MAP5 @ Universit\u00e9 Paris Cit\u00e9
45 Rue des Saints-P\u00e8res, 75006 Paris
Salle des th\u00e8ses (voir plan ci-dessous). <\/p>\n\n\n\n
Zoom<\/strong> ID<\/strong> : Demander le lien par email \u00e0 jonathan.vacher’@’u-paris.fr<\/p>\n\n\n\n Chez Fran\u00e7oise : https:\/\/goo.gl\/maps\/MVAVqyUu7CQ1cVAa6<\/a> – https:\/\/www.hoteldefleurieparis.com\/<\/a><\/p>\n\n\n\n Antoine Salmona<\/em> <\/p>\n\n\n\n Can push-forward models fit multimodal distributions? <\/strong><\/p>\n\n\n\n Les mod\u00e8les g\u00e9n\u00e9ratifs sont aujourd’hui l’un des sujets de recherche les plus populaires en apprentissage automatique, notamment gr\u00e2ce \u00e0 leur impressionnante capacit\u00e9 \u00e0 g\u00e9n\u00e9rer des images synth\u00e9tiques r\u00e9alistes. Cependant, il reste souvent difficile de savoir si ces mod\u00e8les s’approchent correctement de la distribution sous-jacente des donn\u00e9es ou s’ils g\u00e9n\u00e8rent uniquement des \u00e9chantillons qui semblent similaires aux donn\u00e9es. Dans ce travail, nous nous concentrons sur la classe particuli\u00e8re des mod\u00e8les g\u00e9n\u00e9ratifs push-forward<\/em>, qui inclut les Variational Autoencoders<\/em>, les Generative Adversarial Networks<\/em> et les Normalizing Flows<\/em>. Nous montrons que ces mod\u00e8les doivent avoir de grandes constantes de Lipschitz afin de bien approcher les distributions multimodales. Ainsi, comme la majorit\u00e9 des m\u00e9thodes pour stabiliser les mod\u00e8les g\u00e9n\u00e9ratifs consistent \u00e0 limiter, de fa\u00e7on plus ou moins directe, la constante de Lipschitz des r\u00e9seaux de neurones, il existe pour ces mod\u00e8les un compromis entre la stabilit\u00e9 de leur apprentissage et leur expressivit\u00e9.<\/p>\n<\/div><\/div>\n\n\n\n Anton Fran\u00e7ois<\/em><\/p>\n\n\n\n Topological Data Analysis for Train-Free Glioblastoma Segmentation in MRI: Advantages and Potential Impact<\/strong><\/p>\n\n\n\n This presentation will describe a new method for glioblastoma segmentation in MRI scans using topological data analysis (TDA). Accurate segmentation of glioblastomas is critical for effective treatment planning and disease progression monitoring. Our TDA-based approach offers several advantages over traditional machine learning methods, such as the ability to perform segmentation without the need for large annotated datasets and the ability to adapt easily to different data sets and segmentation needs. TDA also provides a more interpretable and stable framework for segmentation by leveraging topological features. Overall, this TDA-based method has the potential to be a valuable tool for the medical imaging analysis.<\/p>\n<\/div><\/div>\n\n\n\n Vadim Lebovici<\/em> <\/p>\n\n\n\n Hybrid transforms for topological data analysis<\/strong><\/p>\n\n\n\n Euler calculus\u2014integration of constructible functions with respect to the Euler characteristic\u2014has led to important advances in topological data analysis. <\/p>\n\n\n\n For instance, Schapira’s inversion theorem of the topological Radon transform is key to the following inverse problem: can one recover a shape embedded in the Euclidean space from the knowledge of the Euler characteristic of its intersections with all affine half-spaces? In this talk, I will introduce integral transforms combining Lebesgue integration and Euler calculus for constructible functions.<\/p>\n\n\n\n In this talk, I will present so-called \u00ab\u00a0hybrid\u00a0\u00bb transforms mixing Euler and Lebesgue calculus. These transforms provide more versatile shape descriptors than their topological analogues. I will show that these transforms output regular functions and are compatible with some topological operations on shapes. Finally, I will present an injectivity result for the hybrid Fourier transform.<\/p>\n\n\n\n Le calcul d’Euler, c’est-\u00e0-dire l’int\u00e9gration des fonctions constructibles par rapport \u00e0 la caract\u00e9ristique d’Euler, a permis d’importantes avanc\u00e9es dans le domaine de l’analyse topologique de donn\u00e9es. Par exemple, le th\u00e9or\u00e8me d’inversion de la transform\u00e9e de Radon topologique d\u00fb \u00e0 Schapira est la cl\u00e9 du probl\u00e8me inverse suivant : une forme de l’espace euclidien est-elle d\u00e9termin\u00e9e par la caract\u00e9ristique d’Euler de ses intersections avec tous les demi-espaces affines ? <\/p>\n\n\n\n Dans cet expos\u00e9, je pr\u00e9senterai des transform\u00e9es int\u00e9grales dites \u00ab\u00a0hybrides\u00a0\u00bb m\u00ealant le calcul d’Euler et l’int\u00e9grale de Lebesgue. Ces transform\u00e9es fournissent des descripteurs de formes plus versatiles que leurs analogues purement topologiques. Je montrerai que ces transform\u00e9es produisent des fonctions r\u00e9guli\u00e8res et conservent une compatibilit\u00e9 \u00e0 certaines op\u00e9rations topologiques sur les formes. Je terminerai la pr\u00e9sentation par un r\u00e9sultat d’injectivit\u00e9 pour la transform\u00e9e de Fourier hybride.