  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.
