Determination of three-dimensional structure in biplane radiography without prior knowledge of the relationship between the two views: theory.

A novel method allows the determination of three-dimensional object structure from two projection images that are obtained at arbitrary, unknown orientations. Only minimal prior information concerning the imaging system is required. First, the image coordinates of eight or more object points that can be identified unambiguously in both views are used to determine the relative geometry of the two projections. Subsequently, the three-dimensional coordinates of the identified object points are determined, to within a scale factor, from the image coordinates of the points and the calculated imaging system geometry. A theoretical description of the overall method is provided, along with techniques for the reduction of effects of experimental errors and numerical errors that may arise in the course of the calculations. Methods to retrieve the absolute scale of the object are discussed also.