IMPROVED DETERMINATION OF BIPLANE IMAGING GEOMETRY FROM 2 PROJECTION IMAGES AND ITS APPLICATION TO 3-DIMENSIONAL RECONSTRUCTION OF CORONARYARTERIAL TREES

A technique has been developed for accurate estimation of three-dimens ional (3D) biplane imaging geometry and reconstruction of 3D objects b ased 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 d etermination of biplane imaging geometry includes (a) the distance bet ween each focal spot and its image plane, SID (the focal-spot to imagi ng-plane distance); (b) the pixel size, p(size) (e.g., 0.3 mm/pixel); (c) the distance between the two focal spots (ff') over bar or the kno wn 3D distance between two points in the projection images; and (d) fo r 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 correspond ing object points in both views, a constrained nonlinear optimization algorithm is applied to obtain an optimal estimate of the biplane imag ing geometry in the form of a rotation matrix R and a translation vect or t that characterize the position and orientation of one imaging sys tem relative to the other. With the calculated biplane imaging geometr y, 3D spatial information concerning the object can then be reconstruc ted. The accuracy of this method was evaluated by using a computer-sim ulated coronary arterial tree and a cube phantom object. Our simulatio n study showed that a computer-simulated coronary tree can be reconstr ucted from two views with less than 2 and 8.4 mm root-mean-square (rms ) configuration (or relative-position) error and absolute-position err or, respectively, even if the input errors in the corresponding 2D poi nts are fairly large (more than two pixels=0.6 mm). In contrast, input image error of more than one pixel (= 0.3 mm) can yield 3D position e rrors of 10 cm or more when other existing methods based on linear app roaches are employed. For the cube phantom images acquired from a rout ine 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 . (C) 1997 American Association of Physicists in Medicine.