Guillaume Tochon

Neural koopman prior for data assimilation

By Anthony Frion, Lucas Drumetz, Mauro Dalla Mura, Guillaume Tochon, Abdeldjalil Aissa El Bey

2024-06-02

In IEEE Transactions on Signal Processing

Abstract

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

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Where is VALDO? VAscular Lesions Detection and segmentatiOn challenge at MICCAI 2021

By Carole H. Sudre, Kimberlin Van Wijnen, Florian Dubost, Hieab Adams, David Atkinson, Frederik Barkhof, Mahlet A. Birhanu, Esther E. Bron, Robin Camarasa, Nish Chaturvedi, Yuan Chen, Zihao Chen, Shuai Chen, Qi Dou, Tavia Evans, Ivan Ezhov, Haojun Gao, Marta Girones Sanguesa, Juan Domingo Gispert, Beatriz Gomez Anson, Alun D. Hughes, M. Arfan Ikram, Silvia Ingala, H. Rolf Jaeger, Florian Kofler, Hugo J. Kuijf, Denis Kutnar, Minho Lee, Bo Li, Luigi Lorenzini, Bjoern Menze, Jose Luis Molinuevo, Yiwei Pan, Élodie Puybareau, Rafael Rehwald, Ruisheng Su, Pengcheng Shi, Lorna Smith, Therese Tillin, Guillaume Tochon, Hélène Urien, Bas H. M. Velden, Isabelle F. Velpen, Benedikt Wiestler, Frank J. Wolters, Pinar Yilmaz, Marius Groot, Meike W. Vernooij, Marleen Bruijne

2023-11-13

In Medical Image Analysis

Abstract

Imaging markers of cerebral small vessel disease provide valuable information on brain health, but their manual assessment is time-consuming and hampered by substantial intra- and interrater variability. Automated rating may benefit biomedical research, as well as clinical assessment, but diagnostic reliability of existing algorithms is unknown. Here, we present the results of the VAscular Lesions DetectiOn and Segmentation (Where is VALDO?) challenge that was run as a satellite event at the international conference on Medical Image Computing and Computer Aided Intervention (MICCAI) 2021. This challenge aimed to promote the development of methods for automated detection and segmentation of small and sparse imaging markers of cerebral small vessel disease, namely enlarged perivascular spaces (EPVS) (Task 1), cerebral microbleeds (Task 2) and lacunes of presumed vascular origin (Task 3) while leveraging weak and noisy labels. Overall, 12 teams participated in the challenge proposing solutions for one or more tasks (4 for Task 1-EPVS, 9 for Task 2-Microbleeds and 6 for Task 3-Lacunes). Multi-cohort data was used in both training and evaluation. Results showed a large variability in performance both across teams and across tasks, with promising results notably for Task 1-EPVS and Task 2-Microbleeds and not practically useful results yet for Task 3-Lacunes. It also highlighted the performance inconsistency across cases that may deter use at an individual level, while still proving useful at a population level.

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Structural analysis of the additive noise impact on the $\alpha$-tree

By Baptiste Esteban, Guillaume Tochon, Edwin Carlinet, Didier Verna

2023-06-30

In Proceedings of the 20th international conference on computer analysis of images and patterns (CAIP)

Abstract

Hierarchical representations are very convenient tools when working with images. Among them, the $\alpha$-tree is the basis of several powerful hierarchies used for various applications such as image simplifi- cation, object detection, or segmentation. However, it has been demon- strated that these tasks are very sensitive to the noise corrupting the image. While the quality of some $\alpha$-tree applications has been studied, including some with noisy images, the noise impact on the whole struc- ture has been little investigated. Thus, in this paper, we examine the structure of $\alpha$-trees built on images corrupted by some noise with re- spect to the noise level. We compare its effects on constant and natural images, with different kinds of content, and we demonstrate the relation between the noise level and the distribution of every $\alpha$-tree node depth. Furthermore, we extend this study to the node persistence under a given energy criterion, and we propose a novel energy definition that allows assessing the robustness of a region to the noise.

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Learning sentinel-2 reflectance dynamics for data-driven assimilation and forecasting

By Anthony Frion, Lucas Drumetz, Guillaume Tochon, Mauro Dalla Mura, Abdeldjalil Aïssa El Bey

2023-05-29

In Proceedings of the 31th european signal processing conference (EUSIPCO)

Abstract

Over the last few years, massive amounts of satellite multispectral and hyperspectral images covering the Earth’s surface have been made publicly available for scientific purpose, for example through the European Copernicus project. Simultaneously, the development of self-supervised learning (SSL) methods has sparked great interest in the remote sensing community, enabling to learn latent representations from unlabeled data to help treating downstream tasks for which there is few annotated examples, such as interpolation, forecasting or unmixing. Following this line, we train a deep learning model inspired from the Koopman operator theory to model long-term reflectance dynamics in an unsupervised way. We show that this trained model, being differentiable, can be used as a prior for data assimilation in a straightforward way. Our datasets, which are composed of Sentinel-2 multispectral image time series, are publicly released with several levels of treatment.

