The geometry of three-dimensional measurement from paired coplanar x-ray images

This article outlines the geometric principles which underlie the process of making craniofacial measurements in three dimensions by combining information from pairs of coplanar x-ray images. The main focus is upon the rationale of the method rather than upon the computational details. We stress particularly the importance of having available accurate measurements as to the relative positions of the x-ray tubes and the film plane. The use of control arrays of radiopaque "points" whose projected images upon the film plane allow the retrospective calculation of the spatial relationship between the x-ray tubes and the film plane is explained. Finally, the question of correcting for movement of the subject between two films of an image pair is considered briefly.