Determination of source position for four radiography systems with orthogonal projections in brachytherapy

Four configurations of two X-ray tube positions are available for determining the position of a point using two orthogonal films. For each configuration, there are many formulas for calculating the coordinate of a point: the least squares methods with and without physical meaning, such as six sets of geometrical solutions, an approximation method with constant magnifications and so on. It is troublesome for a person in charge of treatment planning to directly derive a formula or select an appropriate formula from numerous ones for the four configurations. Thus, a method to easily apply the published formula for a configuration to the other three configurations is described in simulations and a clinical case using rotation matrixes of the right-handed coordinate system. Each diagonal element of the rotation matrixes is 1 or -1, and the other elements are 0.