ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
Increasing the training data set size doesn’t affect the
detection rate significantly, we can see that the range of the
detection rate is between 98.2% and 99.2%; we gain only 1%
in the detection rate when we increase the size of the training
data set from 20 samples to 400 samples. However
increasing the size of the training data set has a significant
effect on the false alarm rate. Increasing the size of the data
set from 20 samples to 400 samples reduce the false alarm
rate from 11.5% to 5.5%; we gain 6.0% improvement in the
false alarm rate by increasing the size of the training data set
from 20 samples to 400 samples. The results using 100
training samples are used in the rest of this research.
4. CONVERTING REGIONS TO POLYGONS
The 2D modified Hough space discussed in the previous
section is helpful in extracting the border lines for the roof
regions. Given all points contributing to a certain cell, a
nonlinear least squares estimation model is used to adjust the
line parameters given the cell locations in the parameter
space as approximate values for the line represented by this
cell. Lines are then grouped recursively until no more lines
with similar parameters are left. Short lines are then rejected.
Figure 6 shows the extracted border lines for two buildings.
Figure 6. Extracted Border Lines for 2 Buildings
The next step is to convert the extracted lines to polygons
using a rule-based system. The rules are designed as complex
as possible to cover a wide range of polygons. Figure 6
shows the challenging in converting the extracted border
lines to polygons. For some polygons they might be
quadrilaterals, however only three borderlines are detected.
Some quadrilateral regions might have more than four
borderlines detected. The mechanism that is developed in
this research works in three steps. The first step is to find all
the possible intersections between the borderlines. However
if the two lines are almost parallel the intersection point is
not considered. If the distance between the end point of the
line and the intersection point is large the intersection point is
rejected. The next step is to generate a number of polygons
from all the recorded intersections. Each combination of four
or three intersection points is considered to be a polygon
hypothesis. Some hypotheses are ignored if the difference in
area between the region and the hypothesized polygon is
more than 50%. If the internal angles between the intersected
lines is out of the range [30°-150°] the hypothesis is
discarded. The third step is to find the optimal polygon that
represents the region borders. The best polygon that
represents the region is chosen from the remaining polygons.
A template matching technique is used to find the best
polygon that represents the region. Figure 7 shows the
extracted polygons for two buildings.
Figure 7. Extracted Image Polygons for 2 Buildings
5. 3D POLYGON EXTRACTION
In this section the process of finding the correspondence
polygons among all images and matching them is discussed.
5.1. Polygon Correspondence
After finding the building roof polygons in the images, we
start finding the correspondence polygons. We designed a
new technique to find correspondence polygons based on
their geometrical properties. All possible polygon
correspondence combinations are considered and for each
combination the vertices of the correspondent polygons are
matched across all available views, since we have more than
one pair of images we can calculate the residuals of the
matched 3D polygon vertices. The matching residuals are
summed for each combination set, and the combination set
with the minimum residual is selected as the best
combination set. Figure 8 describes the process of finding the
correspondence polygons in four images. In order to
minimize the running time, some subsets are rejected before
the matching process using the epipolar geometry and the
minimum and maximum building heights.
Image A Image B Image D
e LU
Polygon Total Total Residual
Combinations Residuals
1111 &2222 R =p ir
ABCD ABCD Ts m
141: 12-&2 22 R =r +r
ABCD “ABCD 2-34
11241. &2212 R =r +r
ABCD "ABCD 3.56
1122 &2 221 R =r +7
ABCD" ABCD 4 7
1211 &2122 R =r +1
ABCD ABCD 59 10
1 212 &2 12 1 R = ty
ABCD "ABCD 6 1112
8
W Combination
Figure 8. The Multi Image Polygon Matching Process