A localization algorithm and error analysis for stereo x-ray image guidance

Stereo x-ray radiography attracts increasing attention in major clinical applications. The purpose of this paper is to analyze the 3D localization error for breast biopsy procedures and provide guidelines for improving its accuracy. Our prototype is a CCD based digital stereo x-ray imaging system. The mathematical model consists of two x-ray sources and one stationary detector plane. A closed form least-squares solution is derived for 3D localization of feature points, particularly a biopsy needle tip, from a pair of 2D digital radiographs. Based on the least-squares formula and its first order approximation, the 3D localization error is analyzed in terms of object location, measurement error, separation between the two x-ray sources, and distance from the source to the detector. The stereo imaging and error estimation formulas are numerically simulated and experimentally validated. The data are in agreement with theoretical prediction. These results can be used for the purpose of system design and protocol optimization.