is 
ont 
che 
C BHO (DDH QS 
the I-subsets; 
. Discrete points, sampled stationary 
. Strings of points, sampled dynamically 
- The standard error o of modelling by the 
I set, which can be differentiated further 
according to the successive densification runs. 
The standard error o, of modelling by the X set 
can be differentiated further according to 
accuracy, and comprehensiveness. 
ag ; 
Ü comprehensiveness (o) 
X 
c 
accuracy (93) 
. Comprehensiveness co. of the I-set depends on the 
completeness of Z-Set (which features should be 
sampled and up to what extent), which depends 
on: 
. The criterion to detect non linearity in 
terrain relief 
. Threshold used in the criterion 
. Accuracy o. of modelling by the I-set depends 
on: 
. Image quality and scale 
. Precision of instrument 
. Operator skill and care 
Sampling mode (stationary, dynamically) 
The standard error on of modelling by the E-set 
depends on: 
. Apriory I-set and Op 
. Grid interval 
. Pointing error 
. Interpolation algorithm 
Because the skeleton information is sampled prior 
to the filling information, it has an influence on 
the I-set, thus Z-set affects strongly the further 
modelling process. 
3.2 Sources of errors 
The accuracy of terrain relief modelling is 
influenced by two main sources of errors: 
. Error of sampling and interpolation 0.» 
mentioned earlier 
. Measuring error c , depending on; setting error, 
the quality of photography, type of terrain, 
model scale, precision of the instrument, and 
the skill and care of the operator. 
Assuming f(x) is the terrain profile, and fi (x) 
is the correct height of a point and gi (X) is the 
sampled height: 
gi (x) = f. (x) + m, (x) (12) 
In photogrammetric measurement m, (x) is considered 
partly systematic, and partly random, thus the 
latter part of m, (x), can be defined as a sequence 
of uncorrelated values, which are normally 
distributed, with the mean equal to zero and the 
variance 62 
Assuming that f.(x) and m, (x) are mutually 
independent and thüs uncorrelated, the variance of 
the error of the modelling is: 
2 = 2 
Op =0 s e (13) 
where c is the error of sampling and 
interpolaËion, and o. is caused by the On 
81 
In (Tempfli, 1986) it has been found that there is 
a simple relation; 
o2, = 2/3 Ax? oz (14) 
In the case of a regular grid and in the absence 
of measuring error, the error of sampling and 
interpolation can be defined as (Tempfli, 1986); 
n/2 -1 
e = I { 1 - H(vk) }2 (15) 
k=-n/2 
Where |F(k)| is the discrete amplitude spectrum of 
the input obtained by FFT. 
  
3.3 Estimation of the sampling error oc. 
Accuracy of DIM can be estimated by analytical, 
semi analytical, or experimental approaches. 
3.3.1 Analytical approach Terrain profile 
(surface) can be transformed into the frequency 
domain (Fourrier Transform). The transfer Function 
of sampling and interpolation can be determined 
and used for quality assessment (Laan,1973). 
  
Fidelity of the reconstruction (transfer ratio) 
can be computed for various sampling interval 
(Ax), and plotted against different Ax (Makarovic, 
1976). 
Transfer Function can be used either for the 
planing purpose or for Accuracy estimation of DTM, 
reconstructed by sampling and interpolation. 
The advantage of this approach is that there is no 
need for classification and also its simplicity in 
practical application, but the approach is 
conceptually involved. 
3.3.2 Semi analytical approach Applying the 
law of error, propagation, the error of the 
reconstruction H - H > min can be computed (Kubik, 
K., 1986). 
A low polynomial (trend) is substructured from the 
input (terrain surface) in order to create the 
stationarity condition, and o_, and the covariance 
are estimated (stochastic assumptions), 9g; 9 ; 
: : mean 
and Sax computed, for error estimation. 
Shortcoming of the method is some simplified 
stochastic assumption on terrain surface 
(homogeneous, stationary, and isotropy) vhich can 
seldom be realised in case of real terrain relief. 
3.3.3 Experimental approach Real terrain 
relief. The reconstructed surface of the real 
terrain relief is compared to the original surface 
and the fidelity of the reconstruction is 
estimated. 
The flow diagram of the approach is shown in 
figure 4. 
The advantage of this approach is that it is 
conceptually simple. 
The shortcoming of the approach is that extensive 
experiments and terrain classification are 
required. 
3.4 Fidelity of DTM obtained by PS 
The fidelity of sampling and interpolation (in 
case of fixed AX) can be studied by its transfer 
function.