SO(3)-invariant asymptotic observers for dense depth field estimation based on visual data and known camera motion

In this paper, we use known camera motion associated to a video sequence of a static scene in order to estimate and incrementally refine the surrounding depth field. We exploit the SO(3)-invariance of brightness and depth fields dynamics to customize standard image processing techniques. Inspired by the Horn-Schunck method, we propose a SO(3)-invariant cost to estimate the depth field. At each time step, this provides a diffusion equation on the unit Riemannian sphere of R
³
that is numerically solved to obtain a real time depth field estimation of the entire field of view. Two asymptotic observers are derived from the governing equations of dynamics, respectively based on optical flow and depth estimations: implemented on noisy sequences of synthetic images as well as on real data, they perform a more robust and accurate depth estimation. This approach is complementary to most methods employing state observers for range estimation, which uniquely concern single or isolated feature points.