Error analysis of marker‐based object localization using a single‐plane XRII

Abstract

The role of imaging and image guidance is increasing in surgery and therapy, including treatment planning and follow-up. Fluoroscopy is used for two-dimensional (2D) guidance or localization; however, many procedures would benefit from three-dimensional (3D) guidance or localization. Three-dimensional computed tomography (CT) using a C-arm mounted x-ray image intensifier (XRII) can provide high-quality 3D images; however, patient dose and the required acquisition time restrict the number of 3D images that can be obtained. C-arm based 3D CT is therefore limited in applications for x-ray based image guidance or dynamic evaluations. 2D-3D model-based registration, using a single-plane 2D digital radiographic system, does allow for rapid 3D localization. It is our goal to investigate-over a clinically practical range-the impact of x-ray exposure on the resulting range of 3D localization precision. In this paper it is assumed that the tracked instrument incorporates a rigidly attached 3D object with a known configuration of markers. A 2D image is obtained by a digital fluoroscopic x-ray system and corrected for XRII distortions (+/- 0.035 mm) and mechanical C-arm shift (+/- 0.080 mm). A least-square projection-Procrustes analysis is then used to calculate the 3D position using the measured 2D marker locations. The effect of x-ray exposure on the precision of 2D marker localization and on 3D object localization was investigated using numerical simulations and x-ray experiments. The results show a nearly linear relationship between 2D marker localization precision and the 3D localization precision. However, a significant amplification of error, nonuniformly distributed among the three major axes, occurs, and that is demonstrated. To obtain a 3D localization error of less than +/- 1.0 mm for an object with 20 mm marker spacing, the 2D localization precision must be better than +/- 0.07 mm. This requirement was met for all investigated nominal x-ray exposures at 28 cm FOV, and for all but the lowest two at 40 cm FOV. However, even for those two nominal exposures, the expected 3D localization error is less than +/- 1.2 mm. The tracking precision was +/- 0.65 mm for the out-of-plane translations, +/- 0.05 mm for in-plane translations, and +/- 0.05 degrees for the rotations. The root mean square (RMS) difference between the true and projection-Procrustes calculated location was 1.07 mm. It is believed these results show the potential of this technique for dynamic evaluations or real-time image guidance using a single x-ray source and XRII detector.