Hrabacek, Jan 
  
WEIGHTED GEOMETRIC OBJECT CONSTRAINTS INTEGRATED IN A 
LINE-PHOTOGRAMMETRIC BUNDLE ADJUSTMENT 
Jan Hrabácek!, Frank A. van den Heuvel? 
! Czech Technical University of Prague, Faculty of Civil Engineering 
Hrabacek@Panurgos.fsv.cvut.cz 
?Delft University of Technology, Faculty of Civil Engineering and Geosciences 
F.A.vandenHeuvel@ geo.tudelft.nl 
KEY WORDS: line photogrammetry, object reconstruction, geometric constraints, weighting, mathematical model, ad- 
justment, accuracy, architecture 
ABSTRACT 
The line-photogrammetric bundle adjustment is a new approach for the 3D reconstruction of polyhedral objects, with sev- 
eral advantages. Observing lines instead of points and integration of additional object information are two of them. Line 
features of an object are often well visible and better recognizable than corner points. Therefore, image lines belonging 
to object features are the main type of observations of the line-photogrammetric bundle adjustment. Furthermore, the 
use of line features makes the reconstruction of occluded object points possible. Due to the coplanarity constraint the 
mathematical model chosen here results in a valid polyhedral description of the object. Polyhedrality and shape regularity 
of an object can be expresed as relations between point, line and plane entities, i.e. as geometric object constraints. 
In the paper, the approach for integration of weighted constraints into the line-photogrammetric model is presented. Ex- 
periments were conducted using the CIPA test data set. The results confirm the need to implement the constraints as 
weighted pseudo-observations. The paper reports on investigations regarding weighting of constraints. The approach 
allows reconstruction of a model on the condition that exterior oriantation parameters are approximately known. Object 
constraints are also applied to support intitial value computation. The major benefit of the approach is that it allows an 
accurate object reconstruction using only a few images. In some cases the reconstruction is not possible without the 
geometric constraints. The least squares adjustment allows a rigorous testing of the weighted constraints. Examples 
demonstrate the potential of constraint-based processing and the quality improvement of the reconstructed object model. 
1 INTRODUCTION 
Architecture has always been a field where the capabilities of photogrammetric methods are exploited. The line-photo- 
grametric approach discussed in this paper is a relatively new method still under investigation. The method is used for 
the reconstruction of objects, which have linear or curved features, or can be generalised as a set of geometric primitives, 
including boxes, tubes, slabs, etc. Measured lines in images, that are placed to fit to the image features, are the basic type 
of observation. 
Many man-made objects often comply to the assumption above, particulary most architectural objects have been con- 
structed consisting of planar faces and straight edges. We have continued the research published in (van den Heuvel, 
1999) where a novel mathematical model designed primarily for the use in architectural applications is proposed. The 
concept of polyhedral generalisation belongs to the main properties of the model. In the same paper ideas regarding the 
use of constraints and a detailed list of possible constraints on object features can be found. The mathematical model 
has been prepared to accomodate constraints in the adjustment via a set of pseudo-observation equations. Considering 
constraints as observations avoids singularities due to possible linear dependencies, therefore it makes the choice of the 
constraints less critical. However, the constraints differ from observations in a classical sense. The solution to the differ- 
ences between diverse types of observations is commonly based on a consistent use of weights. To introduce a rigorous 
adjustment of image line observations and weighted constraints is the primary goal of our research. 
Shape generalisation that is implicitly included in the mathematical model determines the reconstruction method for pur- 
poses like architectural visualisation. With respect to this purpose, regularity of the object shape is to be considered as the 
most important demand. Our effort is targeted on extending the method to be able to provide models with a regular shape. 
Furthermore, low computational and processing costs are desirable. But a deformation of the object shape appears to be 
an obvious consequence of processing less images. Geometric object constraints integrated in the line-photogrammetric 
bundle adjustment are exploited here to support validation of the object shape. In our approach, we aim to obtain a model 
not as precise as possible, but with a sufficient completeness and regularity. Moreover, with as few images as possible. 
The approach redefines the meaning of the word “adjustment”. A tool for processing observations is then changing to a 
tool for modelling a regular object supported by image observations, especially if the amount of non-image observations 
in the form of constraints increases. 
  
380 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.