Improved determination of biplane imaging geometry from two projection images and its application to three‐dimensional reconstruction of coronary arterial trees

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Abstract
A technique has been developed for accurate estimation of three‐dimensional (3D) biplane imaging geometry and reconstruction of 3D objects based on two perspective projections acquired at arbitrary orientations, without the need of calibration. The required prior information (i.e., the intrinsic parameters of each single‐plane imaging system) for determination of biplane imaging geometry includes (a) the distance between each focal spot and its image plane, SID (the focal‐spot to imaging‐plane distance); (b) the pixel size,(e.g., 0.3 mm/pixel); (c) the distance between the two focal spotsor the known 3D distance between two points in the projection images; and (d) for each view, an approximation of the magnification factor, MF (e.g., 1.2), which is the ratio of the SID and the approximate distance of the object to the focal spot. Item (d) is optional but may provide a more accurate estimation if it is available. Given five or more corresponding object points in both views, a constrained nonlinear optimization algorithm is applied to obtain an optimal estimate of the biplane imaging geometry in the form of a rotation matrixRand a translation vectortthat characterize the position and orientation of one imaging system relative to the other. With the calculated biplane imaging geometry, 3D spatial information concerning the object can then be reconstructed. The accuracy of this method was evaluated by using a computer‐simulated coronary arterial tree and a cube phantom object. Our simulation study showed that a computer‐simulated coronary tree can be reconstructed from two views with less than 2 and 8.4 mm root‐mean‐square (rms) configuration (or relative‐position) error and absolute‐position error, respectively, even if the input errors in the corresponding 2D points are fairly large (more than two). In contrast, input image error of more than one pixel () can yield 3D position errors of 10 cm or more when other existing methods based on linear approaches are employed. For the cube phantom images acquired from a routine biplane system, rms errors in the 3D configuration of the cube and the 3D absolute position were 0.6–0.9 mm and 3.9–5.0 mm, respectively.

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