Recovery of elevation from estimated gradient fields constrained by digital elevation maps of lower lateral resolution

Depth measurement techniques like stereo analysis and laser range scanning often yield a lateral resolution below image resolution. In contrast, shading-based methods estimate the elevation model at image resolution. We present a computationally efficient approach to recover a surface of high vertical and high lateral resolution from a noisy gradient field and independently measured elevation data of lower lateral resolution, relying on a minimization of the mean squared difference between the low-pass component of the surface obtained based on shading information and that of the independently measured elevation data. The presented method is compared to a reference approach that minimizes a weighted sum comprised of the mean squared difference between the low-pass components of the estimated gradient field and the optimized model, respectively. The presented algorithm is applied using lunar orbital image data and stereo elevation data and is evaluated regarding orbital laser altimeter measurements of high vertical accuracy.