A 
  
  
INFLUENCE OF LARGE TARGETS ON THE RESULTS OF PHOTOGRAMMETRIC BUNDLE ADJUSTMENT 
Jürgen Dold 
Leica AG, Photogrammetry and Metrology, CH-5035 Unterentfelden, Switzerland 
Tel. +41 62 737 6789, Fax +41 62 737 6834, e-mail: DOJ@PMU.LEICA.CH 
Commission V, Working Group 2 
KEY WORDS: Target, Image Error, Industrial Photogrammetry, Bundle adjustment 
1 Abstract 
To estimate a suitable diameter of a circular target for high precision photogrammetric measurements some requirements have to be 
considered. For precise photogrammetric measurements the diameter of circular targets have to be between a minimal and maximal 
size. Tools for estimating minimal and maximal target sizes will be given and a simulation shows how the bundle adjustment will be 
influenced by using targets that are too large 
2 Introduction 
Most photogrammetric industrial measurement systems use 
circular targets to define the center of points of interest. 
For precise image measurements it is required that the targets 
have a minimum diameter. It is well known that the diameter 
of the target in the digital image should cover at least 3 pixe/ 
(picture elements) to achieve image coordinates with subpixel 
accuracy. 
On the other hand it is mentioned in the literature /Zhou 1986, 
Lenz 1988, Riechmann 1992/ that oversized targets can cause 
measurement errors. The reason for this measurement error is 
briefly explained; Due to the projection of a circular target the 
image of the target will appear as an ellipse if the surface of the 
target (target plane) is not parallel to the image plane. The 
image of the center of a circular target (true target center) is not 
necessarily identical to the center of the ellipse in the image 
(measured target center). The deviation between the true and 
measured target center (offset) can be larger than the 
measurement accuracy of  photogrammetric industrial 
measuring systems if the used target is oversized . 
In general, measurement errors can be detected by the 
photogrammetric bundle adjustment but if they are very 
systematic it is possible that the parameters of a 
photogrammetric bundle adjustment compensate for their 
influence. Until now, publications mention that this 
measurement error exists and that this error is smeared over the 
results of the triangulation but a quantification of which 
parameters in the bundle triangulation are mainly influenced 
was not given. 
This paper presents the results of a simulation in which the 
influence of large target sizes on the results of the 
photogrammetric bundle adjustment were investigated. It will 
be shown which parameters are mainly influenced by this error 
and how large the influence can be and also how to estimate 
suitable target sizes. 
3 Minimal target diameter 
It is known that the image of targets in the measurement 
picture should have a diameter of at least 3 pixel to achieve 
subpixel image measurement accuracy. But for practical use it 
is preferred to have a diameter of about 5 pixels or more. To 
estimate the minimal target diameter in object space the 
following parameters should be known: the focal distance (c), 
the distance between camera and target (h = recording 
distance) and the pixel size of the camera (ps), see also (Fig. 
1). Using this information and taking in account that the target 
should have at least a diameter in the image of pn = 5 pixel (pn 
= number of pixel), equation (1) leads to suitable target sizes 
which are shown in (Fig. 2). 
d-(h/c)=(pn- ps)-(h/c)= D (1) 
(5 . ps). (h / c)< Pan 
object space 
image plane 
D = Target diameter 
d = Target in object space 
diameter in 
image plane 
  
Figure 1: Relation between target diameter in image plane and 
object space 
  
  
  
  
  
    
  
  
  
8 
mot 60 
o i 
ET 
5 E 40 | 5 mm lens 
5 = 
ED 201 
© à : 25mmlens 
A 0 5000 10000 15000 20000 
Recording distance (mm) 
  
  
  
Figure 2: Target size for different lenses assuming that the 
diameter of the target in the image is at least 0.045 
mm which is equal to pn = 5 pixel and ps = 0.009 
mm. 
4 Maximal target diameter 
After estimating the minimal target diameters the estimation of 
maximal target diameters is necessary. As mentioned above 
and illustrated in (Fig. 3) the image of the center of a circular 
target (true target center) is not necessarily identical to the 
center of the eliptical target image (measured target center). 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996