The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
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the equation (5), the linearized form of equation (5) is given in
Eq.7.
Bx + Av+w- 0 (7)
where B is partial matrix with respect to unknowns, namely the
calibration parameters; A is partial matrix with respect to observations;
X is vector of unknowns; V is the vector of residuals; W is the
misclosure vector, i.e. the equation (5) evaluated at current estimate of
the parameters and observations
The solution of equation (7) is adopted by the traditional
approach of least-squares adjustment. Namely, the sum of
weighted squares of the residuals reaches minimization.
Following standard procedures, the resulting final form of the
normal equations used herein is:
x = (B T (AC„A T y l By 1 B T (AC vv A T y l w (8)
with:
i2 (Av) T (AC m A T y'(Av)
a o =
(9)
n-m
D ii =âfB T (AC m A T )- , By'
(10)
where o\ the variance component; C vv the covariance matrix
of observation; n the number of target laser points; m the
number of unknowns.
3.3 Surface Extraction
For the strip adjustment, surfaces are the natural candidates to
be used. The selecting areas are suitable for the adjustment and
improve the estimation of the parameters. For the effect of
noise on the surface parameters, artifacts are introduced into
the observation. The surface model is, therefore, used in the
form a surface constraint in equation (3). Interesting surfaces
and regions can be determined by a least-squares plane fit
through a subset of laser points. The extraction procedure that
is used herein is based on minimizing the weighted quadratic
sum of the distances of the laser points to the plane (Lee,
Schenk 2001).
The standard deviation of unit weight <jq can, therefore, be
interpreted as the standard deviation cr D of the shortest distance
of a point to the plane. The plane is accepted if ct 0 is smaller
than, or equals, a threshold. Experience shows that most of
significant surface have a std. small than 15 cm. The threshold
is the average standard deviation of the distances to the plane
computed by error propagation from the standard deviations of
the laser point positions tested for the plane fit. For a horizontal
plane it is just a function of the z-components, and thus
influenced only by the accuracy in z. The steeper the slope of
the plane, however, the greater will be the effect of the x and y
planimetric components. If a plane is accepted, the neighboring
points are tested statistically for the fit to the plane. If the fitting
error remains smaller than the given threshold, the points are
used to update the plane parameters using sequential
least-squares. Figure 6 to 7 show examples for extracting
surface.
In Fig.6, red points represent the each planes of the building. In
Fig.7, the central region is extracted as well as, but don’t split
up the bottom plane.
Figure 6. Points of extracted slope surface for a building
Figure 7. Points of one flattop plane
4. LABORATORY EXPERIMENT AND DISCUSSION
4.1 Laboratory experiment
Range biases and scan angle biases as mentioned in section 2
result to non-linear effect to the laser points position. The
precision of range and scan angle for single laser point is
analysed by laboratory experiment will help in reducing the
effect and improving the performance of the ALS. The proposal
method here repeats range measurement aiming to the same
target through fixing the scan mirror. Rate of the laser
instrument and scan mirror respectively are 35 kHz and 25 Hz.
We select nine targets to test. 1355 point samples extracted
from whole laser point sets are analysed statistically for each
target. The specific details about the result of range are listed in
Table 1 with R max maximum range value, R m i„ minimum
range value, R mean mean range value, and STDr standard
deviations of range. Range resolved measurement precision is
the standard deviation in the measured range data about the
mean measured value.The corresponding shape of range
