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Title
New perspectives to save cultural heritage
Author
Altan, M. Orhan

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).