Question 1: Why should orthodontists be interested in 3D craniofacial measurement?
The goal of craniofacial measurement has always been the re-assembly of information from multiple sources (study casts of the teeth and jaws, x-ray images of the teeth and skull, and photographs of the face) into a common integrated map. Our region of interest, the skull and face, can be considered conceptually to consist of three layers: an overlying soft tissue layer which we image on facial photographs, an underlying array of teeth which we image primarily on study casts, and an intermediate bony layer, the skull and jaws, which is perceivable only on x-ray images.
Figure 1 - The goal of all orthodontic measurement ---a unified craniofacial model. (after Simon)
But the several layers of the skull make it too complex to be grasped as a whole. In the natural state, some layers obscure other layers. For example, from the outside of the mouth, we cannot see the teeth; from the inside of the mouth, we can see the teeth but not the bony armature which supports them. So orthodontists have very cleverly learned to strip away the layers of the system to see the underlying details more clearly. They do this by constructing a series of physical transforms. The usual physical transforms of orthodontics are study casts, cephalometric x-ray images, facial photographs, and panoramic x-ray images. (See Figure 2.)
Figure 2 - The typical physical transforms of orthodontics.
Each of these transforms, taken by itself, gives us a clearer picture of part of the total system, by completely discarding information about the rest of the system. For example, study casts provide good information about the teeth, but discard all information about the overlying soft issues or the underlying bony scaffolding. Cephalometric x-rays (cephs) provide good information on the scaffold but lose all information about the face surface and retain only attenuated information about the teeth. Facial photographs give us good information about the facial surface, but lose all information about the deeper structures, i.e., the teeth and bones which are perhaps our major concern. Panoramic x-ray images give us valuable information on root contours, but lose all information about arch form and the relationship of the teeth to the facial surface.
However, when orthodontists decompose the skull into separate components, we do not typically retain information on how to put the parts back together with quantitative accuracy. That is why until now the composite illustration from Graber's text has remained a metaphor ---something between a wish and a dream. In current practice, the clinician can do no more than reassemble the information from several transforms conceptually ---as a mental operation, in a process called "clinical judgement". Experienced clinicians do remarkably well at this conceptual task, but with better information we believe that we could deliver even better service to the public.
For example, for purposes of diagnosis and treatment evaluation, we would like to be able to make accurate measurements between physical records of different types (i.e., between study casts and facial photographs, or between study casts and cephalograms). We would like for example to be able to measure precisely how thick the lips are over the canines, how thick the cheeks are over the molars, and what is the relationship between expansion of the maxillary arch and changes in the drape of the buccal soft tissues. Figure 3 attempts to illustrate such relationships, but as may be seen, the very concept is difficult to convey on a two-dimensional image. Information about these and other "tooth to soft tissue" or "tooth to skull" relationships is currently available only for mid-sagittal structures on lateral cephs, and even in that plane the information we have is only marginally trustworthy.
Figure 3a - Measuring between the commissure of the lips and the canine cusp tip.
Figure 3b - Measuring between the cheek surface and the buccal surface of the upper first molar.
The problem in making accurate measurements of these kinds is that there is a constraining geometrical law that limits the merging of information from different sources. Although 3D information can be extracted from study casts, conventional facial photographs and x-ray images contain only 2D information. For registration of data from two 2D images it is sufficient to have 2D information for two points that are common to both images. This strategy is used when orthodontists use two "hash marks" to superimpose a pair of lateral cephs. To merge data from two 3D coordinate maps generated from physical records of the same or different kind, one needs to have 3D information (i.e., "x", "y", and "z") for three points common to both maps. This crucial geometric principle will be explored in greater detail later.
In the remainder of this presentation, we will try to outline methods which have now made possible the quantitative re-integration of fully 3D information from different types of physical record.