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

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