SINGLE STATION SELF-CALIBRATION TECHNIQUES
John G. FRYER
Department of Civil Engineering and Surveying
University of Newcastle
CALLAGHAN, NSW, AUSTRALIA 2308
Commission V, Working Group 2
KEY WORDS Camera, Calibration, Distortions, Close Range
Abstract
Two of the leading photogrammetrists in the field of close range photogrammetry for the past two decades, Wilfried
Wester-Ebbinghaus and Duane Brown, passed away in the period 1993-1994. Both these men had a strong influence on
the camera calibration techniques which are now in common usage for close range photogrammetry, namely the plumb-
line technique and the method of multi-station self calibration. It is not so well-known that both also proposed single
station self-calibration techniques and as a tribute to their inventiveness, this paper describes and compares their
techniques. The method attributed to Wester-Ebbinghaus was published in 1982, but that proposed by Brown was only
disclosed to this author in private conversations during 1985 and, to my knowledge, has never been published.
The paper describes each technique and compares the advantages and disadvantages of their respective application.
Numerical results for each single station self-calibration procedure are presented and compared to the results obtained
when a more conventional multi-station procedure is implemented for the same digital camera.
INTRODUCTION
Wilfried Wester-Ebbinghaus was the Professor of
Photogrammetry at Braunschweig University at the time
of his unfortunate death by drowning in 1993. He was
only 46 years old yet had an enviable reputation in the
field of close range photogrammetry for his work on the
theory of camera calibration, the exploitation of small
format photogrammetry, architectural photogrammetry
and the development of digital scanning reseau cameras.
In 1982 he had published at the Commission V
Symposium in York, England, a paper on single station
self-calibration (Wester-Ebbinghaus, 1982, 533-550) and
a summary is produced in the next section.
Duane Brown was clearly one of the most outstanding
photogrammetrists of the latter half of the twentieth
century. Many of the techniques which are regarded as
commonplace today were the result of his fertile
imagination. Perhaps no other photogrammetrist has
been so successful in transferring from the government to
the private sector and establishing a niche in the field of
close range photogrammetry. The work carried out by the
companies he spawned, DBA Systems (Duane Brown and
Associates) and then GSI (Geodetic Services
Incorporated), spread across the entire range of precise
measurement procedures in highly technical fields. The
aerospace, ship-building, car manufacturing and related
industries use systems he developed. Defence contractors
are also large users of techniques he pioneered, yet by the
very nature of these industries, many of the exciting
developments and projects he worked on will never be
publicly acknowledged.
Many of Brown's earlier theoretical works are to be found
in U.S. Air Force Technical Reports (for example,
Brown, 1956, 1959 and 1964). As early as 1956 he had
178
published a paper entitled "The Simultaneous
Determination of the Orientation and Lens Distortion of a
Photogrammetric Camera" and by 1960 had laid the
foundations for the modern bundle adjustment method (see
Brown, 1976,1). Brown is well-remembered for his
plumb-line technique (Brown, 1971) and it was the good
fortune of this author, while working with him during a
six-month sabbatical at GSI in Florida in 1985, that
Brown discussed his ideas for a single station self-
calibration method. To my knowledge, his concepts had
not been previously published nor were published
subsequently as Brown worked on various other projects
such as Autoset and his range of close range cameras (see,
for example, Fryer and Brown, 1986).
SINGLE STATION CAMERA SELF-
CALIBRATION
The ‘traditional’ method of camera self-calibration usually
involves the bundle adjustment of a series of convergent
photographs of target array taken from four to eight well-
spaced camera stations with a range of camera orientations
and roll angles. The single station techniques proposed
by Wester-Ebbinghaus (1982) and by Brown (1985)
require all images of the target array to be taken from a
single point of exposure.
In the case of Wester-Ebbinghaus, the camera is tilted
alternatively about + and — X and Y axes by
approximately 30° to 45° after an initial image is obtained
from a central viewpoint. Rotation of the camera around
its optical axis after the first exposure aids the
determination of the offsets of the principal point. The
reliability of the solution for the camera and lens
parameters is improved by using relatively large numbers
of targets. In Wester-Ebbinghaus' paper (1982, 544) he
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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