Three-dimensional reconstruction of curves from pairs of projection views in the presence of error. II. Analysis of error.

We have previously described an approach to 3D intracerebral vascular reconstruction that uses an MRA as a reconstruction base. Additional vessels seen only by angiography are added by segmenting 2D curves from projection angiograms and reconstructing these curves into 3D, building upon the MRA. This paper is the second of two that discuss the specific problem of reconstructing a 3D curve from a given pair of 2D curves in the presence of error. The method presented is capable of detecting and handling many errors produced by misregistration, image distortion, or misdefinition of 2D curves. The first paper gives an algorithm. The current paper discusses factors affecting the accuracy of a reconstructed curve, with emphasis upon registration error. We analyze the spatial accuracy of a reconstructed point in terms of the relationships between pixel size, relative viewing angle, 3D point location, and registration error. We provide a theoretical framework that, given the known error properties of a registration algorithm, allows optimization of the viewing geometry so as to produce the highest precision of point reconstruction. A major focus is the effect of registration error upon the reconstruction of a curve. We subdivide registration error into two types, one of which produces smoothly continuous point placement errors and the other of which produces pixel pairing errors. We test our ability to reconstruct a 3D curve in the presence of both. Finally, we summarize approaches to other sources of error. We conclude with a list of recommendations to optimize reconstruction accuracy. When projection points are associated by the rules of epipolar geometry, viewplane point displacements should not exceed 1.5-2 mm along the axis perpendicular to epipolar planes.