INTRODUCTION 
One of the major factors limiting the accuracy of high-precision close- 
range photogrammetric systems is the presence of film unflatness (e.g. Brown, 
1980). This problem is particularly pronounced in non-metric, "amateur" 
cameras which invariably incorporate either crude film flattening mechanisms 
or none at all. Three widely-used approaches to the analytical restitution of 
non-metric photographs are the direct linear transformation (DLT) (Abdel-Aziz 
& Karara, 1971), the ll-parameter solution (Bopp & Krauss, 1978), and analy- 
tical self-calibration with either block- or photo-invariant additional para- 
meter (AP) sets (e.g. Haggrén & Väütäinen, 1980; Faig, 1975). These tech- 
niques are designed primarily to account for the amateur camera's unstable 
interior orientation, lens distortion and, in most cases, lack of fiducial 
marks; but not for the problem of film deformation (principally the non- 
coplanarity of image points). 
It has been demonstrated, both theoretically and experimentally, that 
non-metric cameras can yield moderately high accuracy when used in conjunc- 
tion with either one of the above mentioned analytical data reduction 
schemes, or a similar technique (e.g. Karara & Abdel-Aziz, 1974; van Wijk & 
Ziemann, 1976; Adams, 1980; Haggrén & Váütüinen, 1980). This is in spite of 
the fact that the mathematical models of DLT-type methods are incomplete, to 
varying degrees, and in spite of the specific practical shortcomings of each 
of the three analytical approaches mentioned (e.g. Fraser, 1982). The ab- 
sence of a mechanism to flatten the photographic surface in an amateur camera 
necessitates the carrying of a different set of film deformation parameters 
for each exposure in the self-calibration adjustment. Thus, methods employ- 
ing only block-invariant additional parameters (APs) are not fully appropri- 
ate. On the other hand, analytical self-calibration with only photo- 
invariant APs, e.g. interior orientation, lens distortion, affinity and non- 
orthogonality parameters, exhibits two principal drawbacks. Firstly, the 
precision of recovery of the network parameters is typically lessened, along 
with the degrees of freedom in the adjustment. In the extreme, the resulting 
eigenvalue inflation can lead to numerical stability problems. Secondly, 
photo-invariant interior orientation parameters can only be recovered in 
cases where the object target array is well distributed in three dimensions. 
In this paper a further analytical data reduction technique for non- 
metric imagery is examined. This scheme, which has previously been employed 
in conjunction with the multiple focal setting self-calibration of a non- 
metric camera (Fraser, 1981), involves the use ofa self-calibrating bundle 
adjustment with a mixed block- and photo-invariant AP model. Although the 
approach examined does not suffer from the majority of shortcomings alluded 
to above, it is still subject to imperfect model fidelity. In this regard, 
the mathematical model is potentially incomplete, in that photo-invariant 
film deformation AP terms do not completely compensate for the systematic 
errors which arise in the presence of a significant non-coplanarity of image 
points. Shortcomings in AP modelling can aggravate the analytical solution 
process, leading to high internal consistency and design-level precision, 
coupled with significant accuracy degradation. These aspects are discussed 
in the following sections, and a practical experiment is reported. The in- 
fluence of photo-invariant AP sets of different order on the precision and 
accuracy of non-metric image restitution was examined in the experiment. The 
AP model also included a block-invariant set of "stable" calibration para- 
meters, and both minimal and redundant control configurations were employed 
in the photogrammetric network adjustments carried out. 
Prior to continuing with the discussion, it is important to note that 
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