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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Pierre, Fabien Aujol, Jean-François Bugeau, Aurélie Ta, Vinh-thong University of Bordeaux IMB CNRS UMR 5251 Talence33400 France University of Bordeaux LaBRI CNRS UMR 5800 PICTURA Talence33400 France Bordeaux INP LaBRI CNRS UMR 5800 PICTURA Talence33400 France

ISBN: (纸本)9783319184609

this paper is concerned with a problem arising when editing color images, namely the Luminance-Hue Specification. this problem often occurs when converting an edited image in a given color-space to RGB. Indeed, the colors often get out of the standard range of the RGB space which is commonly used by most of display hardwares. Simple truncations lead to inconsistency in the hue and luminance of the edited image. We formalize and describe this problem from a geometrical point of view. A fast algorithm to solve the considered problem is given. We next focus on its application to image colorization in the RGB color space while most of the methods use other ones. Using directly the three RGB channels, our model avoids artifact effects which appear with other color spaces. Finally a variational model that regularizes color images while dealing with Luminance Hue Specification problem is proposed. © Springer international Publishing Switzerland 2015.

关键词： Luminance

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Regularity and scale-space properties of fractional high order linear filtering

Regularity and scale-space properties of fractional high ord...

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5th international conference on scale-space and PDE methods in computer vision

作者： Didas, S Burgeth, B Imiya, A Weickert, J Univ Saarland Fac Math & Comp Sci Math & Image Anal Grp D-66041 Saarbrucken Germany IMIT Chiba Univ Inage Ku Chiba 2628522 Japan

ISBN: (纸本)3540255478

We investigate the use of fractional powers of the Laplacian for signal and image simplification. We focus both on their corresponding variational techniques and parabolic pseudodifferential equations. We perform a detailed study of the regularisation properties of energy functionals, where the smoothness term consists of various linear combinations of fractional derivatives. the associated parabolic pseudodifferential equations with constant coefficients are providing the link to linear scale-space theory. these encompass the well-known a-scale-spaces, even those with parameter values alpha > 1 known to violate common maximum-minimum principles. Nevertheless, we show that it is possible to construct positivity-preserving combinations of high and low-order filters. Numerical experiments in this direction indicate that non-integral orders play an essential role in this construction. the paper reveals the close relation between continuous and semi-discrete filters, and by that helps to facilitate efficient implementations. In additional numerical experiments we compare the variance decay rates for white noise and edge signals through the action of different filter classes.

关键词： Signal filtering and prediction

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Invertible orientation scores of 3D images 5

Invertible orientation scores of 3D images

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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Janssen, Michiel Duits, Remco Breeuwer, Marcel Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Department of Biomedical Engineering Eindhoven University of Technology Eindhoven Netherlands

ISBN: (纸本)9783319184609

the enhancement and detection of elongated structures in noisy image data is relevant for many biomedical applications. To handle complex crossing structures in 2D images, 2D orientation scores U: 2× S1→ were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores U: 3× S2→ . First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake-wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. For efficient implementation of the different steps in the wavelet creation we use a spherical harmonic transform. Finally, we show some first results of practical applications of 3D orientation scores. © Springer international Publishing Switzerland 2015.

关键词： Image enhancement

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An analysis of variational alignment of curves in images

An analysis of variational alignment of curves in images

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5th international conference on scale space and PDE methods in computer vision, scale-space 2005

作者： Overgaard, Niels Chr. Solem, Jan Erik Applied Mathematics Group School of Technology and Society Malmö University Sweden

In this paper a common variational formulation for alignment of curves to vector fields is analyzed. this variational approach is often used to solve the problem of aligning curves to edges in images by choosing the vector field to be the image gradient. the main contribution of this paper is an analysis of the Gâteaux derivative and the descent motion of the corresponding alignment functional, improving on earlier research in this area. Several intermediate results are proved and finally a theorem concerning necessary conditions for extremals of the alignment functional is derived. the analysis of the evolution is performed using a level set formulation and results from distribution theory. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Image analysis

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Image deblurring in the presence of impulsive noise

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international JOURNAL OF computer vision 2006年第3期70卷 279-298页

作者： Bar, Leah Kiryati, Nahum Sochen, Nir Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel Tel Aviv Univ Dept Appl Math IL-69978 Tel Aviv Israel

Consider the problem of image deblurring in the presence of impulsive noise. Standard image deconvolution methods rely on the Gaussian noise model and do not perform well with impulsive noise. the main challenge is to deblur the image, recover its discontinuities and at the same time remove the impulse noise. Median-based approaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is difficult in current gradient-based edge-preserving restoration methods. the suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view. We present a unified variational approach to image deblurring and impulse noise removal. the objective functional consists of a fidelity term and a regularizer. Data fidelity is quantified using the robust modified L(1) norm, and elements from the Mumford-Shah functional are used for regularization. We show that the Mumford-Shah regularizer can be viewed as an extended line process. It reflects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diffusion. this allows to distinguish outliers from edges and leads to superior experimental results.

