Probabilistic Digital Elevation Model Generation For Spatial Accuracy Assessment

We propose a new method for the measurement of high resolution topography from a stereo pair. The main application area is the study of planetary surfaces. Digital elevation models (DEM) computed from image pairs using state of the art algorithms usually lack quantitative error estimates. This can be a major issue when the result is used to measure actual physical parameters, such as slope or terrain roughness. Thus, we propose a new method to infer a dense bidimensional disparity map from two images, that also estimates the spatial distribution of errors. We adopt a probabilistic approach, which provides a rigorous framework for parameter estimation and uncertainty evaluation. All the parameters are described in terms of random variables within a Bayesian framework. We start by defining a forward model, which mainly consists of warping the observed scene using B-Splines and using a spatially adaptive radiometric change map for robustness purposes. An a priori smoothness model is introduced in order to stabilize the solution. Solving the inverse problem to recover the disparity map requires to optimize a global non-convex energy function, which is difficult in practice due to multiple local optima. A deterministic optimization technique based on a multi-grid strategy, followed by a local energy analysis at the optimum, allows to recover the a posteriori probability density function (pdf) of the disparity, which encodes both the optimal solution and the related error map. Finally, the disparity field is converted into a DEM through a geometric camera model. This camera model is either known initially, or calibrated automatically using the estimated disparity map and available measurements of the topography (existing low-resolution DEM or ground control points). Automatic calibration from uncertain disparity and topography measurements allows for efficient error propagation from the initial data to the generated elevation model. Results from Mars Express HRSC data are presented. A pair of images (including the nadir view) at 30m resolution was used to obtain a DEM with a vertical accuracy better than 10m in well-textured areas. The lack of information in smooth regions naturally led to large uncertainty estimates.