Photogrammetric Restitution Based on Linear Features 
Kurt Kubik 
Professor and Head of School 
Queensland University of Technology, Department of Surveying, George Street, 
Brisbane 4000. Qld., Australia 
ISPRS Commission III 
ABSTRACT 
In industrial metrology, when measuring the actual shapes of industrial tools and jigs, it is often impossible to 
define unique measuring points on an object. Straight edges are however, commonly available. In this paper we 
describe the mensuration procedure using these edges instead of well defined object points. We describe the 
method of computation and the mensuration procedure, with the minimum number of lines necessary to calculate 
the problem successfully. 
1. INTRODUCTION 
In an industrial metrology, we have to determine with high 
accuracy the actual shape of tools and to compare it to the 
desired "blueprint" shape. The problem with this quality 
control process is that no unique points are defined on the 
object itself, but linear or circular features abound (Fig. 1). 
In order that a simple mensuration process can be used, 
and to allow online quality control during the manufacturing 
process, the reconstruction of the 3-D object and its quality 
control should preferably be done using only the available 
edges of the object and no auxiliary measuring tools 
defining virtual points. The problem is thus as follows: 
(1) Can we measure, from different measuring stations to 
arbitrary, non-identical points along the well defined edges 
of the object and reconstruct its 3-D shape (relative 
orientation)? 
(2) Can we transform the "as is" shape of the object into 
the "blueprint" shape using common edges instead of 
common points (absolute orientation)? 
This paper discusses the minimum number of 
measurements to yield a unique solution to the problem. It 
expands on an earlier paper of the author on this topic 
(Kubik, 1991). 
2. ADVANTAGES IN THE MENSURATION PROCESS 
The use of linear features for 3-D reconstruction would 
greatly simplify the mensuration process, as no homologous 
points have to be identified. The reconstruction could take 
place while scanning the image. 
In order to explain this idea, let us assume the use of two 
digital cameras. As each of these cameras scans the 
object scene, it only needs to register the intersections of 
the scan line with the linear features. These intersection 
points are matched in order to find the homologous linear 
features. Here a learning process can be used to fully 
utilise the information derived from the previous scan lines. 
Also, a quality control on the straightness of the object lines 
is possible during this process, as straight object lines 
Should map as straight image lines. 
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Figure 1: A typical tool shape in industrial metrology 
3. ABSOLUTE ORIENTATION USING EDGES 
Let us start with the absolute orientation problem first, as 
this problem is relatively easy. The formulae for the three 
dimensional orthogonal transformations are: 
XU X RX AX (1) 
Where: 
X, = the blueprint coordinates (E,N,H) of a point A; 
X, = the "as is" coordinates; 
the matrices, R,AX = the rotations and shifts respectively; 
A = the scale factor.