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

Stereo x-ray radiography attracts increasing attention in major clinical ap plications. The purpose of this paper is to analyze the 3D localization err or for breast biopsy procedures and provide guidelines for improving its ac curacy. Our prototype is a CCD based digital stereo x-ray imaging system. T he mathematical model consists of two x-ray sources and one stationary dete ctor plane. A closed form least-squares solution is derived for 3D localiza tion of feature points, particularly a biopsy needle tip, from a pair of 2D digital radiographs. Based on the least-squares formula and its first orde r approximation, the 3D localization error is analyzed in terms of object l ocation, measurement error, separation between the two x-ray sources, and d istance from the source to the detector. The stereo imaging and error estim ation formulas are numerically simulated and experimentally validated. The data are in agreement with theoretical prediction. These results can be use d for the purpose of system design and protocol optimization. (C) 2000 Amer ican Association of Physicists in Medicine.