International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
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The result of the first step is used to mask the elevation data 
(Fig. 3). In this way, we obtain different elevation data for 
buildings and non-buildings. Calculating the mean height for 
each building object of the map, a coarse 3D-description is 
constructed by prismatic models. These wire-frame models are 
transformed into a surface model using an automatic 
tri angulation. 
4.2. Flat Roofs 
In case (i), the position of the peak’s maximum is found and this 
value is assigned as the height value to the prismatic object. In 
case (ii), the minor peaks with a certain height distance to the 
main peak are searched for (Fig. 6c). Then, a minimum in the 
histogram between two consecutive peaks (main and minor 
ones) is found and a threshold value is calculated. These 
thresholds are used to segment the elevation data (Fig. 6d-f). 
The segments are labelled and examined for compactness 
(circumference/area). Segments, which are too small or not 
compact, are not taken into consideration for further analysis 
(Fig. 6e). A compact segment of a size greater than a minimum 
area confirms the hypothesis of a superstructure (Fig. 6f) and 
the contour is accepted (Fig. 6g). 
Fig. 4. City model of prismatic objects (buildings). 
4. ROOF RECONSTRUCTION 
Depending on the application, buildings should be 
reconstructed with a varying level of detail. In this research, a 
description of the buildings as shown in Fig. 4 is aimed for. The 
roofs should be reconstructed from elevation data. Simple roof 
structures show characteristic histograms (Fig. 5). 
Fig. 5. Characteristic height histograms of simple roofs. 
Flat roofed buildings show a significant peak in the histogram, 
belonging to an area corresponding to the building outline. If a 
flat roofed building has a flat superstructure (e.g. penthouse) the 
histogram shows an additional peak above the main peak. 
Simple gabled roofs show a rectangular histogram. The width of 
the rectangle depends on the slope of the roof. A hip roof shows 
a trapezoidal histogram. The length of the ridge determines the 
height (frequency) of the right side of the histogram. A cropped 
hip roof shows a mixture of rectangle and trapezoidal form. 
Since the ideal histogram forms are not present in real data, the 
discrimination of sloped roofs by their histograms will be hardly 
possible. 
4.1. Roof Hypotheses 
Based on the histogram of heights, flat roofs and sloped roofs 
are discriminated. If the distance between minimum and 
maximum height is smaller than a threshold, a flat roof without 
superstructures is hypothesized (case (i)). If the distance is large 
enough, the distribution is examined using the entropy relative 
to the elevation range. If this value is low, a flat roof with a flat 
superstructure is hypothesized (case (ii)), otherwise, sloped roof 
parts are assumed (case (iii)). 
Fig. 6. Reconstruction of a flat roof with a superstructure. 
In the following vectorization step of the contour chain, we first 
try to fit the contour by a rectangle (Fig. 6). If the assessment of 
the fit is lower than a given threshold, the contour is rotated to a 
coordinate system parallel to the major orientation of the 
building. After projecting the contour points to the coordinate 
axes, peaks are searched in the histogram to describe the 
contour by a right-angled polygon (e.g. L-structure). If this 
approximation is also insufficient, the contour is approximated