99 
as the relief and anthropic objects such as infrastructures and buildings. A digital representation of 
the continuous variation of relief over space is known as a Digital Elevation Model (DEM). The 
most common data structure for DEM is a bidimensional array, whose elements are interpreted as 
elevation data (Burrough, 1986). Such a model can be generated adopting a wide variety of 
methods and techniques. 
2.1 DIGITAL ELEVATION MODEL 
Two different approaches for DEM reconstruction are available in the system, depending 
on input data availability from digitized contour lines or from regularly sampled points. 
In the first case, the reconstaiction method belongs to the classical techniques which are 
founded on numerical methods of interpolation or approximation of data extracted from contour 
lines of standard topographic maps. When the unknown point are located in the middle of two 
contour lines, the approach implemented in TISS linearly interpolates between known height 
values along the maximum slope direction. In the other situations, where there are more elements 
interacting, the estimate of the elevation is computed through the kriging technique (Davis, 1986). 
The procedure is similar to that used in weighted moving average interpolation except that the 
weights come not from any deterministic spatial function, but from geostatistical spatial analysis 
based on the sample semivariogram, which accounts for the trend of the known values in the 
vicinity of each point to be predicted 
The second method is based on principles of fractal geometry. Classical interpolation 
techniques and stereo reconstruction present a good quantitative accuracy, if measured as RMS 
error between original and reconstructed data. But, as pointed out by Shearer (1990), the 
quantitative accuracy of a DEM do not imply a qualitative accuracy as well. The basic idea 
underlying the fractal approach to DEM is that the irregularity, erraticity. and. at the same time, the 
self-similarity of fractal structures mimics at best the typical behaviour of mountain profiles. 
Recent literature confirms fractal geometry to be a powerful tool for the analysis of heterogeneity 
of many natural phenomena, including terrain shape analysis (Pentland. 1984: Mark and Aronson. 
1984; Polidori et ah. 1991) and three-dimensional landscape synthesis (Yokoya et ah, 1989). 
The advantage of the fractal interpolation is to make the DEM relatively independent from 
the scale factor. In order to reproduce the "erraticity" of a given relief the fractal dimension D is 
estimated by adopting some special mathematical method on finite set of samples. In this approach 
the landscape relief is interpreted as a realization of a fractional Brownian motion tfBm). which is 
a mathematical generalization of a classical Brownian motion. This allows to compute the fractal 
dimension through a variance analysis of the vertical displacements taken at different horizontal 
distances (Brivio et ah, 1992). The role of fractal dimension D is that of an exponent ruling a kind 
of a fractional moving average which filters out high frequency in the original Brownian motion: 
the lower D the smoother the topographic surface, the higher D the higher the erraticity of the 
random function, to the limit where the subset “fills” the whole 3-D space. (Goodchild. 1980). 
Once the fractal dimension is given, it is possible to reconstruct a surface relief using 
different fractal methods which interpolate the original set of elevation data, as fractional Brownian 
motion or Iterated Function Systems (Barnsley, 1988). Experiments conducted confirm that the 
fractal approach is very well suited for high relief terrain modelling (Brivio et al.. 1992; Brivio and 
Marini, 1993).