Terrain Modeling From Lidar Range Data in Natural Landscapes: A Predictive and Bayesian Framework

The Earth's topography, including vegetation and human-made features, reduced to a virtual 3-D representation is a key geographic layer for any extended development or risk management project. Processed from multiple aerial images or from airborne lidar systems, the 3-D topography is first represented as a point cloud. This paper deals with the generation of digital terrain models (DTMs) in natural landscapes. We present a global methodology for estimating the terrain height by deriving a predictive filter paradigm. Under the assumption that the terrain topography (elevation and slope) is regular in a neighboring system, a predictive filter combines linearly the predicted topographic values and the effective measured values. In this paper, such a filter is applied to 3-D lidar data which are known to be of high elevation accuracy. The algorithm generates an adaptive local geometry wherein the elevation distribution of the point cloud is analyzed. Since local terrain elevations depend on the local slope, a predictive filter is first applied on the slopes and then on the terrain elevations. The algorithm propagates through the point cloud following specific rules in order to optimize the probability of computing areas containing terrain points. Considered as an initial surface, the previous DTM is finally regularized in a Bayesian framework. Our approach is based on the definition of an energy function that manages the evolution of a terrain surface. The energy is designed as a compromise between a data attraction term and a regularization term. The minimum of this energy corresponds to the final terrain surface. The methodology is discussed, and some conclusive results are presented on vegetated mountainous areas.