Abstract：Ultrasound probe calibration is a necessary step in the process of 3D ultrasound imaging by a freehand 2D ultrasound probe. In order to calibrate ultrasound probe quickly and effectively with small number of calibration images, a flexible calibration method based on optical tracker was presented for determining the unknown transformation matrix. First, a calibration pattern containing two mutually perpendicular planes was developed. In the process of calibration, the calibration pattern was scanned by a freehand 2D ultrasound probe. Transformation matrice were calculated from camera to calibration pattern and from ultrasound probe to ultrasound image. There were 3 crosspoints between ultrasound beam and three orthogonal axes of the pattern in each trial, which setup 6 calibration equations. The unknown transformation matrix and 2 scaling factors were solved by nonlinear fitting, when at least 2 calibration images were captured. Experiments with synthetic data show that calibration error decreases with increased number of images. The error was 1 mm when the number of images was 30. Experiments with real data show that our method has high accuracy with only 20 calibration images, meeting the demand of ultrasound surgical navigation and lays the groundwork for 3D ultrasound imaging reconstruction.
［1］Chaoui J, Dardenne G, Hamitouche C, et al. Virtual movementsbased calibration method of ultrasound probe for computer assisted surgery［C］//IEEE International Symposium on Biomedical Imaging: From Nano to Macro.Bostoa:IEEE, 2009: 1207-1210.
［2］徐静,杨向东,朱森强,等.用于肝癌介入治疗的术中三维超声导航系统［J］.中国生物医学工程学报,2007,26(5):719-723.
［3］白培瑞,白净.基于二维阵列换能器的实时三维超声成像技术综述［J］.中国生物医学工程学报,2011,30(6):938-945.
［4］Nakamoto M, Nakada K, Sato Y, et al. Intraoperative magnetic tracker calibration using a magnetooptic hybrid tracker for 3-D ultrasoundbased navigation in laparoscopic surgery［J］. IEEE Transactions on Medical Imaging, 2008,27(2):255-270.
［5］MarieAnge J, LouisGilles D, MarieHélène RC, et al. Performance evaluation of a medical robotic 3Dultrasound imaging system［J］. Medical Image Analysis, 2008，12(3):275-290.
［6］Boctor E, Viswanathan A, Choti M, et al. A novel closed form solution for ultrasound calibration［C］//IEEE International Symposium on Biomedical Imaging: Nano to Macro.Arlington:IEEE, 2004:527- 530.
［7］罗杨宇,徐静,鲁通,等.基于磁定位器的手动三维超声图像标定［J］.中国生物医学工程学报,2008,27(2):250-254.
［8］Prager RW, Rohling RN, Gee AH, et al. Rapid calibration for 3D freehand ultrasound［J］. Ultrasound in Medicine & Biology,1998,24(6):855-869.
［9］Birkfellner W, Watzinger F, Wanschitz F, et al. Systematic distortions in magnetic position digitizers［J］. Medical Physics,1998,25(11):2242-2248.
［10］Mercier L, Lang T, Lindseth F, et al. A review of calibration techniques for freehand 3-D ultrasound systems［J］. Ultrasound in Medicine & Biology, 2005,31(4):449-471.
［11］Zhang Zhengyou. A flexible new technique for camera calibration［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(11):1330-1334.
