difference between the original surface f(x,y) and the reconstructed one 
f(x,y) defines the error of the digital (elevation) model: 
e(x,y) = f(x,y) - f(x,y) 
where f stands for elevation, in a DEM, and x,y for the planimetric 
position of a point. As a global accuracy measure for the DEM, the 
r.m.s. error can be used 
LK 
da. 
GARE 
0 
if the DEM covers an area of extension L by K. Investigations /2/, /11/ 
have indicated that good estimates of o can be obtained by using profile 
data instead of the surface data itself; therefore, and also for reasons 
of simplicity, the univariate analogon will be considered in the 
following: 
L 
eJ Comte dx | 
Since equispaced sampling and interpolation by methods such as linear 
interpolation, finite element, moving average, linear prediction, etc., 
represent a linear system, its effect can conveniently be studied in the 
frequency domain, i.e., by the transfer function /4/, /9/. By applying 
Parseval’s theorem /10/, an estimator for c can be derived in the fre- 
quency domain: 
e? (x,y) dx | à 
0 
6% = 82 + 8? 
S R 
n/2 -1 
aA. 2 - 2 2. bh 
e 7 6 x {1 - Hu, >} IF(k)|* ; u, [aix 7 
k=-n/2 
3 
a2: 2 2 E 
On = 2 OM / H (u) du ; u = vix 
0 
ol is the component of the mean square error of the DEM (profile) condi- 
tional on sampling and interpolation; 
2 
9 is the contribution of a purely random height measuring error having 
a standard deviation of Om) 
H(u) is the transfer function; it characterizes the interpolation method 
and defines fidelity in function of the reciprocal sampling density u, 
the product of frequency v of a sinusoidal input and the size of the 
sampling interval Ax; l/u - A/AX, A = l/v; 
- 65h. -