<\/p>\n<\/div><\/div>\n\n\n\n Anna Song<\/em><\/p>\n\n\n\n The geometry and topology of texture in shapes<\/strong><\/p>\n\n\n\n In biology and materials science, porous structures display a wide morphological variety. Their 3D shape texture constitutes an important reservoir of information, and is for instance a marker of disease progression in a vascular network. The disparity of these structures calls for a unified mathematical modelling, which poses real challenges.<\/p>\n\n\n\n First, I will present curvatubes, a generative geometric model for 3D porous shapes. A surface adopts an optimal shape with respect to a curvature energy which makes it fold into tubular or membranous shapes. This model is framed as a novel phase-field formulation compatible with the GPU and satisfying a Gamma-limsup property. This results in geometrically random but statistically controlled textures which has many applications.<\/p>\n\n\n\n Second, I will present a topological method that quantifies a shape by its components, loops and cavities, at several spatial scales. We will give an interpretation of the resulting persistence diagram in terms of thicknesses and gaps, and especially of shape texture. Inhomogeneous mixtures of textures are thus detectable.<\/p>\n\n\n\n Finally, I will show how to combine both approaches to study the remodelling of bone marrow blood vessels by leukaemia.<\/p>\n\n\n\n Eddie Aamarie<\/em> <\/p>\n\n\n\n Minimax Boundary Estimation and Estimation with Boundary<\/strong><\/p>\n\n\n\n In this talk, we study the non-asymptotic minimax rates for the Hausdorff estimation of \ud835\udc51-dimensional manifolds \ud835\udc40 with (possibly) non-empty boundary \ud835\udf15\ud835\udc40. The class of target sets that we consider reunites and extends the most prevalent C\u00b2-type models: manifolds without boundary, and full-dimensional domains. We will consider both the estimation of the manifold \ud835\udc40 itself and that of its boundary \ud835\udf15\ud835\udc40 if non-empty. In the process, we will present a Voronoi-based procedure that allows to identify enough points close to \ud835\udf15\ud835\udc40 for reconstructing it. Explicit constant derivations are given, showing that these rates do not depend on the ambient dimension. If time permits, we will talk about possible extensions of the estimation procedure to smoother manifolds with corners.<\/p>\n<\/div><\/div>\n\n\n\n Fr\u00e9d\u00e9ric Richard (joint work with Paul Escande<\/em>) The anisotropic fractional Brownian field is a non-stationary Gaussian field (Bonami and Estrade, 2003) which has been used for the modeling of image microtextures (Richard, 2016-18). Having stationary increments, its probability distribution is characterized by a semi-variogram whose spectral representation is determined by two non-negative -periodic functions called the topothesy and the Hurst functions, respectively. In this talk, we focus on the issue of estimating these two functions from a single realization of the field.<\/p>\n\n\n\n Solving that issue is a key point for the characterization and the classification of image textures. It would also pave the way to the simulation of realistic textures from the field model. In the literature, this issue has been partially tackled in two different studies. In (Bierm\u00e9 and Richard, 2008), a method was built upon the Radon transform of the field to estimate the Hurst function. But, due to discretisation issues, its application is restricted to a few directions and leads to inaccurate results. In (Richard, 2018), an inverse problem was stated and solved to estimate the topothesy in directions where the Hurst function is minimal.<\/p>\n\n\n\n In this talk, we will present a method for the estimation of the whole topothesy and Hurst functions. This method is based on a turning-band field which was initially proposed for the simulation of anisotropic fractional Brownian field (Bierm\u00e9, Moisan and Richard, 2015), and whose semi-variogram approximates the one of an anisotropic fractional Brownian field. We will set an optimization problem to fit the semi-variogram of the turning-band field to the empirical semi-variogram. This problem is formulated as a non-linear separable least square problem (Golub, 2003). We then use a variable projection method to design an algorithm to solve numerically the problem. The design of this algorithm also includes a multigrid approach to improve the convergence. We will present a numerical study of the performances of this algorithm on textures generated by the python package PyAFBF<\/a>. Eventually, we will show some applications of the approach to mammograms.