Incorporating geometric information into Gaussian Process terrain models from monocular images

This paper presents a novel approach to depth estimation from monocular images that is based on the Gaussian Derivative Process (GDP) formulation. We use an inverse depth parametrisation and learn the mapping from image pixel coordinates to the inverse depth of the corresponding scene point given an estimate of the relative camera motion. We show that information about the geometry of the measurements can be integrated into Gaussian Process (GP) models and learnt jointly with the measurements. We provide a novel formulation of the inverse depth and its derivatives and learn their joint distribution. Experimental results are presented using synthesised examples and real monocular images captured from an Unmanned Aerial Vehicle (UAV). Results show improvement in depth estimation over standard Gaussian Process Regression (GPR). This improvement is presented by a reduction in the GP depth prediction errors and the predictive variance. Finally, we show mathematically that this improvement is due to the augmented derivative covariance terms and the correlations between the inverse depth and the derivatives.