Istanbul 2004 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
2.4 Accuracy Measure 6, prm 0f each DTM Grid point 
t 
: 1 E : . . ee ©, 
For estimating elevation accuracy in every DTM grid point it is y= 
adequate to apply any simple interpolation method’. Our gc 
procedure for this purpose is interpolating the elevation of 
individual grid points based on just those terrain points closely 
surrounding them: applied is a least squares fitting of a tilted 
plane. The elevation accuracy measure sought, o;prw. is 
computed of the RMS values as introduced in section 2.2, and 
of the number n of the surrounding terrain points: 
    
a TR Ltd 
m y 1 ra 
“By A 
ee SPP pes ots v - 
* — mets i e E 
i m om qiue e 
a. 
qp "lcd 
QS 
RMS (1) s 
Oz0TM — AE 
This rule is immediately understandable for horizontal planes, 
where the interpolation is nothing but computing the arithmetic 2 
mean; it is however also true for tilted planes, as shown in the 
m] Appendix B at the end of this paper. We have also to answer the 
question how to find the number n of the surrounding terrain 
| ALS-DTM, points. The overlay as described in section 2.3 provides the Figure 5: Accuracy of an ALS-DTM computed statistically, 
g grid: 5m) curvature of the interpolated surface in all DTM grid points. black: areas without original data 
With these values, the maximum size of a surrounding area will 
be computed, so to assure that within it deviations from a tilted 
plane will not exceed the accuracy of approximation as 
   
Imi 
In our data set for testing, with the accuracy of approximation 
. - > pa 2 rt 
specified as 5cm, areas A vary between 2m' and 512m'. With 
ain curvature. specified (e.g. Briese, Kraus, 2003). Denoting the size of this this area size information A, with density n of the terrain 
'TM grid. The surrounding by A (Figure 4), and applying the point density points (Figure 1), and with accuracy RMS of the individual 
try (Appendix measure n (Figure 1), the number n of the surrounding terrain terrain points, the accuracy 0; pry Of the individual DTM grid 
imum value of points can be computed as : points can be computed applying formulae (1) and (2). Figure 5 
vary between shows the results. Thus, these have been found by statistical 
hus computed methods. The values vary between 4mm and 2.15m. In those 
hology of the = (2) cells of the analyzing grid not containing any terrain points, the 
thophoto). In nznA accuracy measures cannot be computed applying formula (2); 
5 considerably these cells are marked black. 
'eme curvature The *black" areas corresponding to gaps in terrain data are 
bridged over by DTM interpolation more or less acceptably. 
However, the endangered reliability of the interpolated surface 
\ in such areas without terrain data must be documented. In such 
areas. the empirical stochastic approach will be replaced by a 
    
geometrically based one. 
DTM — 
surface 
3. THE GEOMETRICALLY BASED APPROACH 
N 
[n this approach, one of the important parameters is the distance 
between each grid point of the interpolated DTM grid and the 
(original) terrain point next to it. 
  
; 3.1 Distance between each Grid Point of the DTM and the 
Figure 4: Two adjacent DTM grid points with their Terrain Point Next to it 
approximating areas À 
These shortest distances d, can be determined efficiently by 
applying the Chamfer function from digital image processing 
(Borgefors, 1986). Figure 6 shows this information for our data 
set for testing. The maximum shortest distance is 19m. In the 
e 
areas of the gaps in terrain data these values are particularly 
large. 
  
-DTM ' Numerous comparative studies performed earlier have shown 
that the accuracy of DTMs depends very little on the method 
of interpolation. Various interpolation methods result, 
however, in widely differing geomorphologic quality of the 
interpolated surface and in the quality of the filtering 
process.