[Techniques for determining position from more than two radiographs intersecting at arbitrary angles in brachytherapy].

Abstract

The least squares method and geometrical solution for calculating position were used in the two-projection method. Five coordinate systems were defined as a normal system, image system on film intersecting the beam central axes at an arbitrary angle and the projection, virtual coordinate and virtual image coordinate systems with beam central axis as one of the three coordinate axes to determine the geometrical relationship between a point and image on the film. Normal coordinates of the point were calculated by six geometrical solution sets and two forms of the least squares method using the rotation matrixes of the coordinate systems. One least squares method solves simultaneous nonlinear equations, and the other derives a strict solution from simultaneous linear equations. The latter least squares method has little physical meaning and is not as useful as the former. Although the former has physical meaning, the iterative approximation method should be used to determine position since a strict solution cannot be obtained directly. By these least squares methods, position is determined with less error using the projections at more than two focal spots.