Anton François

I am currently a postdoctoral researcher at ENS Paris-Saclay, within the Centre Borelli. I am involved in the ANR-funded project RADIOAIDE, which aims to better understand white matter leukoencephalopathy — a degenerative condition that can arise in patients treated with radiotherapy for brain cancer. In this context, I am responsible for developing image registration methods to establish morphological and geometric correspondences between multiple longitudinal MRI scans acquired from patients. The ultimate goal of the project is to reconstruct the spatiotemporal trajectories of brain voxels and to estimate geometric markers (such as growth, atrophy, and local deformation) that characterize the progression of post-therapeutic leukoencephalopathy.

Since my PhD, I have been developing and maintaining the Demeter-Metamorphosis library, which implements the Metamorphosis algorithm — an extension of the LDDMM (Large Deformation Diffeomorphic Metric Mapping) framework — designed for image registration in settings where the topology may differ between the source and target images. These methods belong to the theoretical framework of shape spaces, whose goal is to model, quantify, and represent geometric variations within a population of shapes, accounting for both diffeomorphic deformations and structural or intensity changes.

These methods belong to the theoretical framework of shape spaces, whose goal is to model, quantify, and represent geometric variations within a population of shapes, accounting for both diffeomorphic deformations and structural or intensity changes.

My research lies at the intersection of several major areas in applied mathematics:

• Differential geometry, which provides the theoretical foundation for shape spaces and allows modeling of deformations through Riemannian structures.

• Optimization, used to solve registration problems under various constraints (regularization, data fidelity, structure preservation).

• Image analysis (and more broadly signal processing), which encompasses a wide range of techniques for processing, transforming, and extracting information from pixel-based data.

• Numerical analysis of partial differential equations (PDEs), as the Metamorphosis framework describes the dynamics of images using models inspired by fluid mechanics.

• Scientific computing, as I implement the algorithms and must manage computational resources such as processing power and memory (both RAM and GPU).

Although my doctorate focused on medical imaging, I also have other scientific interests. Since the beginning of my studies, I have been passionate about complex systems. I have led many projects related to intelligence, both from a biological and computer science point of view. In particular, I was interested in the mysterious nature of synergies between different elements. Due to my ecological awareness, the interactions between the different elements of an ecosystem have also fascinated me (see CV for more details). This is why I would like to use my skills to serve an impactful ecological project.