comp Vis Graph & Pattern Recognit Grp D-68131 Mannheim Germany Univ Rennes 1 IRISA F-35042 Rennes France

ISBN: (纸本)354040368X

We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: the laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. the potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. the performance of the approach is demonstrated with ground-truth experiments and real-world data.

关键词： Laminar flow

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4th international conference on scale space methods in computer vision, scale space 2003

4th International Conference on Scale Space Methods in Compu...

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4th international conference on scale space methods in computer vision, scale space 2003

ISBN: (纸本)354040368X

the proceedings contain 56 papers. the special focus in this conference is on Deep Structure Representation, scale space Mathematics, Equivalences, Implementing scale spaces and Other Evolution Equations. the topics include: Many-to-many matching of scale-space feature hierarchies using metric embedding;content based image retrieval using multiscale top points;feature coding with a statistically independent cortical representation;scale-space image analysis based on hermite polynomials theory;a complete system of measurement invariants for abelian lie transformation groups;equivalence results for TV diffusion and TV regularisation;correspondences between wavelet shrinkage and nonlinear diffusion;a generalized discrete scale-space formulation for 2-d and 3-d signals;real-time scale selection in hybrid multi-scale representations;a scale space for contour registration using minimal surfaces;the maximum principle for Beltrami color flow;the monogenic scale space on a bounded domain and its applications;least squares and robust estimation of local image structure;mode estimation using pessimistic scale space tracking;properties of Brownian image models in scale-space;image decomposition application to SAR images;basic morphological operations, band-limited images and sampling;an explanation for the logarithmic connection between linear and morphological systems;interest point detection and scale selection in space-time;towards recognition-based variational segmentation using shape priors and dynamic labeling;a Markov random field approach to multi-scale shape analysis and regularizing a set of unstructured 3d points from a sequence of stereo images.

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