texturing purposes or obtained by other means, e.g., tourist 
photos, postcard, infrared or ultraviolet images, or even 
historical photos. 
Figure 6. 3D points selection in Polyworks 1 M using the shaded 
images 
Figure 7. Selection of homologous points in 2D image with 
ShapeCapture 1 ^ 
The model is first segmented manually (in the 3D modeling 
software) into mutually exclusive regions. Each region is 
mapped onto a region (entirely comprised) that is a subset of 
one of the 2D images. Then, features are located on a shaded 
version (see Figure 6) of the 3D image using Polyworks 
IMinspect IM and an ASCII file is created that contains those 3D 
points. The same features are located in the 2D image, and the 
relative position between 2D and 3D cameras is found using the 
photogrammetric software, ShapeCapture™ (ShapeQuest Inc.) 
(see Figure 7). We assumed that the 2D camera has already 
been calibrated and that the 3D points generated by 
Polyworks 1 M were imported as control points in 
ShapeCapture 1 M . Pose estimation in this last software uses the 
distortion parameters of the lens computed from the camera 
calibration. We use a 6-parameter lens distortion model. In 
house software to map texture was then used. This last item 
will be available in a future release of ShapeCapture 1 M . The 
calibration can be performed once, before taking the 2D images 
or if the camera if no longer available, then, 3D data points 
found on the 3D model can be used for the lens calibration. 
Other methods based on constraint equations (e.g. 
perpendicularity or parallelism amongst features) are available, 
(El-Hakim, 2001). The 2D images can be taken in an angular 
span of about ± 30 degrees. Grazing angles should be avoided. 
Figure 8. Texture mapping methods, a) the preferred way to 
map texture because it is usable in virtual restoration, b) texture 
map for the colour per vertex method. 
We have experimented with two approaches for the 
construction of a texture-mapped simplified model, again with 
the goal of maximizing the use of commercially available 
software tools. 
The first method prepares the data so that it can be entered into 
the model compression and texture mapping process available 
in Polyworks 1 M . This technique (Soucy et al., 1996b) requires a 
triangulated geometric model with a colour value assigned to 
each vertex. The original high-resolution model is compressed 
into a simplified model through a vertex removal process. The 
appearance of the original model is approximated by computing 
a texture patch for each triangle of the simplified model that 
approximate the appearance of the area represented by the 
removed vertices. As part of the geometric compression, the 
removed vertices are projected onto the larger triangles. When 
the desired level of compression is reached, a texture image is 
created. It is a tessellated image where each triangle of the 
simplified model is mapped onto a colour patch integrating the 
information from the removed vertices. The method was 
designed for arbitrary topologies, and possibly incorrect or 
incomplete models. Thus, it does not attempt to create a 
piecewise parameterization of adjacent triangles on the model 
that would be maintained in the texture image. Rather, each 
triangle is mapped independently (or by adjacent pairs) and 
after affine transformation of the triangle into an isosceles right 
angle triangle for efficient packing. Figure 8b illustrates the 
results. In order to apply this method, the colour information 
contained in the 2D images must be attached to vertices of the 
geometric model. Here, the surface sampling of the original 2D 
images is denser than the geometric sampling. In order to 
incorporate the colour information in the model, triangles are 
subdivided to accommodate the new points. The over-sampled 
model is then fed into the pipeline. One advantage of using this 
method is that all the texture is embedded in a single, 
efficiently occupied texture map, and that the algorithm easily 
allows the generation of maps of different sizes. The major 
inconvenient of this approach is the requirement to process an 
excessively large model. But another one is in the usability of 
the texture map obtained: if there are requirements to modify 
the images, only global corrections (e.g. contrast, brightness) 
can be easily applied to the texture. If, in the course of virtual 
restoration, the original images need to be modified, then the 
entire compression/texture mapping process must be applied 
again.