Bio

Dr. Estellers received her PhD in image processing from Ecole Polythechnique Federale de Lausanne in 2013, and joined the UCLA Vision Lab as a postdoctoral fellow with an SNSF fellowship. Previous to that, she completed Bachelor and Master studies at the Polytechnic University of Catalonia in both Mathematics and Electrical Engineering.

Robust Models and Efficient Algorithms for Imaging

Robust Models and Efficient Algorithms for Imaging

I work on mathematical modeling and computational techniques for imaging. I am interested in the theoretical and physical aspects of the acquisition of images, their mathematical representations, and the development of efficient algorithms to extract information from them. To this purpose, I focus on three lines of research.

Better Models in Image Processing: My dissertation focused on variational models for inverse problems in imaging, that is, the design of minimization problems that reconstruct or analyze an image from incomplete and corrupted measurements. To overcome the ill-posed nature of these problems, prior knowledge about the solution — its geometry, shape, or smoothness — is incorporated into a mathematical model that both matches the measurements and is physically meaningful.

Efficient Algorithms: In the same way that simplifying an algebraic expression speeds its computation and reduces numerical errors, developing an efficient algorithm reduces the computational cost and errors of the numerical minimization. For this reason, my work focuses also on developing algorithms tailored to each problem to overcome the limitations of non-differentiable functionals, high-order derivatives, and non-convex problems.

Stepping out of the Image plane: Computer Vision analyzes 3D scenes from 2D images or videos and therefore requires to step out of the image plane and develop models that account for the 3D nature of the scene, modeling their geometry and topology to account for the occlusions and shadows observable in videos and images.

My research, in a nutshell, brings together models and algorithms into solid mathematical grounds to designs techniques that only extract the information that is meaningful for the problem at hand. It incorporates the knowledge available on the solution into the mathematical model of the problem, chooses a discretization suited to the object being imaged, and designs optimization strategies that scale well and are easy to parallelize.