Ultrasound Probe Calibration Method Based on Optical Tracking Systems

Transcript

1 Chinese Journal of Biomedical Engineering Vol. 32 No. 5 October 213 * mm 2 2 mm R318 A Ultrasound Probe Calibration Method Based on Optical Tracking Systems REN Liang QIU Tian-Shuang * GUO Yong Department of Biomedical Engineering Dalian University of Technology Dalian China 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 3. Experiments with real data show that our method has high accuracy with only 2 calibration images meeting the demand of ultrasound surgical navigation and lays the groundwork for 3D ultrasound imaging reconstruction. Key words ultrasound probe calibration 3D freehand imaging optical tracker 1 X-ray CT MRI 2 doi /j. issn BAJ18B6 * qiutsh@ dlut. edu. cn

2 mm mm 2. 4 mm N M C N D I 3 T CM T DC T ID T CM C M T DC D C T ID I D 9 O M ABC O M CDE 14 F G H M C 1 D I P P M = T CM T DC T ID P I 1 8 cosαcosβ cosαsinβsinγ - sinαcosγ cosαsinβcosγ + sinαsinγ t x sinαcosβ sinαsinβsinγ + cosαcosγ sinαsinβcosγ - cosαsinγ t T ID t x t y t z y α β γ = 2 - sinβ cosβsinγ cosβcosγ t z 1 P M = X M Y M Z M 1 T P M 1. 2 P I = s x u s y v 1 T P 1 F 1 I s x s y x s x u T CM T DC s P M F = = T CM T DC T ID y v 3 T ID t x t y t z α β γ M C 3 T ID t x t y t z α β γ s x s y Y Z G H I D T ID 6 8 N 6N 8 2

3 Fig. 1 1 Illustration of ultrasound probe calibration 3 M X Δf = f ψ - f^ x s x u Δψ Δf f ψ s f X i = = T CM T DC i T y v ID 4 f^ ψ j J f ψ ψ Δf 1 1 Levenberg-Marquardt i = 1 2 N Δψ = ψ j+1 - ψ j = J T J + ηi -1 J T Δf 7 f X 2 i = f X 3 i = 4 η I J Δf Δψ ψ f Y 1 i = f Y 3 i = f Z 1 i = f Z 2 i = f i t x t y t z α β γ s x s y = f i ψ = f X 2 i f X 3 i f Y 1 i = 5 f Y 3 i f Z 1 i f Z 2 i i = 1 2 N ψ = t x t y t z α β γ s x s y N 2 f ψ = f N ψ = f t x t y t z α β f ψ f^ f 1 ψ f 2 ψ γ s x s y = ψ j + δf^ ψ j δψ ψ - ψ j 6 2 j = 1 2 ψ j = δf^ ψ j δψ ψ - ψ j = J Matlab 1 T CM 1 T DC i 1 3 P I i 6 3 F G H f^ i ψ = f F 2 i f F 3 i f G 1 i f G 3 i f H 1 i f H 2 i f i ψ = [ ] Δ f i ψ = f^ i ψ f i ψ 3 N N Δf i ψ i = 1 E mean = 8 3N

4 N 1 8 E mean N A B 25 mm 15 mm 2 mm 3 PC mm C M T CM 5 7 Aloka Prosund α a b C M T CM Fig. 2 Calibration setup for real experiments. 2 5 a Calibration equipment b Calibration pattern D C T DC i F G H 3 4 T ID t x t y t z α β γ s x s y 8 E mean N 3 3 F G H Fig. 3 F G H in ultrasound image ~ E mean N

5 mm 4 1 mm 2 mm Fig. 5 Calibration results with real data 4 Fig. 4 Calibration results with simulation data ~ E mean. 1 mm N mm 4 1. mm 2. 4 mm Cambridge Cross-wire Single-wall Threewire 3 1 Tab. 1 5 Calibration results with real data Cross-wire Single-wall Cambridge Three-wire /mm /mm * * Cross-wire Single-wall Three-wire

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