Date: 02 February 2022
Time: 12:45 – 13:15. Hours
Room: Online
Speaker: José Iglesias (DAMUT-MIA)
Title: implicit surfaces and variational regularization
Abstract:
In this talk, I will give a brief overview of my research interests in the intersection of inverse problems, imaging, and shape analysis, with a geometric flavor. A concept that bridges these areas together is that of level set functions encoding a surface of interest.
One main direction is the study of the level sets of solutions of regularization of inverse problems, which represent objects of interest in an image or recovered material parameters. Here, using PDE and regularity techniques, we can extend the classical regularization theory of inverse problems to include convergence results of the object boundaries instead of just the image values.
The other main direction is the study of deformations of one level set function into another, with a view towards shape spaces. By studying the tangential properties of deformations between level set functions, we can pose energies that model the implicit surfaces as elastic shells. These are well suited to shape analysis tasks, so using the optimal deformation energy as a definition of distance between surfaces one can then try to find shape means and other statistics. Such an approach involves highly nonconvex minimization problems and is in principle computationally heavy, but neural network representations and their associated optimization algorithms may bring it to a new level.