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10.Adjoin the column vectors to /form- the
following matrices:
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Z
7.
The decomposition of the rotational matrix
into the rotational elements can be
performed by investigating corresponding
trigono metric “function ‘values of that
element as presented by Shih (1990).
RESULTS
To test this closed-form space resection
algorithm, a program was written in C, and
was implemented in a close range
photogrammetry application software. Two
image data sets were acquired using a 35 mm
non-metric camera, with focal lengths of
11.000 mm and 51.142 mm. Each set used a
different control field that contained a
number of points. Table 1 and 2 shows the
data for these sets and the results of the
resection solution obtained by using the
proposed newly developed algorithm and that
obtained from the iterative collinearity
solution. Using the new algorithm only
three control points were used. This
resulted in two possible resection
solutions. The collinearity solution was
then obtained by using the algorithm
solution as an initial estimate . The
collinearity solution that result in the
lowest image residuals is adopted as the
final solution.
CONCLUSIONS
The proposed new mathematical model has
been tested and implemented in a newly
developed software for close range
photogrammetry applications. Most of he
users of this software are not formally
trained photogrammetrists, and consequently
a closed-form space resection solution is a
functional software requirement.
The minimum number of object control points
required for the proposed solution are
three. In general this will lead to two
possible solutions. But in this new
approach, the correct solution is achieved
by using the proper focal length sign,
eliminating the more tedious need for
testing and searching for the correct
Spatial position and orientation elements.
Since the proposed approach is based on the
Scale variations of the image distances
between the control points, it can be
modified to work with machine coordinates
instead of photo coordinates. This will
Provide an alternative approach to the use
of DLT for processing non-metric imagery.
393
This approach also can be modified to
process imagery taken with non-conventional
with cameras, such as panoramic cameras and
fish eye lenses.
REFERENCES
Abdel "Aziz, 'Y.T ' and" H.M. Kärara, 1971.
Direct Linear Transformation into Object
Space Coordinates in Close Range
Photogrammetry, Proceedings, Sym. on Close
Range Photogrammetry, pp 1-18.
Dehn, E., 1960, Algebraic Equations, Dover
New York.
Fischler, M.A. ‘and ‘\R.C.: Bolles, 1881,
Random Sample Consensus: A Paradigm for
Fitting with Applications to Image Analysis
and Automated Cartography, Communications
of ACM, Vol. 24, No. 6, pp 381-395,
Rampal, K.K., 1979. A Closed Solution for
Space Resection, Photogrammetric
Engineering & Remote Sensing, PP 1255-1261.
Shih, T.Y., 1990, The Duality and Critical
Condition in the Formulation and
Decomposition of a Rotation Matrix,
Photogrammetric Engineering and Remote
Sensing, Vol. 56, No.8, pp. 1473-1179.
Sobel, I., 1974, On Calibrating computer
controlled cameras for perceiving 3-D
scenes. Artificial Intelligence Journal,
5:184-198.
Zeng, 2. and X. Wang, 1992, A General
Solution of Closed Form Space Resection,
Photogrammetric Engineering and Remote
Sensing, PP 327-338.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996