Propagation and reduction of error in three-dimensional structure determined from biplane views of unknown orientation

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Abstract
We are developing a technique for determination of the three-dimensional (3-D) structure of vascular objects from two radiographic projection images acquired at arbitrary and unknown relative orientations. No separate calibration steps are required with this method, which exploits an inherent redundancy of biplane imaging to extract the imaging geometry as well as the 3-D locations of eight or more object points. The theoretical basis of this technique has been described previously. In this paper, we review the method from the perspective of linear algebra and describe an improvement, not heretofore reported, that reduces the method''s sensitivity to experimental error. We then examine the feasibility and inherent accuracy of this approach by computer simulation of biplane imaging experiments. The precision with which 3-D object structure may be retrieved, together with the dependence of precision on the actual imaging geometry and errors in various measured quantities, is studied in detail. Our simulation studies show that the method is not only feasible but potentially accurate, typically determining object-point configurations with root-mean-square (RMS) error on the order of 1 to 2 mm. The method is also quite fast, requiring approximately one second of CPU time on a VAX 11/750 computer (0.6 MIPS).