Non-rigid point cloud registration plays a crucial role in various fields, including robotics, neuroscience, computer graphics, and medical imaging. This process involves determining spatial relationships between different sets of points, typically within a 3D space. In real-world scenarios, complexities arise from non-rigid movements and partial visibility, such as occlusions or sensor noise, making non-rigid registration a challenging problem. Classic non-rigid registration methods are often computationally demanding, suffer from unstable performance, and, importantly, have limited theoretical guarantees.

The talk will focus primarily on a new way to understand non-rigid alignment and manifold learning of point clouds in Euclidean space using Whitney Extensions machinery developed by the author and his collaborators over the last few years. We will possibly  explore relationships of our work to topological data analysis, optimal transport, neural networks and neuroscience.