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
