Interpolation and regression of rotation matrices

The problem of fitting smooth curves to data on the group of rotations is considered. This problem arises when resampling or denoising data points that consist in rotation matrices measured at different times. The rotation matrices typically correspond to the orientation of some physical object, such as a camera or a flying or submarine device. We propose to compute sequences of rotations (discretized curves) that strike a tunable balance between data fidelity and smoothness, where smoothness is assessed by means of a proposed notion of velocity and acceleration along discrete curves on the group of rotations. The best such curve is obtained via optimization on a manifold. Leveraging the simplicity of the cost, we present an efficient algorithm based on second-order Riemannian trust-region methods, implemented using the Manopt toolbox.