Improved Morphological Interpolation of Elevation Contour Data with Generalised Geodesic Propagations

The objective of this work is to show how geodesic propagation techniques known in mathematical morphology can be employed to reconstruct terrain surfaces, and more generally grid data, from contour maps. We present the so-called generalised geodesic distance that was briefly introduced in a previous article. The shortest paths defined by the generalised geodesic distance can be used to linearly interpolate a given set of contour lines. We extend this concept by incorporating the knowledge of slope values over the contours and perform either Hermite interpolation with this distance or linear interpolation, but with a new weighted geodesic propagation function. Experiments are carried out over synthetic elevation data for which they result in nicely interpolated surfaces. The methodology is generic in the sense that it could be used to reconstruct any 2D or 3D digitised shape from its boundaries.