Imaging in Paris Seminar

Parisian Seminar on the Mathematics of Imaging

Welcome to the website of the Parisian Seminar on the Mathematics of Imaging !

The goal of this seminar is to cover the fields of the mathematics of imaging in a very wide sense (including for instance signal processing, image processing, computer graphics, computer vision, various applications and connexion with statistics and machine learning). It is open to everyone. It takes place in Room 314 (Pierre Grisvard) at IHP on the first Tuesday of each month (the second Tuesday in November and January), from 14:00 to 16:00. Each seminar is composed of two presentations.

You can subscribe or unsubscribe to the mailing list of the seminar and to the agenda of the seminar.

Upcoming seminars

Click on the title to read the abstract.

Claire Launay (LMBA, Université Bretagne Sud)
Dec 5th 2023, 14h-15h, room 314 (Pierre Grisvard).
Title: Modélisation de textures : champs gaussiens autosimilaires et signal monogène ⬇
Abstract: Nos travaux s'intéressent à la représentation de champs gaussiens autosimilaires anisotropes à l’aide du signal monogène. Le signal monogène utilise la transformée de Riesz et permet d’extraire des informations locales d’orientation et de structure d’une image. Une analyse multi-échelle, développée en collaboration avec Hermine Biermé, Céline Lacaux et Philippe Carré, permet d’obtenir des estimateurs non biaisés et fortement consistants des paramètres d’anisotropie et d’autosimilarité de textures gaussiennes particulières, modélisées par des champs élémentaires.

Remy Abergel (MAP5, Université Paris Cité)
Dec 5th 2023, 15h-16h, room 314 (Pierre Grisvard).
Title: Méthodes variationnelles pour l'imagerie par résonance paramagnétique électronique Variational methods for Electron Paramagnetic Resonance Imaging ⬇
Abstract: L'imagerie par résonance paramagnétique électronique (RPE) est une méthode d'imagerie des molécules paramagnétiques. Celle-ci est basée sur la capacité des électrons libres à absorber puis réémettre l'énergie électromagnétique en présence d'un champ magnétique. Cet exposé sera consacré à la modélisation du problème direct reliant les mesures RPE à la cartographie des espèces paramagnétiques en présence dans l'échantillon étudié, ainsi qu'aux méthodes variationnelles proposées récemment pour effectuer son inversion. Travaux en collaboration avec Mehdi Boussâa (MAP5 & LCBPT), Sylvain Durand (MAP5) et Yves-Michel Frapart (LCBPT).

Antoine Salmona (Centre Borelli, ENS Paris Saclay)
Jan 9th 2024, TBA, room 314 (Pierre Grisvard).
Title: TBA ⬇
Abstract: TBA

Théophile Cantelobre (SIERRA, INRIA Paris)
TBA, TBA, room 314 (Pierre Grisvard).
Title: TBA ⬇
Abstract: TBA

Tristan Lazard (CBIO, CMM, Mines Paris, PSL)
TBA, TBA, room 314 (Pierre Grisvard).
Title: TBA ⬇
Abstract: TBA

Previous seminars of 2023-2024

The list of seminars prior to summer 2023 is available here.

Click on the title to read the abstract.

Carole Le Guyader (LMI, INSA Rouen)
Nov 14th 2023, 14h-15h, room 314 (Pierre Grisvard).
Title: A Multiscale Deformation Representation ⬇
Abstract: Motivated by Tadmor et al.’s work dedicated to multiscale image representation using hierarchical ($BV$, $L^2$) decompositions, we propose transposing their approach to the case of registration, task which consists in determining a smooth deformation aligning the salient constituents visible in an image into their counterpart in another. The underlying goal is to obtain a hierarchical decomposition of the deformation in the form of a composition of intermediate deformations: the coarser one, computed from versions of the two images capturing the essential features, encodes the main structural/geometrical deformation, while iterating the procedure and refining the versions of the two images yields more accurate deformations that map faithfully small-scale features. The proposed model falls within the framework of variational methods and hyperelasticity by viewing the shapes to be matched as Ogden materials. The material behaviour is described by means of a specifically tailored strain energy density function, complemented by $L^\infty$-penalisations ensuring that the computed deformation is a bi-Lipschitz homeomorphism. Theoretical results emphasising the mathematical soundness of the model are provided, among which the existence of minimisers/asymptotic results, and a suitable numerical algorithm is supplied, along with numerical simulations demonstrating the ability of the model to produce accurate hierarchical representations of deformations.

