ACCURACY, RELIABILITY AND STATISTICS IN CLOSE-RANGE PHOTOGRAMMETRY
A. Introduction
Analytical close-range systems for point determination are characterized by typi-
cal features, which differ to some extent from the conditions found in aerial
triangulation. The main problem consists in the great variety of quite different
conditions with respect to image geometry, interior orientation, exterior orien-
tation, intersection conditions, control distributions and systematic errors. In
the past this led to many different solution procedures, often reconciled to the
presumptions of a special project.
While in aerial triangulation the handling of large linear systems mostly compli-
cates the application of highly sophisticated mathematical and statistical tech-
niques this is not true in close-range photogrammetry, where the systems gener-
ally are smaller and thus far more convenient to work with in computer programs.
So the creation and application of general, highly developed methods is regarded
as a basic requirement in close-range photogrammetry, especially if the results
have to be of high accuracy and reliability. Thus rigorous procedures of network
design determination (Grafarend /8/, Sehmitt /20/) and a-posteriori variance es-
timation (Ebner /5/, et.al.) nowadays mainly used in geodesy should find more
attention in photogrammetry.
Even relatively simple a-priori accuracy studies on the applied bundle system are
not very popular, though in some non-transparent situations absolutely necessary.
Moreover the reliability of the systems should be studied with more attention.
Based on Baarda's reliability theory /2/, /3/ this topic is strongly connected
with the problem of model errors and mainly used in connection with gross error
detection. A system may be called "reliable" if gross errors of a certain size
can be detected with a certain statistical security. It is important to notice
that a system or parts of it may be accurate without being reliable at all. It is
one objective of this paper to mark off the terms "accuracy" and "reliability"
with the aid of some simple examples.
A highly developed bundle model must include the self-calibration technique. A
comprehensive compensation of systematic image errors requires a general and
flexible additional parameter set. Thus the concept of bivariate orthogonal poly-
nomials is recommended and a suitable set for a 5 x 5 image point distribution
is presented.
In order to perform a widely objective analysis of bundle adjustment results re-
ference is made to general statistical methods and some test criterions are de-
rived to test hypotheses often appearing in point determination problems.
B. The mathematical model of self-calibrating bundle adjustment and the problem
of systematic errors.
In close-range photogrammetry it is generally noticed that with an increasing
number of different problems the number of mathematical models increases. This
leads to a certain confusion and reduces the compatibility and applicability of
existing computer programs.
So a standardization of models seems to be necessary, which may be based on a gen-
