## Lieu

Université Bretagne Sud (LMBA)

Rue André Lwoff, 56000 Vannes

Centre Yves Coppens, Amphi Yves Coppens (voir plan ci-dessous).

**Zoom** **ID** : Demander le lien par email à claire.launay’@’univ-ubs.fr

# Restaurant jeudi soir à 19h30 à Fraya

Fraya : https://www.google.fr/maps/place/Fraya+-+Bar+%26+restaurant

4 rue du Commerce

56000 VANNES

# Programme

## Jeudi 10 octobre 2024

- 14h00-14h30 : Accueil + café (salle D077)
- 14h30-15h15 : Emile Pierret
- 15h15-16h : Léo Davy
- 16h-16h30 : Pause café (salle D077)
- 16h30-17h15 : Barbara Pascal
- 17h15-19h00 : Discussions libres
- 19h30 : Diner au Fraya, sur le port de Vannes

## Vendredi 11 octobre 2024

- 9h45-10h30 : Nicolas Courty
- 10h30-11h : Pause café
- 11h-11h45 : Raphaël Lachièze-Rey
- 11h45-12h30 : Antonin Jacquet
- 12h30 : Pause déjeuner (traiteur, salle D077)
- 14h-14h45 : Béatrice Vedel
- 14h45-15h30 : Discussions sur la suite et fin du projet
- 15h30-17h30 Echanges libres (Amphi Yves Coppens et salle D077 à disposition)

## Accès

- Centre Yves Coppens : Bâtiment jaune sur ce plan.
- Accès en bus avec les lignes 2 et 6, Arrêts Université ou Tohannic.
- Depuis la gare, prendre la ligne 6a, de l’autre côté de la route.

## Hôtels recommandés

- Escale Oceania, entre la gare et le centre ville de Vannes
- Appart’ city, en face de l’université
- Kyriad, sur la ligne du bus 2, proche du centre ville

## Résumés des exposés

*Nicolas Courty*

**Unbalancing Sliced Wasserstein **

Optimal transport (OT) has emerged as a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made over the last decade in designing OT variants which are either computationally and statistically more efficient, or more robust to the measures and datasets to compare. Among them, sliced OT distances have been extensively used to mitigate optimal transport’s cubic algorithmic complexity and curse of dimensionality. In parallel, unbalanced OT was designed to allow comparisons of more general positive measures, while being more robust to outliers. In this talk, I will discuss how to combine these two concepts, namely slicing and unbalanced OT, to develop a general framework for efficiently comparing positive measures. We propose two new loss functions based on the idea of slicing unbalanced OT, and study their induced topology and statistical properties. We then develop a fast Frank-Wolfe-type algorithm to compute these loss functions, and show that the resulting methodology is modular as it encompasses and extends prior related work. We finally conduct an empirical analysis of our loss functions and methodology on both synthetic and real datasets, to illustrate their relevance and applicability.

*Léo Davy*

**Segmentation of anisotropic textures **

Texture segmentation aims to recover homogeneous regions in an image based on texture properties, without relying on edges. Key attributes such as texture smoothness and orientation are crucial in various imaging applications, including multiphase flow analysis and breast cancer detection. The Anisotropic Fractional Brownian Field (AFBF) is a versatile model for describing textures, capable of capturing both these attributes. However, accurately estimating its parameters locally remains a significant challenge. In this work, we introduce an approach based on a multiscale, multiband model of wavelet coefficients derived from AFBFs, enabling the extraction of regularity and orientation features of homogeneous textures. Instead of using a conventional patch-based estimation strategy, we propose solving an inverse problem with regularization, integrating the multiscale model with total variation penalization on the estimated features. We will present an optimization framework that combines convex optimization techniques with learning-based methods, resulting in an efficient segmentation model for heterogeneous AFBFs.

