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Computational Geometry-Based scale-space and Modal Image Decomposition Application to Light Video-Microscopy Imaging

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2nd international conference on scale space and variational methods in computer vision

作者： Chessel, Anatole Cinquin, Bertrand Bardin, Sabine Salamero, Jean Kervrann, Charles INRIA Rennes Rennes France INRA MIA Paris France CNRS Inst Curie F-75700 Paris France Soleil Synchrotron F-91190 Gif Sur Yvette France PICT Inst Curie IBiSA Pune Maharashtra India

ISBN: (纸本)9783642022555

In this paper a framework for defining scale-spaces, based on the computational geometry concepts of a-shapes, is proposed. In this approach, objects (curves or surfaces) of increasing convexity are computed by selective sub-sampling, from the original shape to its convex hull. The relationships with the Empirical Mode Decomposition (EMD), the curvature motion-based scale-space and some operators from mathematical morphology, are studied. Finally, we address the problem of additive image/signal decomposition in fluorescence video-microscopy. An image sequence is mainly considered as a collection of 1D temporal signals, each pixel being associated with its temporal intensity variation.

关键词： Computational geometry

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Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition 6th

Combining Contrast Invariant L1 Data Fidelities with Nonline...

引用

6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Zeune, Leonie van Gils, stephan A. Terstappen, Leon W. M. M. Brune, Christoph Univ Twente Dept Appl Math NL-7522 NB Enschede Netherlands Univ Twente Dept Med Cell BioPhys NL-7522 NB Enschede Netherlands

ISBN: (纸本)9783319587714;9783319587707

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, L-1 data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of L-1-based multi-scale methods with nonlinear spectral decompositions. We compare L-1 with L-2 scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of L-1-TV promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.

关键词： L-1-TV Denoising scale-spaces Nonlinear spectral decomposition Multiscale segmentation Eigenfunction Calibrable sets

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A variational framework for spatio-temporal smoothing of fluid motions

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1st international conference on scale space and variational methods in computer vision, SSVM 2007

作者： Papadakis, Nicolas Mémin, Étienne IRISA/INRIA Campus de Beaulieu 35042 Rennes Cedex France

ISBN: (纸本)9783540728221

In this paper, we introduce a variational framework derived from data assimilation principles in order to realize a temporal Bayesian smoothing of fluid flow velocity fields. The velocity measurements are supplied by an optical flow estimator. These noisy measurement are smoothed according to the vorticity-velocity formulation of Navier-stokes equation. Following optimal control recipes, the associated minimization is conducted through an iterative process involving a forward integration of our dynamical model followed by a backward integration of an adjoint evolution law. Both evolution laws are implemented with second order non-oscillatory scheme. The approach is here validated on a synthetic sequence of turbulent 2D flow provided by Direct Numerical Simulation (DNS) and on a real world meteorological satellite image sequence depicting the evolution of a cyclone. © Springer-Verlag Berlin Heidelberg 2007.

关键词： Flow velocity

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Combining different types of scale space interest points using canonical sets

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1st international conference on scale space and variational methods in computer vision, SSVM 2007

作者： Kanters, Frans Denton, Trip Shokoufandeh, Ali Florack, Luc Ter Haar Romeny, Bart Eindhoven University of Technology Den Dolech 2 Postbus 513 5600 MB Eindhoven Netherlands Drexel University University Crossings 141 Philadelphia United States

ISBN: (纸本)9783540728221

scale space interest points capture important photometric and deep structure information of an image. The information content of such points can be made explicit using image reconstruction. In this paper we will consider the problem of combining multiple types of interest points used for image reconstruction. It is shown that ordering the complete set of points by differential (quadratic) TV-norm (which works for single feature types) does not yield optimal results for combined point sets. The paper presents a method to solve this problem using canonical sets of scale space features. Qualitative and quantitative analysis show improved performance over simple ordering of points using the TV-norm. © Springer-Verlag Berlin Heidelberg 2007.

关键词： Image reconstruction

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Total Directional Variation for Video Denoising 7th

Total Directional Variation for Video Denoising

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

作者： Parisotto, Simone Schonlieb, Carola-Bibiane Univ Cambridge CCA Wilberforce Rd Cambridge CB3 0WA England Univ Cambridge DAMTP Wilberforce Rd Cambridge CB3 0WA England

ISBN: (纸本)9783030223687;9783030223670

In this paper we propose a variational approach for video denoising, based on a total directional variation (TDV) regulariser proposed in [20,21] for image denoising and interpolation. In the TDV regulariser, the underlying image structure is encoded by means of weighted derivatives so as to enhance the anisotropic structures in images, e.g. stripes or curves with a dominant local directionality. For the extension of TDV to video denoising, the space-time structure is captured by the volumetric structure tensor guiding the smoothing process. We discuss this and present our whole video denoising workflow. The numerical results are compared with some state-of-the-art video denoising methods.

