Barbara Gris

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Sorbonne Université
Laboratoire Jacques-Louis Lions
Room 15-16 305
4 Place Jussieu
75005, Paris

bantispam.comgris.mathsplanque.com gmail.com


Welcome to my web page !

I am currently a contract researcher at the Laboratoire Jacques-Louis Lions; Sorbonne University (Pierre-et-Marie-Curie), Paris. I am interested in shape analysis and image processing, more particularly in models for large deformations and their applications to computational anatomy.
Here are a detailed CV and my ResearchGate profile.

Thesis
Modular approach on shape spaces, sub-Riemannian geometry and computational anatomy
ENS Cachan (2016), under the supervisions of S. Durrleman and A. Trouvé.

Publications
Incorporation of a deformation prior in image reconstruction (2018).

This article presents a method to incorporate a deformation prior in image recon- struction via the formalism of deformation modules. The framework of deformation modules allows to build diffeomorphic deformations that satisfy a given structure. The idea is to register a template image against the indirectly observed data via a mod- ular deformation, incorporating this way the deformation prior in the reconstruction method. We show that this is a well-defined regularization method (proving existence, stability and convergence) and present numerical examples of reconstruction from 2-D tomographic simulations and partially-observed images.


Image reconstruction through metamorphosis , with O. Öktem and C. Chen (2018).

This article adapts the framework of metamorphosis to the resolution of inverse problems with shape prior. The metamorphosis frame- work allows to transform an image via a balance between geometrical deformations and changes in intensities (that can for instance correspond to the appearance of a new structure). The idea developed here is to reconstruct an image from noisy and indirect observations by registering, via metamorphosis, a template to the observed data. Unlike a registration with only geometrical changes, this framework gives good results when intensities of the template are poorly chosen. We show that this method is a well-defined regularization method (proving existence, stability and convergence) and present several numerical examples.


A sub-Riemannian modular framework for diffeomorphism based analysis of shape ensembles, with S. Durrleman and A. Trouvé, SIAM Journal of Imaging Sciences, 10.1137/16M1076733 (2018).

Deformations, and diffeormophisms in particular, have played a tremendous role in the field of statistical shape analysis, as a proxy to measure and interpret differences between similar objects but with different shapes. Diffeomorphisms usually result from the integration of a flow of regular velocity fields, whose parameters have not enabled so far a full control of the local behaviour of the deformation. In this work, we propose a new mathematical and computational framework, in which diffeomorphisms are built on the combination of local deformation modules with few degrees of freedom. Deformation modules contribute to a global velocity field, and interact with it during integration so that the local modules are transported by the global diffeomorphic deformation under construction. Such modular diffeomorphisms are used to deform shapes and to provide the shape space with a sub-Riemannian metric. We then derive a method to estimate a Fréchet mean from a series of observations, and to decompose the variations in shape observed in the training samples into a set of elementary deformation modules encoding distinctive and interpretable aspects of the shape variability. We show how this approach brings new solutions to long lasting problems in the fields of computer vision and medical image analysis. For instance, the easy implementation of priors in the type of deformations offers a direct control to favor one solution over another in situations where multiple solutions may fit the observations equally well. It allows also the joint optimisation of a linear and a non-linear deformation between shapes, the linear transform simply being a particular type of modules. The proposed approach generalizes previous methods for constructing diffeomorphisms and opens up new perspectives in the field of statistical shape analysis.


A sub-Riemannian modular approach for diffeomorphic deformations, with S. Durrleman and A. Trouvé, conference paper.
I presented this work (video of the presentation) at the Conference on Geometric Science of Information (2015).

Grant

In November 2017 I received a CNRS-Momentum grant for a project named "A constrained morphometric approach to study the evolution of living organisms".

Teaching
From 2013 to 2016 I taught :