CI PA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
593 
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 
small. 
Relative intersecting area = Ref nOld 
Ref 
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 
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 
Ref_perim 
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