Semidefinite Relaxations of Surface Deformation Problems
In this project I will be working with Justin Solomon to explore how non-convex optimization problems that arise in surface modeling can be suitably relaxed into convex ones. In particular we hope to be able to apply some variation of the technique in the paper "Global Registration of Multiple Point Clouds Using Semidefinite Programming" by Chaudhury et al. to the problem of as-rigid-as-possible surface modeling. This would avoid the problem of local minima instead allowing for recovery of the globally optimal solution.
I'm a senior studying math and CS. I'm interested in the project since it deals with mathematical aspects of machine learning which is a subject I've wanted to explore. I hope to learn some geometric/linear algebraic techniques in surface modeling and the methods used to relax provably hard problems. Constructing an appropriate relaxation that could lead to to better practical results would be very exciting.