OUTLIER DETECTION IN RELATIVE ORIENTATION - 
REMOVING OR ADDING OBSERVATIONS 
Peter Axelsson 
Department of Geodesy and Photogrammetry, Royal Institute of Technology 
100 44 Stockholm, Sweden 
e-mail pax Q geomatics.kth.se 
KEY WORDS: Image Orientation, Robust Estimation, Error Identification, Reliability 
ABSTRACT: 
Outlier detection in relative orientation has been studied using three different strategies, (7), removing bad 
observations, outliers, using data snooping, (ii), adding good observations using Least Median of Squares estimates 
and (iii) finding an optimum between good and bad observations in a cost function using minimum description 
length criteria, MDL. To be able to compare the strategies, relative orientation algorithms based on linear or closed 
formulae were used. Two algorithms for calculating relative orientation without any provisional values were applied. 
For a LS solution a linear solution based on eight unknowns was used. For a direct solution with minimal point 
configurations the same algorithm was used but estimated without any redundancy, i.e., with eight observations. In 
addition to this, two other algorithms were applied to some of the data in order to get the results verified and 
compared. In total, four algorithms tested on a large number of simulated data configurations. The results show that 
large fractions of outliers can be detected for the strategies (ii) and (iii) even with arbitrary image orientations, while 
strategy (i) shows very good stability for normal aerial geometry with few outliers. 
1. INTRODUCTION 
Procedures that do not need provisional values for the 
calculation of relative orientation parameters of a stereo 
pair of images are of great need in general applications 
where approximate locations and attitudes of the cameras 
are unknown. When automating point selection and point 
identification, these procedures must also be more robust 
against large fractions of outliers than in the case of 
manual measurements. 
The traditional way of handling outliers in 
photogrammetry is by investigating diagonal elements in 
the least squares, LS, estimate of the covariance matrix of 
the observations and their residuals. The observations are 
then kept or removed depending on some statistical test, 
e.g., data snooping [Baarda,1967]. In such a procedure, 
all observations are part of the initial LS estimate and 
outliers are removed one at a time. A different strategy is 
to start with a minimum configuration of observations, 
adding points as long as they fulfil some criterion. The 
solution of the minimum point configuration is often 
repeated with different random sets of points and the 
"best" solution chosen, e.g., least median squares, LMedS 
[Rousseeuw,1987] or RANSAC [Fichler and Bolles, 
1981]. Both strategies regard outliers as observations not 
belonging to the model, ie. not having the same 
statistical properties as good observations. A third 
strategy is to extend the mathematical model to include 
also outliers and by a cost function locate a minimum 
where the optimal number of outliers is found, Such a 
cost function has been formulated within the minimum 
description length, MDL, principle [Rissanen, 1983] and 
used as an estimator with robust properties [Axelsson, 
1992]. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
2. AIMOF THE INVESTIGATION 
A comparison of the three strategies was made regarding 
the robustness against outliers when calculating the 
relative orientation of a stereo pair of images. The three 
strategies are: 
i Removing bad observations, outliers, using LS 
estimates and data snooping 
ii Adding good observations using LMedS 
iii Finding an optimum between good and bad 
observations in a cost function using MDL 
To be able to compare the strategies, only relative 
orientation algorithms based on linear or closed formulae 
were considered. For the LS solution a linear solution 
based on eight unknowns were used [Tsai and Huang, 
1984], [Philip, 1989]. For the direct solution with 
minimal point configurations the same algorithm as for 
the LS solution was used, but estimated without any 
redundancy, i.e., with eight observations. 
In addition to this, two other algorithms were applied to 
some of the data in order to get the results verified and 
compared. In total, four algorithms were used in the 
investigation: 
1. Linear overdetermined LS estimate [Philip, 1991] 
Linear LS estimate with minimal point 
configuration. 
3. Closed six-point formula [Hoffman-Wellenhof, 
1979]. 
4. Iterative LS solution with five unknowns 
    
  
  
   
   
   
   
   
  
  
  
  
  
  
  
  
  
   
  
  
   
  
  
  
  
  
  
   
  
  
  
     
  
   
   
   
  
   
  
  
  
  
   
  
  
  
  
    
   
   
  
   
   
   
    
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