Annett Faber
3.2 Sensor model
The sensor model describes the sensor, which is used to get input data, specifically its geometrical and radiometrical
properties.
In our project images of the MOMS-02 camera are used. As the flying height is large compared with surface undulations
and the viewing angle is small we can expect small geometric differences between object and image. The resolution of
5-6 m in the panchromatic channel limits the detectability of individual objects. This is the reason why we modeled roads
as linear objects not as area objects. The multispectral channels of the MOMS-02 camera with a resolution less than 10
m pixel size do not appear sufficient for road extraction in urban areas.
3.3 Image model
The image model describes the expected appearance of the object in the image. It formally may be derived from the object
and the sensor model.
In our case the partitioning of the map into map regions can be used directly except for the detailed geometry. We assume
the road elements to appear as bright or dark lines. The width of the lines is expected between a half and one pixel. They
can be expected to be disturbed by traffic or trees and of course sensor noise. Therefore no complete network can be
reconstructed. This is the reason why we did not require connectivity of the road elements in the object model.
The image model therefore consists of the same partitioning of the map as describe above. However, the road segments
will partially be lost, additional segments may appear, e. g. due to linear structures in building areas. All segments will
show errors in length, usually being too short, and orientation which depends on their extracted length. The statistics of
the line segments may be learned from example segmentations.
At the moment we assume the number of disturbing line segments to be less than 25 96 of the good line segments. For
simplicity, we also assume the orientation errors to be independent on the length of the extracted line segment.
4 ANALYSIS
4.1 Aspects and Assumptions
The analysis has to cope with a set of problems. The following Tabular (Tab. 1) will describe and give possibilities to
solve these problems.
Problem
Roads within a region with the same dominant ori-
entation have directions which differ by multiples of
90^. The unknown multiplicity needs to be eliminated
to come to a unique estimated direction di for each
region S; (Fig. 3).
Roads not belonging to a region, i. e. roads which
cross the region at an arbitrary angle, should not in-
fluence the estimate of the direction of that regions.
Orientation of roads is not available between the
roads. In order to obtain closed boundaries orienta-
tion values should be made available for all positions
in the map.
The analysis should be robust with respect to varia-
tions in the density of the road network.
Solution
The representation of directions should map the orien-
tation ¢;; of each road segment belonging to the same
region to the same value. To eliminate the multiplic-
ity of the angle we use the 4 fold angle a;; = 4¢;;.
Thus 4ó;; mod 2x — (44; + k;)r/2 mod 2x = 46;.
We use a robust estimate for the fourfold orientation
angle, allowing up to 25 96 outliers.
We use an iconic description of the map, i. e. we
Work on a raster image of the map. For each pixel
of this map we robustly estimate the mean orientation
of all roads in a certain neighborhood. For this pur-
pose we perform a vector-raster transformation of the
extracted line segments.
Up to now, we assume approximately homogeneous
density of the roads, which is reasonable in densely
populated areas.
Table 1: Problems of analysis and their solution
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
