(1987), Chen, Huang (1990) and Zhang, Faugeras 
(1991). The use of surface data (digital terrain 
models) as control information in block triangulation 
and absolute orientation was treated by Ebner, Strunz 
(1988) and Rosenholm, Torlegärd (1988). 
In this paper a systematic overview concerning the use 
of points, lines and surfaces for photogrammetric 
orientation and object reconstruction tasks is given. It 
is shown, which tasks can be performed, and the 
respective minimum number of features needed for a 
solution is derived. Some remarks on degenerate 
configurations are given and the evaluation of 
precision using general geometric features is shown by 
means of simulated examples. 
2. MINIMUM CONFIGURATIONS 
In the following first some basic considerations 
concerning the use of points, lines and surfaces for 
photogrammetric orientation and object reconstruc- 
tion tasks are given, and then the minimum number 
of general geometric features needed for the solution 
is derived. It is assumed that the extraction of features 
and the precise determination of their locations in 
image space has already been accomplished and that 
the correspondences between these features are estab- 
lished, which in general are non-trivial problems. 
Furthermore, it is supposed that for the orientation 
tasks approximate values of the unknown parameters 
are available, so that linear models can be derived 
from the nonlinear models and the problem is solved 
iteratively. Linear algorithms as such are not 
discussed. 
The general method for image orientation and object 
reconstruction is based on a bundle block adjustment, 
where the orientation parameters of multiple images 
and the coordinates of the object points are estimated 
simultaneously. Basic orientation tasks, which are 
implicitly comprised in multiple image orientation, 
can be classified into space resection (2D-3D), relative 
orientation (2D-2D), and absolute orientation (3D- 
3D). The mathematical model used in 2D-3D and 2D- 
2D orientation is based on perspective projection, 
which can be formulated by the collinearity equations, 
the underlying model of 3D-3D orientation is a spatial 
similarity transformation. 
Lines in 2D image space can be described in several 
forms, e.g. parametric or implicit. If we assume a line 
to be represented by the image coordinates of a 
specific number of points, which uniquely define the 
line, then the collinearity equations can be used for 
points as well as for lines. In this paper only two types 
of algebraic lines are considered: straight lines and 
circular lines in object space, which in general 
correspond to straight lines or ellipses in image space. 
Basically the image lines can result from the 
114 
perspective projection of 3D lines or from occluding 
contours of 3D surfaces, the 3D positions of which 
depend on the exterior orientation of the images. 
However, these contours can not be used for 2D-2D 
correspondence. According to the specific orientation 
task the lines and surfaces can serve as "tie" features 
or as control features. This means that the spatial 
position and orientation of a particular feature is 
either unknown and has to be determined in the 
course of the orientation process or is given as control 
information in object space. 
In the following for the basic orientation tasks the 
minimum number of corresponding features is 
derived, which is necessary to yield a solution. 
Degenerate configurations are not considered. An 
overview is given in Tab. 1 - 3, where n is the number 
of observation or condition equations and u is the 
number of unknowns. 
2.1 Space resection (2D-3D) 
Space resection involves the determination of the 
exterior orientation of a single image, and is described 
by 6 parameters. 
Points in image space: 
A point is defined by 2 coordinates in image space, 
which are given as observations, and 3 coordinates 
in object space, which are unknowns. 
- Point to point correspondence: 
If the corresponding feature in object space is a 
given point, its 3 object coordinates are known. 
Therefore, 3 image points and their corresponding 
object points are necessary to determine the 
exterior orientation parameters. The solution is 
based on fitting the bundle of rays to the corre- 
sponding object points. 
- Point to line correspondence: 
If the corresponding feature in object space is a 
given line, 2 conditions are imposed on the 3 
unknown object coordinates. Consequently, 6 
points in image space and their corresponding 
lines in object space are needed. The solution is 
based on fitting the bundle of rays to the corre- 
sponding line features in object space. 
Lines in image space: 
A straight line is uniquely defined by 2 parameters 
(observations) in image space and 4 parameters 
(unknowns) in object space. An ellipse is defined 
by 5 parameters (observations) in image space and 
in case the corresponding feature is a circle in 
object space it is described by 6 (unknown) 
parameters. 
- Line to line correspondence: 
Straight line: If the straight line is given in object 
space, its 4 line parameters are known. Therefore, 
3 straight lines in image space and the correspon- 
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