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Robust Image Orientation with Balanced Observations in Close-Range Photogrammetry 
Manfred Fellbaum 
Rollei Fototechnic 
Salzdahlumer Straße 196 
38126 Braunschweig 
Phone: 49/53 1/6800 205 
Fax: 49/53 1/6800 243 
KEY WORDS: Orientation, robust, balanced observations 
0. ABSTRACT 
Image triangulation through bundle adjustment is performed in linear models. Therefore, initial values for the unknown parameters 
have to be provided. Their calculation has ever been a most difficult task. The main reason for that is the presence of errors in the 
data. The following paper gives a short overview on robust estimation procedures and describes the new technique of parameter 
estimation with balanced observations. 
1. INTRODUCTION 
In the past years, multi-image triangulation through bundle adjustment has become an increasingly important issue in close range 
photogrammetry. Different efficient orientation programs are available (ref. Fellbaum 1994). Most of them also allow the 
processing of non photogrammetric observations in object space (ref. Wester-Ebbinghaus 1985). The issue of bundle adjustment is 
a problem that has not been focused on in scientific developments lately. 
The determination of initial values for bundle adjustment in close range photogrammetry still represents a difficult and time 
consuming calculation procedure. The extensions introduced in this article shall contribute to simplify and automate the technique 
of determining initial values and is aiming at introducing the method of bundle adjustment to a wider range of users. 
The most important problem in the determination of initial values is the identification of defective information which does not only 
include false measurements and point identifications. It is just as important to identify miscalculated object co-ordinates due to a 
bad ray intersection geometry. The determination of initial values thus represents a highly difficult and demanding step which is 
often more time consuming than the bundle adjustment itself. Only qualified personnel with detailed photogrammetric knowledge 
_ is able to handle the full capacity of the existing systems. 
2. FUNCTIONAL RELATIONS IN THE DETERMINATION OF INITIAL VALUES 
In the following, some basic functional relations for the determination of initial values are briefly outlined. Intersection and 
resection in space work with the functional relation of central projection (equation 1 and 2). 
* 
Xjj -xH - dx - Ay 
Xj -YH -dy T à a 
p" ij Y, 
P. 
Xi. 
* 
Y, - D(oj,9j,kj)| li -Yoj Q) 
Z* Zi — Zoj 
ij 
  
With Xii» Xij being co-ordinates of the image point Pj; in the image co-ordinate system; c being the calibrated focal length; xyy, yr 
being co-ordinates of the principal point in the image co-ordinate system; dx, dy being systematic image errors in the image co- 
: * * * ; : . ; 1i ; ; 
ordinate system; X ij Y ij: Z ij being co-ordinates of the point P; in the auxiliary co-ordinate system parallel to the image co- 
ordinate system; Xoj; Yoj Loi being co-ordinates of the projection centre O; in the object co-ordinate system; D(9,; Xj) being the 
rotation matrix to transfer the object co-ordinate system into a position parallel to the auxiliary co-ordinate system; Xj, Yi, Zi being 
co-ordinates of the point P; in the object co-ordinate system. 
In these equations, the parameters of the interior orientation, the parameters of the exterior orientation and the three co-ordinates of 
the object points are included. The model of central projection is extended by parameters for systematic image errors (e. g. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995