Terrain reconstruction with an adaptive surface mesh

Describes a new class of adaptive mesh surface for terrain analysis. The novelty of the contribution resides in the control of the mesh. We use a variance-bias criterion to select the optimal areas for the triangular facets of the mesh. In this way the mesh adapts itself to offer the best tradeoff between increasing the facet area to minimise the noise variance and decreasing the facet area to minimise the bias of the fitted facet parameters. We provide a illustration of the effectiveness of the new mesh control methodology for the case where the faces of the mesh represent planar patches. The piecewise planar mesh is shown to be effective in the modelling of an area of complex terrain structure in Southern England.