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n Pascal Barbara<\/em><\/p>\n\n\n\n Texture segmentation based on fractal attributes using convex functional minimization with generalized Stein formalism for automated regularization parameter selection.<\/strong><\/p>\n\n\n\n Texture segmentation still constitutes an ongoing challenge, especially when processing large-size real world images. The aim of this work is twofold.<\/p>\n\n\n\n First, we provide a variational model for simultaneously extracting and regularizing local texture fractal features, namely the local regularity and the local variance. For this purpose, a scale-free model, based on wavelet leaders, penalized by a Total Variation regularizer, is embedded into a convex optimisation framework. The resulting functional is shown to be strongly-convex, leading to a fast minimization scheme.<\/p>\n\n\n\n Second, we investigate Stein-like strategies for the selection of regularization parameters. A generalized Stein estimator of the quadratic risk is built, taking into account the covariance structure of leader coefficients. Then it is minimized via a quasi-Newton algorithm relying on a proposed generalized estimator of the gradient of the risk with respect to hyperparameters, leading to an automated and data-driven tuning of regularization parameters.<\/p>\n\n\n\n The overall procedure is illustrated on multiphasic flow images, analyzed as part of a long-term collaboration with physicists from the Laboratoire de Physique of ENS Lyon. <\/p>\n<\/div><\/div>\n\n\n\n Julien Rabin<\/em><\/p>\n\n\n\n Semi-discrete Optimal Transport for Texture Generation and Image Stylization<\/strong><\/p>\n\n\n\n In this presentation we focus on the problem of image generation in the specific setting of textures.<\/p>\n\n\n\n Various techniques have been proposed in the last decades to synthesize realistic images from a single example, from patch-based copy approaches to neural network training with perceptual features.<\/p>\n\n\n\n After a short overview, we introduce a new model which aims at taking advantages of these techniques by optimizing the optimal transport cost between the distributions of synthetic and exemplar features.<\/p>\n\n\n\n We will show that such model is capable of interpolating between characteristics from several textures.<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":" Lieu MAP5 @ Universit\u00e9 Paris Cit\u00e945 Rue des Saints-P\u00e8res, 75006 ParisSalle des th\u00e8ses (voir plan ci-dessous). Zoom ID : Demander le lien par email \u00e0 jonathan.vacher’@’u-paris.fr Restaurant jeudi soir \u00e0 19h30 Chez Fran\u00e7oise : https:\/\/goo.gl\/maps\/MVAVqyUu7CQ1cVAa6A\u00e9rogare des Invalides, 75007 Paris Programme … Continuer la lecture Restaurant jeudi soir \u00e0 19h30<\/h1>\n\n\n\n
A\u00e9rogare des Invalides, 75007 Paris<\/p>\n\n\n\nProgramme<\/h1>\n\n\n\n
Jeudi 6 avril 2023<\/h2>\n\n\n\n
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Can push-forward models fit multimodal distributions ?<\/em><\/li>\n\n\n\n
Topological Data Analysis for Train-Free Glioblastoma Segmentation in MRI: Advantages and Potential Impact<\/em><\/li>\n\n\n\n
Hybrid transforms for topological data analysis<\/em>.<\/li>\n\n\n\n
The geometry and topology of texture in shapes<\/em>.<\/li>\n\n\n\n
Minimax Boundary Estimation and Estimation with Boundary<\/em>.<\/li>\n\n\n\nVendredi 7 avril 2023<\/h2>\n\n\n\n
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Full inference for the anisotropic fractional Brownian field<\/em>.<\/li>\n\n\n\n
Texture segmentation based on fractal attributes using convex functional minimization with generalized Stein formalism for automated regularization parameter selection.<\/em><\/li>\n\n\n\n
Semi-discrete Optimal Transport for Texture Generation and Image Stylization<\/em><\/li>\n\n\n\n
Discussions : Images, Textures et Perception<\/em>.<\/li>\n\n\n\nH\u00f4tels recommand\u00e9s<\/h2>\n\n\n\n
R\u00e9sum\u00e9s des expos\u00e9s<\/h2>\n\n\n\n
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Full inference for the anisotropic fractional Brownian field <\/strong><\/p>\n\n\n\n
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