Romain Petit (MaLGa, University of Genoa)
Nov 14th 2023, 15h-16h, room 314 (Pierre Grisvard).
Title: Reconstruction of piecewise constant images via total (gradient) variation regularization ⬇
Abstract: In this talk, I will consider the reconstruction of some unknown image from noisy linear measurements using total (gradient) variation regularization. Empirical evidence and theoretical results suggest that this method is particularly well suited to recover piecewise constant images. It is therefore natural to study the case where the unknown image has precisely this structure. I will present two works on this topic, which are collaborations with Yohann De Castro and Vincent Duval. The first concerns a noise robustness result, stating that, in a low noise regime, the reconstruction is also piecewise constant, and one exactly recovers the number of shapes in the unknown image. The second is about introducing a new numerical method for solving the variational regularization problem. Its main feature is that it does not rely on the introduction of a fixed spatial discretization (e.g. a pixel grid), and builds a sequence of iterates that are linear combinations of indicator functions.

Valentin Penaud-Polge (CMM, Mines Paris, PSL)
Oct 3rd 2023, 14h-15h, room 314 (Pierre Grisvard).
Title: GenHarris-ResNet: A Rotation Invariant Neural Network Based on Elementary Symmetric Polynomials ⬇
Abstract: We propose a rotation invariant neural network based on Gaussian derivatives. The proposed network covers the main steps of the Harris corner detector in a generalized manner. More precisely, the Harris corner response function is a combination of the elementary symmetric polynomials of the integrated dyadic (outer) product of the gradient with itself. In the same way, we define matrices to be the self dyadic product of vectors composed with higher order partial derivatives and combine the elementary symmetric polynomials. A specific global pooling layer is used to mimic the local pooling used by Harris in his method. The proposed network is evaluated through three experiments. It first shows a quasi perfect invariance to rotations on Fashion-MNIST, it obtains competitive results compared to other rotation invariant networks on MNIST-Rot, and it obtains better performances classifying galaxies (EFIGI Dataset) than networks using up to a thousand times more trainable parameters.

Jonathan Vacher (MAP5, Université Paris Cité)
Oct 3rd 2023, 15h-16h, room 314 (Pierre Grisvard).
Title: Perceptual Measurements, Distances and Metrics ⬇ [Slides]
Abstract: Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined perceptual scale. The perceptual scale can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the perceptual scale of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured perceptual scale corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the perceptual scale is mostly driven by the stimulus power spectrum. Finally, we propose that these measure of perceptual scales is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.

Organizers

Thanks

The seminar is hosted by IHP, and is labelled by the SIGMA group of the SMAI and the RT MIA. We gratefully acknowledge support from the Agence Nationale de la Recherche (CIPRESSI, ANR-19-CE48-0017-01).

En français

Bienvenue sur le site du Séminaire Parisien des Mathématiques Appliquées à l’Imagerie.

Le but de ce séminaire est de couvrir le domaine des mathématiques de l’imagerie. Il est ouvert à tous. Cette année, le séminaire a lieu en Salle 314 (Pierre Grisvard) à l’IHP le premier mardi de chaque mois (le deuxième mardi de novembre et janvier), de 14h00 à 16h00. Chaque séance est composée de deux exposés.

La liste des séminaires antérieurs à l’été 2023 est disponible ici.

Vous pouvez vous abonner ou désabonner à la liste de diffusion du séminaire.