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 connections with statistics and machine learning). It is open to everyone. It takes place at Institut Henri Poincaré on the first Tuesday of each month from 2pm to 4pm. Each seminar is composed of two presentations.
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Click on the title to read the abstract.
Kimia Nadjahi (CNRS, ENS PARIS)
Abstract: Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores, which fail to fully exploit the geometric structure of multivariate outputs, such as in multi-output regression or multiclass classification. Recent methods addressing this limitation impose predefined convex shapes for the prediction sets, potentially misaligning with the intrinsic data geometry. We introduce a novel CP procedure handling multivariate score functions through the lens of optimal transport. Specifically, we leverage Monge-Kantorovich vector ranks and quantiles to construct prediction regions with flexible, potentially non-convex shapes, better suited to the complex uncertainty patterns encountered in multivariate learning tasks. We prove that our approach ensures finite-sample, distribution-free coverage properties, similar to typical CP methods. We then adapt our method for multi-output regression and multiclass classification, and also propose simple adjustments to generate adaptive prediction regions with asymptotic conditional coverage guarantees. Finally, we evaluate our method on practical regression and classification problems, illustrating its advantages in terms of (conditional) coverage and efficiency. This is joint work with Gauthier Thurin (CNRS, ENS Paris) and Claire Boyer (Université Paris-Saclay).
November 4th, 2pm, room Amphi Darboux (Borel building).
Title: Optimal Transport-based Conformal Prediction ⬇
Laetitia Chapel (Institut Agro Rennes-Angers, IRISA)
Abstract: Optimal Transport (OT) has emerged as a fundamental tool in modern machine learning, mainly due to its ability to provide meaningful comparisons between probability distributions. One of the key strengths of OT is its dual nature: it not only introduces a mathematically rigorous framework defining Wasserstein distances but also constructs an optimal coupling (or transport plan) between distributions. This coupling reveals explicit correspondences between samples, enabling a broad spectrum of applications. Despite the numerous successes of optimal transport in machine learning and the availability of many tools to approximate Wasserstein distances, computing OT plans remains computationally challenging. In this talk, I will present a new methodology to efficiently approximate sliced OT plans. The formulation can be recast as a bilevel optimization problem, and I will propose a differentiable generalized approximation that can be further adapted to data residing on manifolds. Finally, I will demonstrate the practical value of this approach by introducing a novel sliced OT-based conditional flow matching method for image generation, an application where fast computation of transport plans is crucial.
November 4th, 3pm, room Amphi Darboux (Borel building).
Title: Sliced optimal transport plans with an application to conditional flow matching ⬇
Samuel Hurault (CNRS, LIGM)
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December 2nd, 2pm, room Room Yvette Cauchoix (Perrin building).
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Nils Laurent (LASPI Roanne)
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December 2nd, 3pm, room Room Yvette Cauchoix (Perrin building).
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Louis Hauseux (INRIA)
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January 6th, 2pm, room Room Yvette Cauchoix (Perrin building).
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January 6th, 3pm, room Room Yvette Cauchoix (Perrin building).
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February 3rd, 2pm, room Room Yvette Cauchoix (Perrin building).
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February 3rd, 3pm, room Room Yvette Cauchoix (Perrin building).
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Nelly Pustelnik (CNRS, ENS Lyon)
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March 10th, 2pm, room Room Yvette Cauchoix (Perrin building).
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March 10th, 3pm, room Room Yvette Cauchoix (Perrin building).
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April 7th, 2pm, room Room Yvette Cauchoix (Perrin building).
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April 7th, 3pm, room Room Yvette Cauchoix (Perrin building).
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May 5th, 2pm, room Room Yvette Cauchoix (Perrin building).
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May 5th, 3pm, room Room Yvette Cauchoix (Perrin building).
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June 2nd, 2pm, room Room Yvette Cauchoix (Perrin building).
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June 2nd, 3pm, room Room Yvette Cauchoix (Perrin building).
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The list of seminars prior to summer 2025 is available here.
Raphaël Achddou
(ESIEE Paris, LIGM)
Abstract: Neural Networks have surpassed traditional prior-based approaches in solving inverse problems, but their black-box nature hinders their interpretability and confidence. To address these issues, a potential approach is to synthesize training images with controlled statistical properties. In this talk, I’ll present how a simple occlusion-based image model called the Dead Leaves model can be used to generate high-quality training data for various image restoration tasks. I’ll then show how this model can be adapted to incorporate essential image properties like texture, depth, and complex object geometry. The resulting trained restoration models perform similarly to those trained on real images while offering additional benefits, such as insightful ablation studies, inherent invariance properties, and faster convergence, which I’ll discuss further.
October 7th, 2pm, room Room Pierre Grisvard (Borel building).
Title: Synthetic training of deep image restoration networks : principles and applications ⬇
The seminar is hosted by IHP, and supported by RT-MAIAGES, Télécom Paris and CMM Mines Paris - PSL.