International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
A IMAGE
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IMAGE
PLANE 2
Figure 5. Vector projected in ground plane (left). Vector
projected in vertical plane (right).
The trunk tilting angles towards image planes were calculated
from vector components a, b, and c and angles « and p. In
future processing images are rectified to plane parallel to the
tree trunk.
4. ERROR ANALYSIS
During the field measurement, rotation angels ® (x-axis), ¢ (y-
axis) and Kk (z-axis) were determined with simple instruments, a
hypsometer, a compass and a tube level. Influence of rotation
errors to tree crown dimension determination was considered.
4.1 Errorin O
Rotation along x-axis, €, was measured with hypsometer.
Accuracy of hypsometer rotation measurement was estimated to
be + 1°. This estimation was based on instrument ruler index
and field measurement experience. The error influence was
simulated rotating image plane 1? degrees and -1 ? around
image bottom edge and calculating shift of each pixel compared
to the correct image. Pixel movement was two directional.
Figure 6. Error surfaces. Pixel dx shift for +1° w error (up left).
Pixel dy shift for -1? c error (up right). Pixel dx shift for -1° ®
error (bottom left). Pixel dy shift for -1? « error (bottom right).
The plane rotation away from the camera inflicted expanding of
the image plane. Tendency of error behaviour is expressed in
Figure 6. Respectively the plane rotation towards the camera
inflicted shrinking of image plane. Maximum errors were
calculated from surface values:
Dxz2. Imax(dx) (8)
Dy= |min(dy) + |max(dy)
The maximum errors are illustrated in table 1. In order to
compare values for other data sources errors were transformed
from pixels to metric values. Scale was expressed as ratio
distance between project centre and rectification plane (f+dc)
and distance between projection centre and target D:
iter bre (9)
(f * dc)
During the field measurement image capture distance was
typically 25 meter, but all images were taken from less than 30
meters. Maximum errors in meters for 30 m distance are
calculated in Table 1.
4.0 Errorin K
Rotation around z-axis (K) was adjusted to zero with tube level.
Maximum error in rotation measurement was estimated to be +
2?. Maximum error in dimension measurement was carried out
if distance was measured from edge to edge. For image size
3945x2928 errors are:
3945 — 3945 / cos(2)
2928 — 2928 / cos(2)
24
zLs
ü
N
Maximum errors in metric values for 30 m distance are
calculated in Table 1.
Error, m,
Rotation Error Error, for
Angle type pixels distance
30 m
Q1? Dx 62 0.48
Q1? Dy 48 0.38
œ=-1° Dx -62 -0.50
w=-1° is Dy 46 -0.37
K=2° Dx -2.4 -0.002
K=2° Dy -1.8 0.014
K=-2° Dx -2.4 -0.002
K=-2° Dy -1.8 0.014
Table 1. Maximum errors
4.3 Errorin¢
Image capture direction (¢) was straight towards the tree trunk.
After image capture ¢ was measured with compass. Error in ¢
measurement does not affect inner accuracy of image
measurement. Objects, which are in rectification plane,
perpendicular towards the imaging direction, are geometrically
correct. Error has influence when measurements are compared
to other data sources. Eranto, (declination between compass
north and Finnish local co-ordinate system vertical axis) is 6° in
Southern Finland. To improve measurement accuracy compass
measurement were carried out by two persons and value was
calculated as average of observations.
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