ant matching on the basis of curved lines has been carried 
out by Schenk et al. (1991) using the y-s representation 
of zero crossings (see also Ballard, Brown 1982 for an 
explanation of the y-s domain). 
An elegant rotation and scale invariant solution which 
can also determine the overlap between the images is 
relational matching (Shapiro, Haralick 1987; Vosselman 
1992). It should be noted, however, that relational mat- 
ching is still a subject of intensive research, and it is 
difficult and time consuming to define, extract, and match 
structures suitable for imagery with different image con- 
tent. Therefore, from a practical point of view rotation 
and scale differences should be eliminated or at least 
measured during the image acquisition phase, and image 
overlap should be determined prior to matching. For 
instance, in aerial triangulation standard overlap values 
are available, and rotation and scale differences usually 
do not exist or are at least approximately known. The 
same holds true for satellite imagery. Also in close range 
applications rotation differences around the optical axis 
are not common. An image scale varying within the im- 
ages, however, is a common issue in close range applica- 
tions, and complicates automatic relative orientation of 
these images considerably. 
Once approximate values for overlap, rotation, and scale 
differences have been determined, the orientation para- 
meters can be refined in a coarse-to-fine approach. It is 
argued here that feature based matching with point pri- 
mitives should be used for this task, because points are 
geometrically more stable than lines and areas. For in- 
stance, a relative orientation based on straight lines is 
only possible with a minimum of three images (see e.g. 
Strunz 1993) and has to deal with a number of singular 
cases. A disadvantage of points is that they are less 
distinct, and usually can’t be interpreted in a semantic 
way. However, the distinction of points can be increased 
by defining them as intersections between lines, and sem- 
antic interpretation of the features to be matched is not 
needed in relative orientation. For point extraction - to 
be carried out in each image separately - a number of 
so-called interest operators exists in the literature (e.g. 
Moravec 1977; Hannah 1980; Forstner 1986; Deriche, 
Giraudon 1993). 
In the next step conjugate points are to be found. At this 
stage approximate orientation parameters are already 
known. Therefore, the collinearity equations can be used 
304 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
  
Figure 4: Illustration of the epipolar constraint: The con- 
jugate points P' and P’’ lie on the epipolar lines ¢’ and e”’. 
e’ and e’’ are the intersections of the epipolar plane and 
the 2 image planes. The epipolar plane is defined by the 
point P and the base b between the 2 projection centres. 
for mapping points from one image to the next, leading 
to the epipolar constraint (see figure 4). This geometric 
constraint reduces the search space from two dimensions 
to one, and thus increases the speed and reliability of the 
algorithm. Besides, a radiometric check should be incor- 
porated. Assuming the model surface to be locally a 
horizontal plane, the correlation coefficient can be con- 
sidered an appropriate measure, because scale and rota- 
tion difference have already been taken care of. Points 
are then considered to be candidates for conjugate 
points, if they fulfil at least approximately the epipolar 
constraint, and the corresponding cross correlation coef- 
ficient is above a predefined threshold. Note, however, 
that the epipolar constraint is valid for central perspecti- 
ve imagery only. 
For the actual parameter computation an iterative stand- 
ard or a robust least squares bundle approach can be 
used. An interesting alternative is the so-called "8-point- 
algorithm" in which relative orientation is formulated as 
a linear problem of eight independent parameters. Solu- 
tions of this kind have long been known to exist (Rinner 
1963; see also discussion in Brandstätter 1992). The 8- 
point-algorithm as it is used today was suggested by 
Longuet-Higgins (1981) and has since been investigated 
a number of times in computer vision (e.g. Tsai, Huang 
1984; Huang, Faugeras 1989; Weng et al. 1989; Hartley 
1995). Some applications can also be found in photo- 
grammetry (Brandstätter 1992; Müller, Hahn 1992; 
Wang 1994). There are two advantages of a linear algo- 
   
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