陈志祥 须颖 石锦洋

摘要：工业计算机断层成像技术（computer tomography，CT）系统几何参数不准确会影响重建图像的质量和尺寸测量的精度。为校正工业 CT 几何位姿失配参数，提出基于标准球板模体的几何校正方法。首先，利用球板在两个不同位置的投影图求解出射线源到探测器的距离以及射线源到运动平台的距离。再在360°范围内间隔一定角度均匀采集球板投影信息，拟合球心投影轨迹，解析求解探测器偏角η、φ和探测器中心点坐标。最后根据重建出的体素模型的球心距测量结果，利用牛顿迭代法，以工业 CT 尺寸测量最大允许误差为约束条件迭代求解探测器偏角θ。实验结果显示：该文幾何校正方法可以求解出所有工业 CT 几何位姿失配参数。参数校正后，提升图像质量，消除重建图像伪影，且工业 CT 球心距测量最大误差由44.8μm 降低到16.3μm，表明该几何校正方法可以满足实际工业 CT 系统校正的要求。

关键词：工业 CT;几何校正;校正模体;图像重建

中图分类号： TP391.4文献标志码： A文章编号：1674–5124（2021）12–0023–06

Geometric parameter calibration of industrial CT system

CHEN Zhixiang，XU Ying，SHI Jinyang

（School of Mechanical and Electrical Engineering， Guangdong University of Technology， Guangzhou 510006， China）

Abstract： Incorrect geometric parameters of the industrial CT （computer tomography） system will affect the qualityof thereconstructedimageandtheaccuracyof dimensionalmeasurement. Inordertocalibrate geometric mismatching parameters of industrial CT， a geometric calibration method based on the standard spherical plate phantom was proposed. Firstly， the distance from the ray source to the detector and the distance from the ray source to the rotating platform were calculated by using the projection of the spherical plate at two different positions. Then， the projection information of the spherical plate was uniformly collected at a certain angle interval within 360° range， fitted the sphere center projection trajectory， and the detector deflection angle η ， φ and the detector center point coordinates were calculated analytically. Finally， based on the spherical- center distance measurement results of the voxel model， the Newton iteration method was used to solved the detectordeflectionangle θ bytakingtheMaximumPermissibleErrorof theindustrialCTdimensional measurementastheconstraintcondition. Theexperimentalresultsshowedthatthegeometriccorrection method could solved all the geometric position mismatch parameters of industrial CT. After the parameters were calibrated， the image quality was improved， and the reconstructed image artifacts were eliminated. The maximum error of industrial CTspherical distance measurement was reduced from 44.8μm to 16.3μm，indicated that the geometric calibration method could met the requirements of actual industrial CT system calibration.

Keywords： industrial computer tomography; geometry calibration; calibration phantom; image reconstruction

0引言

工业计算机断层成像技术（ computer tomography，CT）是一门集光学、机械、控制和计算机科学于一体的数字化 X 射线成像技术，其利用物体对 X 射线吸收率的不同来获取物体的多角度投影图，并根据这些投影图重建出物体的三维图像[1]。目前这项技术正在向尺寸测量领域发展，但因为工业 CT 通常采用 FDK 算法对投影数据进行重建，而 FDK（ Feldkamp-Davis-Kress）算法要求工业 CT系统几何位姿满足理想条件[2]，实际情况下，工业 CT 系统难于满足理想条件，系统几何参数会存在偏差。……