关键词： Total directional variation Video denoising Anisotropy structure tensor variational methods

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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...

引用

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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Nonlinear Flows for Displacement Correction and Applications in Tomography 6th

Nonlinear Flows for Displacement Correction and Applications...

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Dong, Guozhi Scherzer, Otmar Univ Vienna Computat Sci Ctr Oskar Morgenstern Pl 1 A-1090 Vienna Austria Austrian Acad Sci Johann Radon Inst Computat & Appl Math RICAM Altenbergerstr 69 A-4040 Linz Austria

ISBN: (纸本)9783319587714;9783319587707

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We show a preliminary convergence result of a relaxed convexification of the non-convex optimization problem. Some properties on the behavior of the solutions of these filtering flows are studied by numerical analysis. At the end, we provide examples for correcting angular perturbations in tomographical data.

关键词： Non-convex regularization Nonlinear flow Displacement correction Radon transform Angular perturbation

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Theoretical Foundations for Discrete Forward-and-Backward Diffusion Filtering

引用

2nd international conference on scale space and variational methods in computer vision

作者： Welk, Martin Gilboa, Guy Weickert, Joachim Univ Saarland Math Image Anal Grp Fac Math & Comp Sci Campus E1-1 D-66041 Saarbrucken Germany 3DV Syst IL-20692 Yokneam Israel

ISBN: (纸本)9783642022555

Forward-and-backward (FAB) diffusion is a method for sharpening blurry images (Gilboa et al. 2002). It combines forward diffusion with a positive diffusivity and backward diffusion where negative diffusivities are used. The well-posedness properties of FAB diffusion are unknown, and it has been observed that standard discretisations can violate a maximum-minimum principle. We show that for a novel nonstandard space discretisation which pays specific attention to image extrema, one can apply a modification of the space-discrete well-posedness and scale-space framework of Weickert (1998). This allows to establish well-posedness and a maximum-minimum principle for the resulting dynamical system. In the fully discrete 1-D case with an explicit time discretisation, a maximum-minimum principle and total variation reduction are proven in spite of the fact that negative diffusivities may appear. This provides a theoretical justification for applying FAB diffusion to digital images.

关键词： Diffusion

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Wasserstein Barycenter and Its Application to Texture Mixing

Wasserstein Barycenter and Its Application to Texture Mixing

引用

3rd international conference on scale space and variational methods in computer vision

作者： Rabin, Julien Peyre, Gabriel Delon, Julie Bernot, Marc ENS Cachan CMLA Cachan France Ceremade Univ Paris France LTCI Paris France Thales Alenia Space Paris France

ISBN: (纸本)9783642247842

This paper proposes a new definition of the averaging of discrete probability distributions as a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time complexity involved by the numerical solving of such problem, the original Wasserstein metric is replaced by a sliced approximation over 1D distributions. This enables us to introduce a new fast gradient descent algorithm to compute Wasserstein barycenters of point clouds. This new notion of barycenter of probabilities is likely to find applications in computer vision where one wants to average features defined as distributions. We show an application to texture synthesis and mixing, where a texture is characterized by the distribution of the response to a multi-scale oriented filter bank. This leads to a simple way to navigate over a convex domain of color textures.

关键词： Optimal transport texture synthesis and mixing barycenter of distributions

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Compressing Audio Signals with Inpainting-Based Sparsification 7th

Compressing Audio Signals with Inpainting-Based Sparsificati...

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

作者： Peter, Pascal Contelly, Jan Weickert, Joachim Saarland Univ Math Image Anal Grp Fac Math & Comp Sci Campus E1-7 D-66041 Saarbrucken Germany

ISBN: (纸本)9783030223687;9783030223670

Inpainting techniques are becoming increasingly important for lossy image compression. In this paper, we investigate if successful ideas from inpainting-based codecs for images can be transferred to lossy audio compression. To this end, we propose a framework that creates a sparse representation of the audio signal directly in the sample-domain. We select samples with a greedy sparsification approach and store this optimised data with entropy coding. Decoding restores the missing samples with well-known 1-D interpolation techniques. Our evaluation on music pieces in a stereo format suggests that the lossy compression of our proof-of-concept framework is quantitatively competitive to transform-based audio codecs such as mp3, AAC, and Vorbis.

关键词： Image compression

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