IS
Based on the potential theory, these 14 constraints can be classified into
eight ones of the first group and six ones of the second group. Thus, the
[=]
parameters of Equation 11' may be given as
n-=4, Np = 14, N. - 2, N, = 2, and N, = 4
Then, we can see that the four overlapped pictures have the potential to
provide six independent orientation unknowns. The geometrical properties
of this self calibration problem will be clarified as follows (See Figs.-
8a,8b,8¢c,and 8d).
The first stereo model is formed by means of the coplanarity condition for
the first and second photographs. During this phase, seven orientation
elements (five exterior and two interior) are determined. Further, the
one-to-one correspondence between the first stereo model and the object
has eight independent orientation unknowns (seven exterior and one inter-
ior). The geometrical characteristics of the second stereo model con-
struction with the third and fourth pictures are entirely the same as those
of the first stereo model. Thus, four conventional interior orientation
elements can be obtained from the coplanarity conditions for both stereo
models. Then, the transformation of the second stereo model into the first
one must be described in terms of nine independent orientation elements
(seven exterior and two interior), when these two stereo models include
the same part of the object.
If the same part of the object has not been imaged in common on the first
and fourth photographs, the modified technique for the self calibration
must be employed. Among the interior orientation parameters of the first,
second, and third pictures, we have constraints such that:
Oy = 02 = 4, * 8, g 757570
Xu "Xu m^" a2:
. These nine constraints can be classified into eight ones of the first group
and one constraint of the second group. Thus, the first united model formed
with these three pictures becomes similar to the object, which means that
all the six interior orientation unknowns of the two non-metric cameras
can already be determined in this process. In addition, the second, third,
and fourth photographs have the same geometrical properties. Consequently,
the modified self calibration method with the four overlapped pictures can
be explained as is shown in Figs.-8c and 8d.
6. CONCLUDING DISCUSSIONS
The orientation problem of overlapped photographs has been explored under
different constraints among the interior orientation parameters. The con-
cept of a fictitious three-dimensional picture has been used for relating
such constraints to the coplanarity and model connection conditions. Fur-
ther, it has been clarified that constraints regarding the interior orien-
tation of the system can be classified into two groups:
(a) Constraints of the first group
The number of constraints of the first group is eight in all. These con-
straints do not affect the coplanarity and model connection conditions,
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