Finding corresponding points between images is challenging, particularly when objects change their pose non-rigidly, in wide-baseline conditions, or when instances of a perceptual category are compared. In this talk I will present an algorithm for finding a geometrically consistent set of point matches between two images. Given a set of candidate matches that may include many outliers, our method seeks the largest subset of these correspondences that can be aligned using a non-rigid deformation that exerts a bounded distortion. I will discuss theoretical guarantees and show experimentally that this algorithm produces excellent results on a number of test sets, in comparison to several state-of-the-art approaches. In the second part of the talk I will introduce a convex framework for problems that involve singular values. Specifically, the framework enables optimization of functionals and constraints expressed in terms of the extremal singular values of matrices. I will show applications of this framework in geometry processing problems such as non-rigid shape registration and computing extremal quasi-conformal maps.
This is joint work with Yaron Lipman, Stav Yagev, Roi Poranne, David Jacobs, Shahar Kovalsky and Noam Aigerman.