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.