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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
7
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Figure 2. Imaging geometry and rectification plane. The side
view (left) and top view (right).
Based on the relative orientation between the image plane and
the rectification plane and camera widening angles, locations of
the image corner co-ordinates were calculated on the rectified
image plane. These co-ordinates and traditional least minimum
square adjustment were utilized to determine eight parameters
of projective transformation from image plane to plane (Mikhail
et al, 2001):
mi at ER (1)
ex+fy+1 ext ue
Co
e (2)
A - 0 Aixe0cki0l^l rx
Y 3n. —rvuh 0 — 0 —] P» iy
A
us f
Sı
82 |
where X, y = image coordinates,
X, Y = co-ordinates in rectification plane and
€9,€,,€5, fy fi J25 8182 7
unknown parameters.
After rectification process objects were geometrically correct in
rectification plane. As the relative orientation of image plane
and rectification plane were constant for all images, same
transformation parameters were utilized for all image
rectifications.
Figure 3. Original image (left). distortion free image (middle)
and rectified image (right).
3.3 The tree crown dimension measurements
The parameters for individual trees, such as tree height and
crown height, were extracted from the images. Reference scale
bar height and crown width to left and right from trunk in 0.5 m
elevation intervals were also extracted. The origin for height
measurements was tree base. The pixel units were transformed
to metric units based on the known distance in the image,
reference scale bar, for enabling comparison to other data
sources.
Figure 4. The tree height and crown widths were measured from
first and second image.
3.4 The determination of trunk tilting
In remote sensing aided forest inventory tree trunks are typically
assumed to be straight. In this study, trunk tilting was estimated.
The tree top shift dx, that is deviation from vertical line initiated
from the tree base, in horizontal direction was determined in
both images. The trunk was represented as a vector (Figure 5).
Vealtbtck (3)
where 7 i and k are unit vectors in direction of co-ordinate
system axes, a and b are unknown parameters and c is vertical
component of trunk vector. A vertical trunk vector is simplified
Pack (4)
where c is the height of the tree. Unknown parameters a and 5
were solved from equation pair:
a=aa+ab
; (5)
b = bb— ba
where a and bb are projections of shifts dx/ and dx2 to co-
ordinate system axis:
Ix dxl
meta bbs ee (6)
cos( B — / 2) cos(@X)
ab and ba are calculated from angles between image planes and
parameters a and 5 (Figure 5):
ab - b-tan(B —z/2) (7)
ba = a -tan(a)