*Antonin Jacquet*

**Patterns crossed by geodesics in first-passage percolation **

In first-passage percolation, we consider a family of nonnegative, independent and identically distributed random variables indexed by the set of edges of the graph Z^d, called passage times. The time of a finite path is defined as the sum of the passage times of each of its edges. Geodesics are then the paths with minimal time. A pattern is a local property of the time environment. We fix a pattern and are interested in the number of times a geodesic crosses a translate of this pattern. The main result presented in this talk guarantees, under mild conditions, that apart from an event with exponentially small probability, for any geodesic, this number is linear in the distance between the endpoints of the geodesics. The aim of this talk is to introduce the notion of patterns and illustrate how they can be used to obtain some results in first-passage percolation.

*Raphaël Lachièze-Rey*

**Functional CLT for Gaussian topological functionals**

Given a centred stationary real Gaussian field X on R^d and a threshold l, we investigate functionals B_n(l) of the excursion of X at level l. We are particularly interested in topological functionals such as the number of components, the Euler characteristic, or more generally the Betti numbers. Using Morse theory, such functionals can be written as stabilising functionals on the process of critical points of X, and we can use the Kac-Rice formulae and generalisations, combined with classical stabilisation techniques from stochastic geometry, to obtain variance and central limit theorems in the large window asymptotics. Motivated by the parametric evolutions studied in Topological Data Analysis, our main result is a functional CLT when the level l varies, i.e. we show the convergence of B_n towards a Gaussian process G(l) in a weak sense. To avoid dealing with intersection of components with the window boundary, our study is restricted to regimes where one of the phase does not percolate.

*Barbara Pascal*

**Detection of change in cancer breast tissues from fractal indicators: a brief introduction**

It has been known for decades that mammograms, consisting in X-ray images of breasts, exhibit a scale-invariance, characteristic of fractal textures akin to fractional Brownian fields. Recent works have thus leveraged fractal features to characterize the microscopic structure of breast tissues. An overarching goal of these studies is early detection of tissue disruption, which is an evidence of homeostasis loss impairing the ability of the tissue to suppress precancerous lesions.

Local fractal features are estimated through sliding window analysis, performed on thousands patches extracted from the mammogram to categorized three types of tissues based on their Hölder exponent: fatty, dense or disrupted. Based on the amount of disrupted tissues in the breast and on the asymmetry between the two breasts, this procedure is capable to detect and quantify tumor-associated loss of homeostasis in mammograms. Intensive numerical experiments on large mammograms datasets have proven the statistical power of tests based on the proposed aggregated indicators for cancer risk assessment.

This presentation is a survey of the research conducted at CompuMAINE on this topic during the past years and of the perspective it opens for the image processing and stochastic geometry communities. I will first recall the general principles of the multifractal formalism and of the Wavelet Transform Modulus Maxima method. Then, the datasets, test methodologies and conclusions drawn from the analysis performed at CompuMAINE Laboratory will be discussed. Finally, complementary experiments and perspectives will be presented.

*Emile Pierret***Stochastic super-resolution for Gaussian textures **

Super-Resolution (SR) is the problem that consists in reconstructing images that have been degraded by a zoom- out operator. This is an ill-posed problem that does not have a unique solution, and numerical approaches rely on a prior on high-resolution images. While optimization-based methods are generally deterministic, with the rise of image generative models more and more interest has been given to stochastic SR, that is, sampling among all possible SR images associated with a given low-resolution input. In this paper, we construct an efficient, stable and provably exact sampler for the stochastic SR of Gaussian microtextures. Even though our approach is limited regarding the scope of images it encompasses, our algorithm is competitive with deep learning state-of-the-art methods both in terms of perceptual metric and execution time when applied to microtextures. The framework of Gaussian microtextures also allows us to rigorously discuss the limitations of various reconstruction metrics to evaluate the efficiency of SR routines.

*Béatrice Vedel*

**Weighted tensorized fractional Brownian textures**

In this talk we introduce a new class of self-similar gaussian textures. They are obtained by relaxing the tensor-product structure that appears in the definition of the fractional Brownian sheet and allows to model reticulated textures. Some statistical and regularities properties will be presented.

*Journées associées à l’ANR MISTIC – Journées MAIAGES/IASIS*