Roots, symmetries and conjugacy of pseudo-Anosov mapping classes

An algorithm is proposed that solves two decision problems for pseudo-Anosov elements in the mapping class group of a surface with at least one marked fixed point. The first problem is the root problem: decide if the element is a power and in this case compute the roots. The second problem is the symmetry problem: decide if the element commutes with a finite order element and in this case compute this element. The structure theorem on which this algorithm is based provides also a new solution to the conjugacy problem

Edge detection using topological gradients: a scale-space approach

International audienceWe provide in this paper a link between two methods of edge detection: edge detection using scale-space analysis, and edge detection using topological asymptotic analysis. More precisely, we show that the topological gradient associated with an image u is given by a combination of the gradients of two smoothed versions of the image u at two different scales, namely φ⋆u and (φ⋆φ)⋆u, where φ is the fundamental so- lution of the elliptic restoration equation. In the same setting we propose a new edge detector based on the maximization of the variance of the image. Then we generalize our approach to Gaussian kernels considering a topological asymptotic analysis of the parabolic heat equation. A numerical comparison of these detectors together with the Canny edge detector is presented

Identification of velocity fields for geophysical fluids from a sequence of images

International audienceWe propose an algorithm to estimate the motion between two images. This algorithm is based on the nonlinear brightness constancy assumption. The number of unknowns is reduced by considering displacement fields that are piecewise linear with respect to each space variable, and the Jacobian matrix of the cost function to be minimized is assembled rapidly using a finite element method. Different regularization terms are considered, and a multiscale approach provides fast and efficient convergence properties. Several numerical results of this algorithm on simulated and real geophysical flows are presented and discussed

Variational algorithms to remove stationary noise. Application to microscopy imaging.

International audienceA framework and an algorithm are presented in order to remove stationary noise from images. This algorithm is called VSNR (Variational Stationary Noise Remover). It can be interpreted both as a restoration method in a Bayesian framework and as a cartoon+texture decomposition method. In numerous denoising applications the white noise assumption fails: structured patterns (e.g. stripes) appear in the images. The model described here addresses these cases. Applications are presented with images acquired using different modalities: scan- ning electron microscope, FIB-nanotomography, and an emerging fluorescence microscopy technique called SPIM (Selective Plane Illumination Microscope)

The Generalized Graetz Problem in Finite Domains

We consider the generalized Graetz problem associated with stationary convection-diffusion inside a domain having any regular three-dimensional translationally invariant section and finite or semi-infinite extent. Our framework encompasses any previous “extended” and “conjugated” Graetz generalizations and provides theoretical bases for computing the orthogonal set of generalized two-dimensional Graetz modes. The theoretical framework includes both heterogeneous and possibly anisotropic diffusion tensors. In the case of semi-infinite domains, the existence of a bounded solution is shown from the analysis of two-dimensional operator eigenvectors which form a basis of L2 . In the case of finite domains a similar basis can be exhibited, and the mode’s amplitudes can be obtained from the inversion of newly defined finite domain operator. Our analysis includes both the theoretical and practical issues associated with this finite domain operator inversion as well as its interpretation as a multireflection image method. Error estimates are provided when numerically truncating the spectrum to a finite number of modes. Numerical examples are validated for reference configurations and provided in nontrivial cases. Our methodology shows how to map the solution of stationary convection-diffusion problems in finite three-dimensional domains into a two-dimensional operator spectrum, which leads to a drastic reduction in computational cost

PROCESSING STATIONARY NOISE: MODEL AND PARAMETER SELECTION IN VARIATIONAL METHODS.

International audienceAdditive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white noise setting. We recently proposed a variational algorithm to address this issue. In this paper, we analyze this problem from a statistical point of view and then provide deterministic properties of variational formulations. In the first part of this work, we demonstrate that in many practical problems, the noise can be assimilated to a colored Gaussian noise. We provide a quantitative measure of the distance between a stationary process and the corresponding Gaussian process. In the second part, we focus on the Gaussian setting and analyze denoising methods which consist of minimizing the sum of a total variation term and an l2 data fidelity term. While the constrained formulation of this problem allows to easily tune the parameters, the Lagrangian formulation can be solved more efficiently since the problem is strongly convex. Our second contribution consists in providing analytical values of the regularization parameter in order to approximately satisfy Morozov's discrepancy principle

Activation Sites Estimation using a Fast Algorithm Based on an Eikonal Equation

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Anisotropic Diffusion in ITK

Anisotropic Non-Linear Diffusion is a powerful image processing technique, which allows to simultaneously remove the noise and enhance sharp features in two or three dimensional images. Anisotropic Diffusion is understood here in the sense of Weickert, meaning that diffusion tensors are anisotropic and reflect the local orientation of image features. This is in contrast with the non-linear diffusion filter of Perona and Malik, which only involves scalar diffusion coefficients, in other words isotropic diffusion tensors. In this paper, we present an anisotropic non-linear diffusion technique we implemented in ITK. This technique is based on a recent adaptive scheme making the diffusion stable and requiring limited numerical resources. (See supplementary data.

Imaging by modification: numerical reconstruction of local conductivities from corresponding power density measurements

International audienceWe discuss the reconstruction of the impedance from the local power density. This study is motivated by a new imaging principle which allows to recover interior measurements of the energy density by a non invasive method. We discuss the theoretical feasibility in two dimensions, and propose numerical algorithms to recover the conductivity in two and three dimension. The efficiency of this approach is documented by several numerical simulation

Analyse de la convection-diffusion entre deux tubes parallèles plongés dans un domaine cylindrique

Nous étudions la convection-diffusion tri-dimensionelle entre tubes parallèles par une formulation théorique bi-dimensionnelle précédement proposée. L’implémentation de cette formulation bi-dimensionnelle par éléments finis permet de calculer une vaste classe de configurations physique, hydrodynamiques et géométriques. Nous nous attachons à l’étude du champ de température et de l’évolution des flux en fonction du nombre de Péclet Pe, l’écart entre les deux tubes d, le rayon des tubes r et les vitesses des écoulements au sein des tubes