关键词： image deblurring restoration impulse noise salt and pepper noise variational methods

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Learning Local Regularization for variational Image Restoration 8th

Learning Local Regularization for Variational Image Restora...

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

作者： Prost, Jean Houdard, Antoine Almansa, Andrés Papadakis, Nicolas Univ. Bordeaux Bordeaux INP CNRS IMB UMR 5251 Talence33400 France Université de Paris MAP5 CNRS Paris75006 France

ISBN: (纸本)9783030755485

In this work, we propose a framework to learn a local regularization model for solving general image restoration problems. this regularizer is defined with a fully convolutional neural network that sees the image through a receptive field corresponding to small image patches. the regularizer is then learned as a critic between unpaired distributions of clean and degraded patches using a Wasserstein generative adversarial networks based energy. this yields a regularization function that can be incorporated in any image restoration problem. the efficiency of the framework is finally shown on denoising and deblurring applications. © 2021, Springer Nature Switzerland AG.

关键词： Image reconstruction

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A multigrid platform for real-time motion computation with discontinuity-preserving variational methods

A multigrid platform for real-time motion computation with d...

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5th international conference on scale-space and PDE methods in computer vision

作者： Bruhn, Andres Weickert, Joachim Kohlberger, Timo Schnoerr, Christoph Univ Saarland Math Image Anal Grp Fac Math & Comp Sci D-66041 Saarbrucken Germany Univ Mannheim Dept Math & Comp Sci Comp Vis Graph & Pattern Recognit Grp D-68131 Mannheim Germany

variational methods are among the most accurate techniques for estimating the optic flow. they yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases-even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 x 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.

关键词： partial differential equations variational methods optic flow multigrid methods

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Estimation of the optimal variational parameter via SNR analysis

Estimation of the optimal variational parameter via SNR anal...

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5th international conference on scale space and PDE methods in computer vision, scale-space 2005

作者： Gilboa, Guy Sochen, Nir A. Zeevi, Yehoshua Y. Department of Mathematics UCLA Los Angeles CA 90095 United States Department of Applied of Mathematics Tel-Aviv Univ. Tel-Aviv 69978 Israel Department of Electrical Engineering Technion Haifa 32000 Israel

We examine the problem of finding the optimal weight of the fidelity term in variational denoising. Our aim is to maximize the signal to noise ratio (SNR) of the restored image. A theoretical analysis is carried out and several bounds are established on the performance of the optimal strategy and a widely used method, wherein the variance of the residual part equals the variance of the noise. A necessary condition is set to achieve maximal SNR. We provide a practical method for estimating this condition and show that the results are sufficiently accurate for a large class of images, including piecewise smooth and textured images. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Parameter estimation

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Image deblurring in the presence of impulsive noise

Image deblurring in the presence of impulsive noise

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5th international conference on scale-space and PDE methods in computer vision

作者： Bar, Leah Kiryati, Nahum Sochen, Nir Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel Tel Aviv Univ Dept Appl Math IL-69978 Tel Aviv Israel

关键词： image deblurring restoration impulse noise salt and pepper noise variational methods

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Data-driven sub-riemannian geodesics in SE(2) 5

Data-driven sub-riemannian geodesics in SE(2)

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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Bekkers, E.J. Duits, R. Mashtakov, A. Sanguinetti, G.R. Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Department of Biomedical Engineering Eindhoven University of Technology Eindhoven Netherlands

ISBN: (纸本)9783319184609

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group SE(2) = 2 S1 with a metric tensor depending on a smooth external cost C: SE(2) → [δ, 1], δ > 0, computed from image data. the method consists of a first step where geodesically equidistant surfaces are computed as a viscosity solution of a Hamilton- Jacobi-Bellman (HJB) system derived via Pontryagin’s Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. We show that our method produces geodesically equidistant surfaces. For C = 1 we show that our method produces the global minimizers, and comparison with exact solutions shows a remarkable accuracy of the SR-spheres/geodesics. Finally, trackings in synthetic and retinal images show the potential of including the SR-geometry. © IFIP international Federation for Information Processing 2015.

关键词： Wavefronts

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