1480 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975
high accuracy. Although it is basically regarded as camera calibration, errors such as af-
finity and non-perpendicularity of axes of the comparator can be included into the
model, which means that in effect a calibration of the system is accomplished.
CALIBRATION
Calibration provides the link between metric and non-metric cameras, considering
that I have defined the latter as being cameras whose interior orientation is completely
or partially unknown and potentially instable!°. Interior orientation, of course, encom-
passes in this context the basic parameters principal point and principal distance (cali-
brated focal length or camera constant) as well as radial (symmetric) lens distortion, de-
centering (frequently considered in form of its components asymmetric and tangential)
lens distortion, film deformation, and affinity. In addition, non-perpendicularity of the
comparator axes is included for the system calibration.
Calibration is commonly carried out in three forms: laboratory, on the job, and self
calibration.
ABsTRACT: In this paper a method of self calibration applicable to
non-metric cameras is presented and discussed in connection with
various other calibration approaches. The method is extremely gen-
eral and includes radial symmetric and decentering lens distortions,
affinity, and non-perpendicularity of axes. Although it provides in-
terior orientation parameters for each photograph separately, the
minimum control requirement remains at two horizontal and three
vertical control points.
RésuMÉ: Cette étude expose une méthode d'auto-étalonnage des
chambres non-métriques. Également l’étude délibère sur d’autres
methodes d’étalonnages. Cette méthode est bien génerale, elle inclus
la distortion symétrique radiale et de décentrement de l’objectif,
l’affinité et la non-perpendicularité des axes. Même si cette méthode
fournit les paramètres de l’orientation intérieure de chaque cliché, la
quantité minimum de levées demeure deux repères horizontaux et
trois verticaux.
ZUSAMMENFASSUNG: Im Zusammenhang mit anderen Kalibrierungs-
methoden wird im vorliegenden Artikel ein Selbstkalibrie-
rungsverfahren für Amateurkameras erläutert. Der Ansatz des
Verfahrens ist äusserst generell und berücksichtigt symmetrisch
und asymmetrisch radiale sowie tangentielle Verzeichnungen, Af-
finität und Nichtortogonalitat der Achsen. Obleich die Parameter
der inneren Orientierung für jede Photographie getrennt be-
rechnet werden, reichen zwei Lage—und drei Höhenpasspunkte
zur Lösung aus.
LABORATORY CALIBRATION
Several types of calibrations appear under this heading, the common fact being that
calibration is completely separated from object photography. Therefore metric cameras
are ideally suited for this approach. Besides goniometers, collimator banks, and similar
arrangements, test areas of various sophistication have been used for laboratory calibra-
tion as described in the literature (e.g., 278.1518.2122), The mathematical formulation is
normally based on the collinearity equations, with each object space control point pro-
viding two equations. As pointed out by Linkwitz!? five control points are required to
solve for the principal point and principal distance with a slight overdetermination
(three interior plus six exterior orientation parameters determined with ten equations).
With the inclusion of additional parameters, the number of object space control points
has to increase accordingly. The mathematical formulations for laboratory calibration are