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Why is the winner the best?

By Matthias Eisenmann, Annika Reinke, Vivienn Weru, Minu D. Tizabi, Fabian Isensee, Tim J. Adler, Sharib Ali, Vincent Andrearczyk, Marc Aubreville, Ujjwal Baid, Spyridon Bakas, Niranjan Balu, Sophia Bano, Jorge Bernal, Sebastian Bodenstedt, Alessandro Casella, Veronika Cheplygina, Marie Daum, Marleen de Bruijne, Adrien Depeursinge, Reuben Dorent, Jan Egger, David G. Ellis, Sandy Engelhardt, Melanie Ganz, Noha Ghatwary, Gabriel Girard, Patrick Godau, Anubha Gupta, Lasse Hansen, Kanako Harada, Mattias P. Heinrich, Nicholas Heller, Alessa Hering, Arnaud Huaulmé, Pierre Jannin, Ali Emre Kavur, Oldřich Kodym, Michal Kozubek, Jianning Li, Hongwei Li, Jun Ma, Carlos Martı́n-Isla, Bjoern Menze, Alison Noble, Valentin Oreiller, Nicolas Padoy, Sarthak Pati, Kelly Payette, Tim Rädsch, Jonathan Rafael-Patiño, Vivek Singh Bawa, Stefanie Speidel, Carole H. Sudre, Kimberlin van Wijnen, Martin Wagner, Donglai Wei, Amine Yamlahi, Moi Hoon Yap, Chun Yuan, Maximilian Zenk, Aneeq Zia, David Zimmerer, Dogu Baran Aydogan, Binod Bhattarai, Louise Bloch, Raphael Brüngel, Jihoon Cho, Chanyeol Choi, Qi Dou, Ivan Ezhov, Christoph M. Friedrich, Clifton D. Fuller, Rebati Raman Gaire, Adrian Galdran, Álvaro Garcı́a Faura, Maria Grammatikopoulou, SeulGi Hong, Mostafa Jahanifar, Ikbeom Jang, Abdolrahim Kadkhodamohammadi, Inha Kang, Florian Kofler, Satoshi Kondo, Hugo Kuijf, Mingxing Li, Minh Luu, Tomaž Martinčič, Pedro Morais, Mohamed A. Naser, Bruno Oliveira, David Owen, Subeen Pang, Jinah Park, Sung-Hong Park, Szymon Plotka, Élodie Puybareau, Nasir Rajpoot, Kanghyun Ryu, Numan Saeed, Adam Shephard, Pengcheng Shi, Dejan Štepec, Ronast Subedi, Guillaume Tochon, Helena R. Torres, Helene Urien, João L. Vilaça, Kareem A. Wahid, Haojie Wang, Jiacheng Wang, Liansheng Wang, Xiyue Wang, Benedikt Wiestler, Marek Wodzinski, Fangfang Xia, Juanying Xie, Zhiwei Xiong, Sen Yang, Yanwu Yang, Zixuan Zhao, Klaus Maier-Hein, Paul F. Jäger, Annette Kopp-Schneider, Lena Maier-Hein

2023-02-27

In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (CVPR)

Abstract

International benchmarking competitions have become fundamental for the comparative performance assessment of image analysis methods. However, little attention has been given to investigating what can be learnt from these competitions. Do they really generate scientific progress? What are common and successful participation strategies? What makes a solution superior to a competing method? To address this gap in the literature, we performed a multi-center study with all 80 competitions that were conducted in the scope of IEEE ISBI 2021 and MICCAI 2021. Statistical analyses performed based on comprehensive descriptions of the submitted algorithms linked to their rank as well as the underlying participation strategies revealed common characteristics of winning solutions. These typically include the use of multi-task learning (63%) and/or multi-stage pipelines (61%), and a focus on augmentation (100%), image preprocessing (97%), data curation (79%), and postprocessing (66%). The “typical” lead of a winning team is a computer scientist with a doctoral degree, five years of experience in biomedical image analysis, and four years of experience in deep learning. Two core general development strategies stood out for highly-ranked teams: the reflection of the metrics in the method design and the focus on analyzing and handling failure cases. According to the organizers, 43% of the winning algorithms exceeded the state of the art but only 11% completely solved the respective domain problem. The insights of our study could help researchers (1) improve algorithm development strategies when approaching new problems, and (2) focus on open research questions revealed by this work.

