International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
algorithms and imaging system of photogrammetry (Ho, 1995;
Schenkel and Teller, 1998).
Although the system of MIT City Scanning Project is used in a
specific application, the concept of “hemisphere” used in their
algorithm can be regarded as an attempt to have the images be
transformed into a better geometric form that can be easily
handied. This idea is pretty much the same as to calibrate and
rectify the images of photographs. This is a good approach, but
the algorithm is designed to handle images of the geometric
limited its further
shape of hemisphere, and this has
applications.
There are several approaches toward a more generalized
photogrammetry , and they can usually be regarded as multiple-
camera photogrammetry (El-Hakim et al., 1998; Mostafa et al.,
2001; Zhang et al., 2000).
another
In this paper, the author presents
approach through the development of general
photogrammetric algorithms, and the objective is to have the
system to accept different input data sources in a single
This
photographs are taken by different cameras with totally
photogrammetric process. means that even the
different interior orientations, the algorithm will still be working
normally. The design principles ofthe algorithms are:
l. Independent of specific input data sources
2. Relevant to geometry
3. Built-in with three-dimensional architecture
4. No default automation will be executed or ignored if
ambiguous conditions are encountered
Here below shows the detailed geometries and descriptions of
the algorithms.
2.1 Geometry of space resection
The design of one of the two geometric algorithms is used to
solve space resection problem: suppose that we have three
points gy, gj. g; of known geographic coordinates (Fig. 1), their
corresponding image points pe, pr, p? in a photograph, and the
focal lengthare known values. How to re-construct the position
and orientation of the camera at the time that it took the
photograph, in terms of a positional vector of the coordinate
system of the three ground points?
With the problem stated above, and according to the geometry
shown in Fig. 1, the following notations are defined:
fo Focal length of photograph 0
Cy Focus of photograph 0
09 FC of photograph 0
po. Pi. P Image points of go, gi, g
80.81.,3 Control points (with known coordinates )
g, A randomly selected point of reference
qi. q Line qq; is a parallel with p;-p,
r, nn Nearest points of go on lines eq-p; and c-p;
$1, $ Two proposed values of gy, g,
Figure 1: The geometry of proposed space resection method.
It should be noted that g, is not necessary gy, and in
most cases, g, is not gg. It was drawn as the same
point to show the geometry more clear.
A pinhole perspective projection model is assumed in this
algorithm, and re-constructing the position and orientation of the
photograph 0 is stated in the following:
By providing a value of d, the algorithm calculates its
corresponding two values of e, as shown in the lie-flat lower left
drawing, and derives their c values by the geometry of triangle
" (g-S,-$5" or the distance between s, and s,. The orientation of
photograph 0 is derived when mz::c is of the same proportion
with x:yzz. Spatial coordinates of gy, gi, g», their corresponding
image points py, pi. p», the interior orientation of photograph 0,
and g3 are known values, where g3 is used to select which of the
two candidates is the right one.
It should be noted that the position and orientation, combined
represented as a positional vector, will, in most cases, have two
possible candidates since the procedure is generalized based on
geometry.
And additional information, ie. gs, is needed to
determine which the actual one is.
The ratio of the three sides of triangle po-p;-p» is proportional to
its counterpart of triangle go-q;-q». therefore these two triangles
are parallel in 3D space. The lower left drawing of Fig. 1 is a lie-
flat version of part of the geometry. It shows the basic idea we
used to find two possible candidate geometries of m:n:.
2.2 Relative orientation
It is sufficient if we take every photograph ideally with enough
control points when we do photogrammetry only by space
resection. [n practice, however, most of the photographs do not
even have a single control point, and this is why we have to
develop another algorithm, with similar geometry of Fig. I, to
determine how adjacent photographs are related.
