Agnès Desolneux: turning images into equations

Agnès Desolneux, whose mother was a mathematician, took a very early interest in the discipline. She studied for the 2-year preparatory course for the competitive exam in Paris, then passed the ENS Paris exam before going on to achieve a distinguished track record, including an undergraduate degree, a 1st year Master’s, a DEA (Advanced Studies Diploma, the equivalent of a 2nd year Master’s nowadays) and an ‘agrégation’ (teaching qualification). The young student believed that her two passions of mathematics and film would never be able to come together. However, over the course of her studies at ENS, she found out that this was not true. “Tutors at the school directed me to a research centre for mathematical image processing at Université Paris Dauphine. I thought it was absolutely brilliant!”
 

Combining mathematics and film

Agnès Desolneux began a PhD on the statistical analysis of geometric event detection in images, supervised by Jean-Michel Morel. She defended it in the year 2000 at the Centre for Mathematics and its Applications (CMLA) at ENS Cachan (ENS Paris-Saclay today). The PhD student got to know the American researcher, David Mumford (winner of the Fields Medal in 1974) during a thematic term at the Institut Henri Poincaré. “Although he focused on pure mathematics at the beginning of his career, I was lucky enough to meet him when he became interested in image modelling.” The mathematician made her his teaching assistant and offered to write a book based on her notes. After several trips back and forth between France and the United States, the book was published in 2010.

In the meantime, the researcher was taken on by CNRS in 2001 as a research associate in the Applied Mathematics Laboratory at Paris 5 (MAP5 – CNRS/Univ. Paris Cité). She stayed there for ten years before returning to the CMLA in 2011 following her appointment as Director of Research at CNRS.
 

From medical imaging to video games

Mathematical models are used to test the behaviour of the objects under study at the point where probability and the physics of imaging systems intersect. “I think of images as mathematical objects. Based on this, I ask myself questions such as how can poor quality images be fixed? How can we detect in images or generate new ones for various applications?” explains Agnès Desolneux.

Among the possible applications of this work, medical imaging holds a special place, and more specifically questions related to the early detection of breast cancer. “Using mammograms, we model the detectability of structures. We try to show what is detectable and what is not,” explains the mathematician, who is collaborating with GE Healthcare in this area. She also produces computer-generated images for virtual clinical trials. “For example, we use these images to simulate lesions or calcifications. We then make statistical estimates to determine whether it is possible to detect them and, if so, at what size.”

Other more fun applications exist, such as improving images in video games and animated films, which are demanding ever greater realism. At the other end of the scale, there is also image restoration, which involves for example the removal of signs of chemical deterioration from rolls of old films.
 

Identifying the composition of very old materials

The mathematician is now working with the Major area of interest or DIM Material heritage - innovation, experimentation and resilience (PAMIR) of the Île-de-France region. The research being carried out is part of the development of the “data, modelling and statistics” aspect of the analysis of ancient heritage materials. “Using spectral images of materials obtained from the SOLEIL synchrotron’s electron and energy flux, we model the physical phenomenon in order to analyse, for example, the chemical composition of the materials,” explains Agnès Desolneux.

The researcher is also a member of the Thematic Network of Mathematics of Imaging, Learning and Stochastic Geometry (RT MAIAGES) which brings together the entire national scientific community involved in mathematics and imaging. “Generally speaking, my work consists of finding a balance between the complexity of the mathematical models developed (to be as realistic as possible and reflect the physical phenomenon) and simplicity (to be as calculable as possible),” explains the researcher.
 

Mathematics at Université Paris-Saclay

In her role as a guest lecturer at ENS Paris-Saclay, Agnès Desolneux teaches in the Department of Mathematics Teaching and Research. “Although few in number, ENS students are very interested and make the perfect audience.” The mathematician actively encourages them to continue with their training during their PhD work. “The research-based education offered at ENS Paris-Saclay is extremely beneficial. Students learn about research and most of them enjoy it.”

Agnès Desolneux is also the Director of the Hadamard Doctoral School of Mathematics (EDMH) since October 2024. In particular, she is responsible for ENS Paris-Saclay. “The bringing together of all mathematics at Université de Paris-Saclay represents a real change.” She is also on the board of the Université Paris-Saclay Mathematics Graduate School. “I find it natural to get involved in collective tasks to ensure that the institutions run smoothly, but also to work with students, in particular to help them with their PhDs. Beyond the time-consuming meetings and administrative hurdles, it's fascinating to see the diversity of personalities and research topics in mathematics.”