266 research outputs found
Phase field method for mean curvature flow with boundary constraints
International audienceThis paper is concerned with the numerical approximation of mean curvature flow satisfying an additional inclusion-exclusion constraint . Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a -convergence result and then show some numerical comparisons of these two different models
Divergence-free Wavelets for Navier-Stokes
In this paper, we investigate the use of compactly supported divergence-free
wavelets for the representation of the Navier-Stokes solution. After reminding
the theoretical construction of divergence-free wavelet vectors, we present in
detail the bases and corresponding fast algorithms for 2D and 3D incompressible
flows. In order to compute the nonlinear term, we propose a new method which
provides in practice with the Hodge decomposition of any flow: this
decomposition enables us to separate the incompressible part of the flow from
its orthogonal complement, which corresponds to the gradient component of the
flow. Finally we show numerical tests to validate our approach.Comment: novembre 200
The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AMâFM images
The synchrosqueezing method aims at decomposing 1D functions into superpositions of a small number of âIntrinsic Modesâ, supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the timeâfrequency plane, together with a reconstruction of each mode. In this paper, a bidimensional version of the synchrosqueezing transform is defined, by considering a well-adapted extension of the concept of analytic signal to images: the monogenic signal. We introduce the concept of âIntrinsic Monogenic Modeâ, that is the bidimensional counterpart of the notion of Intrinsic Mode. We also investigate the properties of its associated Monogenic Wavelet Decomposition. This leads to a natural bivariate extension of the Synchrosqueezed Wavelet Transform, for decomposing and processing multicomponent images. Numerical tests validate the effectiveness of the method on synthetic and real images
The Fourier-based Synchrosqueezing Transform
The short-time Fourier transform (STFT) and continuous wavelet transform (CWT) are intensively used to analyze and process multicomponent signals, ie superpositions of mod- ulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relations, inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the continuous wavelet transform, it provides a sharp, con- centrated representation, while remaining invertible. This technique received a renewed interest with the recent publi- cation of an approximation result, which provides guarantees for the decomposition of a multicomponent signal. This paper adapts the formulation of the synchrosqueezing to the STFT, and states a similar theoretical result. The emphasis is put on the differences with the CWT-based synchrosqueezing, and all the content is illustrated through numerical experiments
Primal-dual formulation of the Dynamic Optimal Transport using Helmholtz-Hodge decomposition
This work deals with the resolution of the dynamic optimal transport (OT) problem between 1D or 2D images in the fluid mechanics framework of Benamou-Brenier [6]. The numerical resolution of this dynamic formulation of OT, despite the successful application of proximal methods [36] is still computationally demanding. This is partly due to a space-time Laplace operator to be solved at each iteration, to project back to a divergence free space. In this paper, we develop a method using the Helmholtz-Hodge decomposition [23] in order to enforce the divergence-free constraint throughout the iterations. We prove that the functional we consider has better convexity properties on the set of constraints. In particular we explain that in 1D+time, this formulation is equivalent to the resolution of a minimal surface equation. We then adapt the first order primal-dual algorithm for convex problems of Chambolle and Pock [12] to solve this new problem, leading to an algorithm easy to implement. Besides, numerical experiments demonstrate that this algorithm is faster than state of the art methods for dynamic optimal transport [36] and efficient with real-sized images
On the Mode Synthesis in the Synchrosqueezing Method
Publication in the conference proceedings of EUSIPCO, Bucharest, Romania, 201
Convex Super-Resolution Detection of Lines in Images
International audienceIn this paper, we present a new convex formulation for the problem of recovering lines in degraded images. Following the recent paradigm of super-resolution, we formulate a dedicated atomic norm penalty and we solve this optimization problem by means of a primalâdual algorithm. This parsimonious model enables the reconstruction of lines from lowpass measurements, even in presence of a large amount of noise or blur. Furthermore, a Prony method performed on rows and columns of the restored image, provides a spectral estimation of the line parameters, with subpixel accuracy
Comment un genre de sites construit des niches professionnelles
De la mĂȘme façon que leurs ancĂȘtres imprimĂ©s, audio et visuels, les mĂ©dias numĂ©riques sont accompagnĂ©s de discours qui suivent leur naissance et leur dĂ©veloppement en termes dâusage et de modĂšles dâactivitĂ© aussi bien quâen termes de modĂšles de communication. RĂ©cemment, les blogs, Ă la suite des sites web, ont Ă©tĂ© prĂ©sentĂ©s dans ces discours comme Ă©tant trĂšs innovants et rĂ©volutionnaires pour les journalistes et pour le journalisme, allant jusquâĂ changer les rĂšgles de communication dans lâensemble. Ces discours produisent des « imaginaires » sur eux-mĂȘmes. Une fois de plus, en 2009, on a entendu les mĂȘmes thĂšmes en ce qui concerne les soi-disant « rĂ©seaux sociaux » comme la marque nommĂ©e Twitter. Cet article analyse les effets de ce cycle discursif sur le journalisme et sur ses pratiques.In the same manner as their printed, audio and visual ancestors, digital media are escorted by discourses, that follow their birth and development, in terms of usage and business models, as well as communication models. Recently, weblogs, following websites, have been presented, in these discourses, as being very innovative and revolutionary for journalists and journalism, even changing the rules of communication as a whole. These discourses produce âimaginariesâ about them. Again, in 2009, the same themes were heard, concerning the so-called âsocial networks,â such as the brand named Twitter. The article analyses the effects of this discursive cycle on journalism and its practices
Mod\'elisations de textures par champ gaussien \`a orientation locale prescrite
This paper presents two new models of oriented texture, based on a new class
of Gaussian fields, called locally anisotropic fractional Brownian fields, with
prescribed local orientation at any point. These fields are a local version of
a specific class of anisotropic self-similar Gaussian fields with stationary
increments. The simulation of such textures is obtained using a new algorithm
mixing the tangent field formulation with the Cholesky method or the turning
band method, this latter method having proved its efficiency for generating
stationary anisotropic textures. Numerical experiments show the ability of the
method for synthesis of textures with prescribed local orientation.Comment: in Frenc
Texture Modeling by Gaussian fields with prescribed local orientation
International audienceThis paper presents a new framework for oriented texture modeling. We introduce a new class of Gaussian fields, called Locally Anisotropic Fractional Brownian Fields, with prescribed local orientation at any point. These fields are a local version of a specific class of anisotropic self-similar Gaussian fields with stationary increments. The simulation of such textures is obtained using a new algorithm mixing the tangent field formulation and a turning band method, this latter method having proved its efficiency for generating stationary anisotropic textures. Numerical experiments show the ability of the method for synthesis of textures with prescribed local orientation
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