Abstract: This talk presents a formulation and evaluation of visual odometry. This problem consists of determining the transformation between two sensors with overlapping measurements or tracking a moving sensor using its sequential measurements. To be more precise, let X and Z be two point clouds that are to be aligned by the action of a group G, i.e. find h∈ G such that X and hZ are the "same.'' By transforming these clouds into functions on a suitable reproducing kernel Hilbert space, the alignment can be found via gradient descent. In this talk, I will show how this approach works in various geometries.