The International Archives of the Photovrammetrv. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
Table 1: The affine transformation parameters, range and step for
search
Parameter
Range
Step
Translation
dx, dy
—25.0 < dx,dy < 25.0
0.1 meter
Rotation
9
-5.0 <6 < 5.0
0.5 degree
Scaling
s
-0.90 < s < 1.10
0.01
Figure 5: The illustration of tree overlap. A[i\ is the tree crown in
the projected on-ground map. B\j] is the segmented region from
satellite image.
3.3.1 Initial Registration Using the positional information
of the east tower, we performed roughly registration of the satel
lite image to map.
3.3.2 Finding The projected on-ground crown map was over
lapped to the satellite image using affine transformation. In or
der to find the optimum registration, we performed tree-to-tree
matching and calculated fitness value in each overlap. The equa
tion of the affine transformation is defined as:
Figure 6: The projected on-ground map of 102 canopy trees.
Figure 7: 911 regions of tree crown were detected by classifica
tion after segmentation from satellite image.
x _ cos 6 — sin 9 s 0 xo + dx , ^
y ~ sin 6 cos 6 0 s yo dy
where (xo, yo) is the location of the east tower at initial regis
tration. The affine parameters range of search and step size are
shown in Table 1.
3.3.3 Matching For each tree crown in the map, we find out
the same tree among segmented regions from satellite image,
which has the highest corresponding possibility to the tree crown
in the map. Figure 5 shows illustration of tree overlap.
The degree of tree overlap is defined as:
When the fitness value becomes the maximum, we obtain the op
timum parameters of affine transformation for rectifying satellite
image to the map coordinate, and identify tree crowns.
4 RESULTS
4.1 The Projected On-Ground Map
The projected on-ground map created from the measurement data
of 102 canopy trees is shown in Figure 6.
4.2 Image Segmentation
OL\i\\j\ =
A[i\ n B\j]
AW
A[i\ n B[j]
B[j]
(2)
where A[i]{i — 1... N} is the tree crown in the projected on
ground map, and B[j]{j == 1... M} is the segmented region
from satellite image. The region B[ki]{ki = 1... M} of the
highest value is defined as:
OL[i][h] > OL[i\[j] for j = 1... M. (3)
3.3.4 Fitness value The tree-to-tree matching algorithm is per
formed using the fitness value of the location and octagonal shape
of both tree crowns in the satellite image and the projected on
ground map.
The fitness value P at each overlap by affine transformation is
defined as:
N
P(dx,dy,6,s) = jj'^20L[i][k i \. (4)
i= 1
The tree crowns were detected by classification. Figure 7 shows
the 911 regions of tree crown.
4.3 Tree-to-Tree Matching
The affine transformation parameters at optimum image-to-map
rectification is shown in Table 2. The initial registration of tree-
to-tree matching and the histogram of tree overlap are shown in
Figure 8. The optimum registration of tree-to-tree matching and
the histogram of tree overlap are shown in Figure 9. The aver
age of the tree overlap at the optimum registration was increased
from 0.437 to 0.509 compared to the initial registration. The lo
cations of the towers in the projected on-ground map overlapped
with the locations of the towers by visual inspection in satellite
image. Using the method in this study, we obtained equivalent
result with the accuracy of image registration by using ground
control points. By the method in this study, the optimum regis
tration were obtained without ground control points. Figure 10
shows rendering the satellite image on the octagonal shapes of
tree crown. Figure 11 shows perspective projection of canopy 3D
model using OpenGL.