p=--=+, 
‘Rules ‘ 
L-4- 
  
2 e 
M heck pts! 
po mm MN m TT 
[ Classification Rules] 
been Jd 
mL 
! Classified , 
1 
: ! 
Jnput | 
    
   
- 
pum 4 eU 
Input i— WSampling Pan lnterpolation J Output, 
tine, Surf. a DIM 
'C 
Comparison 
a a. 
= = 
' i les! 
| Discrepancies| 
   
Pas > 
; Statistical | 
t Tools I 
Soe ee am - 
Statistical 
Analysis 
rre. 
' Accuracy m 
i i 
(Estimate | 
  
Figure 4: Experimental Approach to accuracy 
estimation of real terrain relief 
Strictly speaking, in the case of irregularly 
spaced points, the application of a single 
transfer function to study the problem of fidelity 
in the Fourrier transform is not possible. 
In progressive sampling the point density is 
doubled in each run a composed transfer function 
can be constructed for PS (Tempfli, 1986) and used 
to assess the fidelity of DTM resulting from PS. 
H(v,Th,r) = 1-V202 (v,Th,r) (16) 
This is a function composed of segments of the 
partial transfer functions, for incomplete regular 
grids of different densities corresponding to the 
successive sampling runs r, applied to sinusoids 
sin(2nvAX) with different frequencies v E (0,172). 
To this end a limiting fidelity function is 
introduced; 
$(Vk,Th) - (P(wk) - a-Th]/P(wk) (17) 
Where a-Th is the maximum error acceptable in 
progressive sampling and the factor "a" depends on 
the magnitude of the threshold and on the type of 
the input (Makarovic, B., 1976). 
  
  
  
i 
Vo V, V v 
Figure 5: Composed transfer function 
By considering criteria 
sampling, the sections of Transfer Function (TF) 
below the & curve should be rejected, and the 
composed TF used for for the purpose of accuracy 
estimation. 
inherent in progressive 
Estimation of the accuracy as function of fidelity 
of PS can be approached from the viewpoint of the 
two extremes: 
- Lower bound accuracy (Cin) 
- Upper bound accuracy (o ux) 
82 
The lower bound accuracy (o in) of PS can be 
estimated by using the transfer function for the 
regular grid with AX = Bry ; and discrete 
amplitude spectrum which is compüted by FFT. 
2 n/2 -1 
o=E {1- Hp Th )}2 [Fk]? (18) 
s k=-n/2 
Where P(w) - 2|F(k)|, |F(k)| = the discrete 
amplitude “spectrum of the input obtained by FFT. 
The upper bound accuracy (0...) of PS can be 
max x 
estimated by using the composed ffansfer function. 
The . actual accuracy of PS based on 
interpolation would be: 
sampling and 
min s %actual 3 “max (19) 
The estimation of the accuracy by means of the 
Transfer Function is possible only when the 
amplitude spectrum of the terrain is known. When 
terrain exhibits a predictable amplitude spectrum, 
an approximate estimation of the overall accuracy 
is possible. 
Because investigations were performed with the 
help of some artificial ideal geometric 
primitives, where the input was precisely known as 
well as with real terrain relief, the experimental 
approach to accuracy estimation was obvious. 
As it was stated earlier the overall 
error (o,) of the reconstructed 
very suitable for the assessment of accuracy. In 
this investigation, however, the following 
additional measures are used for the quality 
assessment of DTM. 
standard 
surface is not 
- The efficiency of the surface modelling process, 
which is affected by factors such as 
distribution of the sampled points ( points 
representing skeleton information and those 
representing the filling information), and the 
average 
area. 
number of the sampled points per unit 
. The maximum discrepancy 
modelled height. 
between true and 
- Reliability is quantified by the 
correct heights divided by the 
number of 
total number of 
heights. 
. Fidelity of the modelled relief: can be defined 
by a transfer function, which describes the 
combined effects of sampling and interpolation 
(Makarovic, 1976). 
3.5 Assessment criteria 
Quality of the reconstruction is influenced by the 
following factors; 
- Amount of skeleton information (X) 
- Quality of skeleton information (0,) 
- Sampling interval for filling 
(1) 
- The value of threshold used for densification 
- Number of densification runs 
- Number of sampled points 
information 
Real terrain relief 
Quality of the reconstruction of the real terrain 
relief can be assessed using the folloving 
criteria: 
- The mean error ps of PS is determined for all 
the 
the 
Wher 
and 
poin 
For 
is 
patc 
- The 
Opc» 
(R5 
are 
CS 
wher 
and 
poin 
obvi 
howe 
same 
This 
betw 
surf 
meas 
prim 
MAXE 
- The 
of s 
el 
i 
For 
diff 
perf 
rela 
loss 
magn 
Ac = 
Rati 
Ro 
CS 
Rati 
CS 
A MA 
Rati 
MAX 
Rati 
MAX