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 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. 
Nadege Zarrouati, Emanuel Aldea, Pierre Rouchon
math.OC cs.CV