The Taub Faculty of Computer Science Events and Talks

We present the Accelerated Quadratic Proxy (AQP) - a simple first order algorithm for the optimization of geometric energies defined over triangular and tetrahedral meshes. The main pitfall encountered in the optimization of geometric energies is slow convergence.​ ​We observe that this slowness is in large part due to a Laplacian-like term existing in these energies. Consequently, we suggest to exploit the underlined structure of the energy and to locally use a quadratic polynomial proxy, whose Hessian is taken to be the Laplacian. This improves stability and convergence, but more importantly allows incorporating acceleration in an almost universal way, that is independent of mesh size and of the specific energy considered. Experiments with AQP show it is rather insensitive to mesh resolution and requires a nearly constant number of iterations to converge; this is in strong contrast to other popular optimization techniques used today such as Accelerated Gradient Descent and Quasi-Newton methods, e.g., L-BFGS. We have tested AQP for mesh deformation in 2D and 3D as well as for surface parameterization, and found it to provide a considerable speedup over common baseline techniques.

Joint work with Shahar Kovalsky and Yaron Lipman

​​Short Bio
Ph.D in Applied Mathematics, Weizmann Institute of Science, Title: “Multigrid Algorithms for Optimal Computations in Statistical Physics”; Associate Staff Scientist, Main research fields: Computer vision, Geometric Processing, Optimization algorithms.