Ermes, Pierre 
  
elements can be connected, The latter situation yields several constraints for the direction of the two elements and for 
the position of their coinciding ends. The radii of the two elements might also be equal. 
The integration of internal and external constraints with the model-based measurement method has several benefits: 
-  Facilitates measurement. When a straight pipe is connected to an already known element, its direction and position 
are determined, leaving only its length to be measured. 
- Enables measurement in complex situations. In industrial installations often piping elements occlude each other and 
are not entirely visible in the images. The application of constraints decreases the degrees of freedom of the CAD- 
model, which allows the reconstruction of the installation with less measurements. 
- Simultaneous adjustment of adjacent models. Figure 2a shows two cylinders connected to a curved element. The 
transitions between the elements are smooth and only the contours give a good enough contrast for accurate 
measurement. The piping elements can be reconstructed by applying direction constraints and position constraints 
between the connections. This also means that the parameters of the different elements are correlated with each 
other and that a change of a parameter of one element might affect its neighboring elements. Piper can include 
neighboring elements in the adjustment during the interactive measurements. The operator can select the number of 
neighbors that will be included in the adjustment. 
- Extended measuring capabilities compared to other methods. Benning (1997), Hilgers et al. (1998) and Jones et al. 
(1996) describe methods or systems that focus on the measurement of piping elements. For the reconstruction of 
curved elements these methods rely on the complete measurement of the neighboring straight cylinders. The 
absence of clear transitions as in Figure 2a will cause problems and in situations where two or more curves are 
connected to each other, as in Figure 2b, these methods will even fail. Piper combines constraints with 
measurements on the contours to reconstruct these elements. 
  
a b 
Figure 2. Examples of images of an industrial installation. The reconstructed piping 
elements are drawn on top using the hidden-line projection. 
4 THE CONNECTION CONSTRAINTS 
A set of primitive shapes is implemented within Piper. The set consists of a sphere, a cylinder, a box, a torus, a wedge, 
and a prism. These primitives can be combined using Boolean operations and constraints can be applied between the 
primitives. We will discuss two primitives (cylinder and torus) and three types of constraints (parameter, position, and 
direction constraints) in more detail. These primitives and constraints are used frequently in the reconstruction of 
industrial installations. 
A cylinder, as shown in Figure 3, is constructed relative to its own coordinate system. The base of the cylinder is 
positioned at (0,0,0), the symmetry axis coincides with the Z-axis and the top of the cylinder is located at (L, 0, 0), 
where L is the length of the cylinder. The length together with the radius of the cylinder r, define the shape of the 
cylinder. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 217