PROMPT - A NEW BUNDLE ADJUSTMENT PROGRAM USING
COMBINED PARAMETER ESTIMATION
Manfred Fellbaum
Rollei Fototechnic GmbH
Salzdahlumer Straße 196
38126 Braunschweig
Germany
Commission III
KEY WORDS: Bundle Adjustment, Orientation, Adjustment, Analysis of Data
ABSTRACT:
In the past years, multi image triangulation through bundle adjustment has become an increasingly important issue in close
range photogrammetry. The new Rollei Fototechnic software PROMPT (PRofessional Orientation applying Modern
Parameter adjustment and analysis Tools) takes advantage of the WINDOWS environment. It has been designed to operate
large amounts of data and to ensure most efficient and reliable results by introducing semi automatic analysis and adjust-
ment tools.
1. INTRODUCTION
The functional relation used in bundle adjustment pro-
grams is the central projection [WESTER-
EBBINGHAUS 1985] where the parameters of the
interior orientation, the parameters of the exterior orien-
tation and the three co-ordinates of the object points are
included (ref. equations 1, 2 and figure 1a, 1b).
[ +]
X ln dne d
E HX
* =
LA LA
With Xij Yij being co-ordinates of the image point P; in
the image co-ordinate system; c being the calibrated focal
length; xz, yp being co-ordinates of the principal point
in the image co-ordinate system; dx, dy being systematic
image errors in the image co-ordinate system; x à vi
7 being co-ordinates of the point P; in the auxiliary co-
ordinate system parallel to the image co-ordinate system;
Xoj Y oj; Zoj being co-ordinates of the projection center
O; in the object co-ordinate system; D(o jojkp being the
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
rotation matrix to transfer the object co-ordinate system
into a position parallel to the auxiliary co-ordinate sys-
tem; X, Y;, Z; being co-ordinates of the point P; in the
object co-ordinate system.
The geometric model of central projection is extended by
parameters for systematic image errors (e.g. distortion
parameters) for applications which require high accuracy.
Besides photogrammetric image co-ordinate measure-
ments the introduction of additional (geodetic) observa-
tions is possible as well.
Figure. 1a: Geometry of the central projection
Image
P )
Figure. 1b
2. ADJU!
Within ph
there are «
serve. Bes
of redund:
the adjus
multiple
equations
nation of t
most impc
Within th
the metho
of the par:
Let there
norm of tl
can be m
absolute \
method c
so-called
Tschebys
LAVE is :
following
method c
normal di
errors foll
