Creating Digital Elevation Models
Overview
Digital elevation models (DEMs) are routinely employed in GIS applications such as:
- Planning: eg determining terrain viewshed, aspect, slope
- Hydrology: eg determining drainage networks, watersheds, hydrological response
- Telecommunications: eg determining antenna coverage
DEMs may be derived directly by remote sensing techniques,
but contour data is generally more widely available and more affordable.
There are several existing methods for deriving DEMs from contour data these fall into two categories
- General scattered-data interpolation methods:
- Inverse-distance weighted (IDW) (eg ARC/INFO GRID)
- Via triangulated irregular network (TIN)
- Contour-specific methods:
- IDRISI INTERCON (ray-based)
- ARC/INFO TOPOGRID (spline-based)
Using Radial Basis Functions
Radial basis functions (RBFs) provide an alternative method for performing scattered-data interpolation, with the
following characteristics:
- The result is guaranteed to be the smoothest interpolant (in the sense that the second derivatives are minimised)
that fits the original data
- In 2D, the solution is a "thin plate spline"; i.e. it is equivalent to the shape that a thin metal plate would assume
if constrained to pass through the data points
- Radial basis functions have long been recognised as the smoothest interpolant, but had been considered to be
computationally impractical for anything but the smallest problems, prior to the work of RK Beatson (Mathematics & Statistics Dept, University of Canterbury)
Results
An RBF was fitted to contours (20m interval) and spot heights from LINZ map M36 (NZMS260 1:50,000), a total of 96441 points.
A DEM was then generated by evaluating the RBF over a subset of the map, on a 600x600 pixel grid, with 5m pixels.
Contours were then derived from this grid (a). Another DEM was generated by evaluating the RBF on a 720x720 pixel grid,
with 25m pixels (b, c and d).
A LINZ orthophoto was draped over this DEM (e). Finally a view of a circular region around Quail Island was produced (f).
