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New perspectives to save cultural heritage
Altan, M. Orhan

CI PA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey
4.3 Visualization of the accuracy analysis
4.4 Analysis of the accuracy of lake forms
After performing the 9-parameter transformation, the residuals
on identical points can be depicted and analysed. The
visualization is not only performed in the original historical
data set, but also in the data set previously transformed to the
national coordinate system. This procedure allows the
correction of obviously wrong defined points in the historical
data set as well as the check of the visualization methods,
particularly of the correct orientation of differences (Figure 7).
Figure 7. Differences on identical points in XY direction, left in
original data set, right in the transformed data set; their
comparison allows for the check of visualization procedures.
In order to obtain a view of the relief distortion as a whole, a so
called distortion grid is generated (Figure 8). It represents the
depiction of the current kilometre or geographic grid in the old
map (e.g. Beineke, 2001). The distortion grid is based on the
Delaunay triangulation on identical points: in the intersections
of the current grid with the triangle sides the residuals in X and
Y directions are linearly interpolated. The interpolated residuals
are connected to form the horizontal and vertical lines. For the
visualization of the distortions in the height, contour lines of
the same height difference are interpolated in a similar way.
Once transformed to the national coordinate system, the
complete historical data set is georeferenced and the position
and shape of its features such as roads, rivers, lakes etc. can be
compared with the current reference data. The lakes represent
one of the main characteristics of the area of Central
Switzerland and as such they always had been objects of
particular interest for old map makers. Therefore an
investigation on the accuracy of lakes representation in the
Pfyffer's relief was performed (in 2D).
For this purpose the measures originally developed for the
quality assessment of building reconstruction (Niederoest, M.,
2003) were used (Equation 2). The common lake area in respect
to the current reference data (relative intersecting area) gives
useful information on how good the two areas fit. The total
relative shape dissimilarity represents the not common lake
areas divided by the reference area; the ratio which should be
Relative intersecting area = Ref nOld
Lake in the reference, but not in the relief = Ref \ Old
Lake in the relief but not in the reference = Old \ Ref
Total relative shape dissimilarity = Ref \ Old + Old \ Ref
where Ref = lake area in the current reference data
Old = lake area in the Pfyffer's relief
The meaning of Equation 2 is illustrated in Figure 9b. It is
visible that the lake in the historical relief is rather good if only
the shape would be considered, but the shift between the two
lake depictions is very big. Therefore for the area comparisons
in the history of cartography it is suggested to treat the location
and form of the feature independently: before computing the
measures from Equation 2, the historical data is shifted to the
centre of gravity of the reference (Figure 9c). Additionally, two
new measures are defined:
Figure 8. The distortion grid of the Pfyffer's relief in XY-
direction (red lines). The light grey dotted lines represent the
current 2-km grid.
Distance between the centres of gravity =
V^R.r-Xa.y+OW-Yo,,,) 2
A verage shape difference = Ref \ Old + Old \ Ref
where X Rcf , Y Rcf = centre of gravity of the reference lake
X 0 id, Y 0 id = centre of gravity of the lake in the relief
Ref = lake area in the current reference data
Old = lake area in the Pfyffer's relief
Ref_perim = lake perimeter in the reference data
Figure 9. Quantitative analysis of the lake contours accuracy.
(a) The lake in Pfyffer's relief overlaid with the reference,
(b) Red: reference and relief (Ref n Old), blue: reference
without relief (Ref \ Old), green: relief without reference
(Old \ Ref), (c) The same analysis including the shift of the
relief data to the reference centre of gravity