CLOSE RANGE PHOTOGRAMMETRY USING GEOMETRIC PRIMITIVES 
FOR EFFICIENT CAD MODELLING OF INDUSTRIAL PLANT 
M. A. Jones, D. P. Chapman, and A. A. Hamid 
University College London 
United Kingdom 
A. T. D. Deacon 
As-Built Solutions Ltd. 
United Kingdom 
Commission V, Working Group 3 
KEY WORDS: 
ABSTRACT 
Industrial, Close Range, Geometry, Mathematics, Modelling, CAD 
This paper outlines the straightforward derivation of several simple mathematical models describing the relationship between 
some given 3D geometric primitives in the world co-ordinate system and the 2D primitives forming the projected views of 
those 3D objects. 
As a starting point, the co-planarity condition is adapted to relate the parameters of a line in the world co-ordinate system, to 
the parameters of the corresponding 2D line in an image. An extension of the same co-planarity condition is then employed, 
to link the parameters describing a cylinder to the parameters of the two lines defining the occluding edges in an image of that 
cylinder. Basic geometry and simple vector algebra are then used to complete the model for the cylinder, with the third set of 
equations linking the parameters of a cylinder to the ellipses forming the images of it's end-caps. 
These mathematical models have been partially integrated into an existing system designed for the remote measurement of 
industrial plant. Their potential, to increase the ease with which CAD models of existing plant may be either generated or 
updated, will be demonstrated. 
1. INTRODUCTION 
Due to increasingly stringent safety regulations imposed by 
the relevant governing authorities, and a desire to replace or 
alter existing equipment, as-built CAD models of industrial 
plants are necessarily becoming more sought after by those 
companies operating industrial sites. 
In some instances CAD models may already exist from the 
planning stages, but may not reflect a true picture of the site, 
since necessary and unforeseen changes had to be made 
during the plant construction. For older sites red lined 
design drawings may be the only record of the plant layout. 
Conventional or digital terrestrial photogrammetry provides 
a relatively efficient means to generate or update CAD 
models, see (Chapman et al., 1992). By providing a record 
of the plant in question the images may then be used 
immediately or archived for future use. At any point in time 
they may be used to determine a few critical dimensions, to 
model a small local section of the site, or to create a model of 
the entire site. 
An industrial plant is often a highly complex environment 
consisting of great quantities of equipment separated by 
narrow corridors for access. Such an environment requires 
the stationing of cameras at frequent intervals with a 
separation of the order of several metres, in both the 
horizontal and vertical sense. At each location a panorama 
of images will have to be captured. This scenario is essential 
in order to provide full coverage of the plants equipment and 
enable that equipment to be modelled to the required 
accuracy. 
With the large numbers of images relating to each site, both 
the localisation of camera positions and subsequent plant 
modelling can become very labour intensive. Any 
automation of this process necessarily provides an increase 
284 
in productivity. It will be shown how an existing CAD 
model may be used to effect some level of automation. In 
addition, images within such an archive may often be found 
which are crucial to linking together the three dimensional 
grid of camera locations, but which see few points which 
could be used as part of a conventional bundle adjustment. 
This paper will indicate how the use of edges and cylinders 
may help overcome these problems. 
The equipment comprising the majority of many industrial 
plants may be modelled by a number of basic geometric 
primitives (cylinders, spherical dishes, boxes, tori). The 
standard collinearity equations can be used to determine 
points on the surface or edges of objects viewed in any two 
or more images, after which primitive fitting routines may 
be used to determine the descriptive parameters of the viewed 
object. 
An alternative approach is to by-pass the collinearity 
equations, and to use equations relating the descriptive 
parameters of the objects in the world co-ordinate system, 
and the parameters describing the actual or occluding edges 
in the image of that object. A considerable amount of work 
has already be done in this area for lines, for example 
(Schwermann, 1994; Tetsa & Patias, 1994; Tommaselli & 
Tozzi, 1992), and for some other geometric objects, (Li & 
Zhou, 1994). Some alternative mathematical models 
describing these relationships for a 3D line and a cylinder in 
the world co-ordinate system are given in this paper. These 
models are relatively simple, two based largely upon the co- 
planarity condition, and do not involve the introduction of 
any unwanted parameters. They could be used during the 
localisation stage, to help determine the camera locations 
and an initial set of primitives for the CAD model. Their use 
during the subsequent modelling stage using the localised 
camera positions is demonstrated. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
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