CIPA 20' XIX"' International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
The results of the transformation are summarized in Table 2. 
The 221 tested points deviate from the current map in average 
of absolute values about 387 m in the plane and 76 m in the 
height, corresponding to 3.3 and 0.7 cm within the object. 
Considering the conditions under which the relief was 
constructed - a definitely unfavourable age for landscape 
exploration and surveying, poor available maps and a very large 
area modelled in detail - Franz Ludwig Pfyffer’s achievement 
is even from today’s point of view admirable. The more 
detailed cartographic-historical inteipretation of the results as 
well as a comparison of the relief with the old maps of that 
period can be found in (Niederoest, 2002b). 
Scale 
In X: 1:1 T688 (±29) 
In Y: 1:11 '414 (±21) 
InZ: 1:11 '136 (±672) 
Declination from the north 
30.3° (±0.001) 
Accuracy: 
A. 
Average of differences 
in absolute values 
In X: 392 m (3.4 cm in rei.) 
In Y: 382 m (3.3 cm in rei.) 
In Z: 76 m (0.7 cm in relief) 
B. 
Sigma aposteriori in 
coordinate directions 
(tfo) 
374 m (3.2 cm in relief) 
In X: 418 m (3.6 cm in rei.) 
In Y: 482 m (4.2 cm in rei.) 
InZ: 109 m (1.0 cm in rei.) 
C. 
Sigma of a spatial 
point ( C7 0 • VJ ) 
648 m (5.6 cm in relief) 
Table 2. Metric parameters of the Piyffer's relief (results of 
the 9-parameter transformation of identical points 
with weighted observations) 
4.2 Transformation of image, height and vector data 
When analysing the accuracy of historical relief models (and 
old maps respectively), we are not only interested in their 
metric parameters based on the transformation of identical 
points. In addition to procedures presented in the previous 
section, the transformation of the image, height and vector data 
to the modem coordinate system can be of great use for the 
research in the history of cartography. The complete historical 
data set transformed and georeferenced in this way allows 
overlays with current data and, in case of historical relief 
models, simple comparison of terrain models. Two approaches 
were developed for this purpose: transformation of historical 
data using global parameters and a mesh-wise transformation 
using local parameters. In (Niederoest, 2002a) was shown that 
the latter transformation, an often used method for the 
geometrical correction of historical maps (Fuse, 1998; Shimizu, 
1999; Baletti, 2000) is less suitable for analyses of historical 
maps and relief models than the one using global parameters. 
In the following the transformation of historical image, height 
and vector data to the modem coordinate system using global 
parameters is described. The procedures (a) and (c) can be in an 
analogue manner applied for analysis of (planar) old maps. In 
this case, use formulas of appropriate two-dimensional 
transformation instead of Equation 1 and do not consider 
algorithm steps dealing with the height information. 
Using the previously estimated 9 parameters of the general 
spatial transformation of identical points (d x , d y , d z , m x , m y , m z , 
a, p, y) the orthoimage, DTM and the vector data set are 
transformed to the national coordinates as follows. 
(a) Transformation of the image data. For each pixel U, V of 
the new texture image an algorithm similar to the orthoimage 
rectification procedure is applied (indirect method to avoid 
creation of holes): 
1. Using georeferencing information (pixel footprint and 
coordinates of image comers), calculate X, Y 
2. Find Z’ value of the nearest DTM node of the 
transformed historical data set (nearest neighbour 
interpolation) 
3. Calculate x, y for X, Y, Z’ as an inversion of Eq. 1 
4. Calculate corresponding pixel u, v of historical image 
using georeferencing information 
5. Take grey values of u, v as transformed radiometric 
information for U, V pixel of the new image 
As the image data of historical relief models - or the old maps 
respectively - are usually very large, the algorithm allows user- 
defined tiling of the transformed data set. This is particularly 
useful in the case when the dataset after the transformation 
declines from the north significantly. The seamless division of 
one huge image to several georeferenced tiles helps to optimize 
the performance of visualization. 
(b) Transformation of the height data. The transformed DTM 
of the historical relief is primarily needed for the comparison 
with the current height model (a raster of 25 m grid width). To 
avoid errors from the double interpolation at this step, the DTM 
of the Piyffer's relief is transformed point-by-point applying the 
Equation 1, resulting to an irregular 3D point cloud. This raw 
data serves as a basis for the DTM comparison (Section 4.5). 
For the visualization purposes a regular raster of 25 m grid 
width is calculated using already mentioned package DTMZ 
which performs Delaunay triangulation and finite element 
interpolation. 
(c) Transformation of the vector data. Each layer of the three- 
dimensional historical vector data set is transformed point-by- 
point using the Equation 1. The transformed points are 
reconnected to form the same linear features as in the original 
data set. 
As a result, all DTM, orthoimage and vector features of the 
historical data set are in national coordinates now and thus can 
be overlaid with current map information (Figure 6), used for 
the visualization of the results (section 4.3) and for the further 
analysis (sections 4.4 and 4.5). 
Figure 6. A part of the orthoimage of Pfyffer’s relief (Lake 
Lucerne) in national coordinate system overlaid with current 
lake outlines (dark blue polygons).