Gaussian process modeling of large-scale terrain

Building a model of large‐scale terrain that can adequately handle uncertainty and incompleteness in a statistically sound way is a challenging problem. This work proposes the use of Gaussian processes as models of large‐scale terrain. The proposed model naturally provides a multiresolution representation of space, incorporates and handles uncertainties aptly, and copes with incompleteness of sensory information. Gaussian process regression techniques are applied to estimate and interpolate (to fill gaps in occluded areas) elevation information across the field. The estimates obtained are the best linear unbiased estimates for the data under consideration. A single nonstationary (neural network) Gaussian process is shown to be powerful enough to model large and complex terrain, effectively handling issues relating to discontinuous data. A local approximation method based on a “moving window” methodology and implemented using k‐dimensional (KD)‐trees is also proposed. This enables the approach to handle extremely large data sets, thereby completely addressing its scalability issues. Experiments are performed on large‐scale data sets taken from real mining applications. These data sets include sparse mine planning data, which are representative of a global positioning system–based survey, as well as dense laser scanner data taken at different mine sites. Further, extensive statistical performance evaluation and benchmarking of the technique has been performed through cross‐validation experiments. They conclude that for dense and/or flat data, the proposed approach will perform very competitively with grid‐based approaches using standard interpolation techniques and triangulated irregular networks using triangle‐based interpolation techniques; for sparse and/or complex data, however, it would significantly outperform them. © 2009 Wiley Periodicals, Inc.