Uses tools from Riemannian geometry
The images of 3-D points in two views are related by the so-called _essential matrix_. There have been attempts to characterize the space of valid essential matrices as a Riemannian manifold. These approaches either put an unnatural emphasis on one of the two cameras, or do not accurately take into account the geometric meaning of […]
Imagine a wireless camera network, where each camera has a piece of local information, e.g., the pose of the object from a specific viewpoint or the relative poses with respect to the neighboring cameras. It is natural to look for distributed algorithms which merge all these local measurements into a single, globally consistent estimate. I […]
I worked on distributed optimization problems involving variables lying on non-linear spaces (that is, Riemannian manifolds) using extensions of gradient descent algorithms with fixed step size. I developed novel theoretical tools which significantly broadened the state of the art for determining sufficient conditions for global behaviors (algorithm convergence) using only local information. These tools have […]