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Leveraging neural koopman operators to learn continuous representations of dynamical systems from scarce data

By Anthony Frion, Lucas Drumetz, Mauro Dalla Mura, Guillaume Tochon, Abdeldjalil Aïssa-El-Bey

2023-02-17

In Proceedings of the 48th IEEE international conference on acoustics, speech, and signal processing (ICASSP)

Abstract

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.

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The cost of dynamism in static languages for image processing

By Baptiste Esteban, Edwin Carlinet, Guillaume Tochon, Didier Verna

2022-10-10

In Proceedings of the 21st international conference on generative programming: Concepts & experiences (GPCE 2022)

Abstract

Generic programming is a powerful paradigm abstracting data structures and algorithms to improve their reusability, as long as they respect a given interface. Coupled with a performance-driven language, it is a paradigm of choice for scientific libraries where the implementation of manipulated objects may change depending on their use case, or for performance purposes. In those performance-driven languages, genericity is often implemented statically to perform some optimization. This does not fit well with the dynamism needed to handle objects which may only be known at runtime. Thus, in this article, we evaluate a model that couples static genericity with a dynamic model based on type erasure in the context of image processing. Its cost is assessed by comparing the performance of the implementation of some common image processing algorithms in C++ and Rust, two performance-driven languages supporting some form of genericity. Finally, we demonstrate that compile-time knowledge of some specific information is critical for performance, and also that the runtime overhead depends on the algorithmic scheme in use.

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Estimation de la fonction de niveau de bruit pour des images couleurs en utilisant la morphologie mathématique

By Baptiste Esteban, Guillaume Tochon, Edwin Carlinet, Didier Verna

2022-06-15

In 28e colloque sur le traitement du signal et des images

Abstract

Le niveau de bruit est une information importante pour certaines applications de traitement d’image telles que la segmentation ou le débruitage. Par le passé, nous avons proposé une méthode pour estimer ce niveau de bruit en s’adaptant au contenu d’une image en niveau de gris et nous avons montré que ses performances dépassent celle de l’état de l’art. Dans cet article, nous proposons une extension de cette méthode aux images couleurs dont les valeurs multivariées, dénuées de relation d’ordre naturelle, impliquent de nouvelles problématiques. Afin de les résoudre, nous utilisons deux outils provenant de la morphologie mathématique : l’arbre des formes multivarié et l’apprentissage de treillis complet. Enfin, nous confirmons les conclusions de nos précédents travaux pour l’estimation de la fonction de niveau de bruit couleur, montrant que l’adaptation au contenu d’une image donne de meilleures performances que l’utilisation de blocs carrés.

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Généricité dynamique pour des algorithmes morphologiques

By Baptiste Esteban, Edwin Carlinet, Guillaume Tochon, Didier Verna

2022-06-15

In 28e colloque sur le traitement du signal et des images

Abstract

La généricité est un paradigme puissant dont l’usage permet d’implémenter un unique algorithme et de l’exécuter sur différents types de données. De ce fait, il est très utilisé lors du développement d’une bibliothèque scientifique, notamment en traitement d’images où les algorithmes peuvent s’appliquer à différents types d’images. Le langage C++ est un langage de choix pour ce genre de bibliothèque. Il supporte ce paradigme et ses applications sont performantes compte tenu de sa nature compilée. Néanmoins, contrairement à des langages dynamiques tels que Python ou Julia, ses capacités en matière d’interactivité, utiles lors des étapes de prototypage d’algorithmes, sont limitées en raison de sa nature statique. Nous proposons donc dans cet article une revue des différentes techniques qui permettent d’utiliser à la fois le polymorphisme statique et dynamique, puis nous évaluons le coût du transfert d’information statique vers des informations connues à l’exécution. En particulier, nous montrons que certaines informations d’une image sont plus importantes que d’autres en matière de performance, et que le surcoût dépend aussi de l’algorithme utilisé.

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Analyse structurelle de l’influence du bruit sur l’arbre alpha

By Baptiste Esteban, Guillaume Tochon, Edwin Carlinet, Didier Verna

2022-06-14

In 29e colloque sur le traitement du signal et des images

Abstract

L’arbre alpha est une représentation hiérarchique utilisée dans divers traitements d’une image tels que la segmentation ou la simplification. Ces traitements sont néanmoins sensibles au bruit, ce qui nécessite parfois de les adapter. Or, l’influence du bruit sur la structure de l’arbre alpha n’a été que peu étudiée dans la littérature. Ainsi, nous proposons une étude de l’impact du bruit en fonction de son niveau sur la structure de l’arbre. De plus, nous étendons cette étude à la persistance des nœuds de l’arbre en fonction d’une énergie donnée, et nous concluons que certaines fonctionnelles sont plus sensibles au bruit que d’autres.

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