Hybrid optical-vision tracking in laparoscopy: accuracy of navigation and ultrasound reconstruction

Figures & data

Figure 1. Transformation diagrams: (A) hybrid tracking of a LUS. (B) Free-hand ultrasound calibration. (C) Hand-eye calibration and tracking accuracy evaluation. (D) Ultrasound compounding evaluation.

Figure 2. Tracking accuracy results: (A) tracking error vs distance from the laparoscopic camera. (B) Tracking error distribution along xz plane, averaged along yz planes. Left camera is located at the position (0,0) in the image.

Figure 3. Ultrasound reconstruction results: (A) phantom CT segmentation. (B) Ultrasound compounding. (C) Ultrasound compounding segmentation (light grey). (D) Ultrasound compounding rendering. (E) Distance between center of mass of tumor in ultrasound reconstruction and CT: a is the distance between tumor and LUS probe; b is the distance between laparoscopic camera and LUS probe.

Table 1. Hausdorff and centers of mass distances between CT and US.

Metric	Hausdorff distance (mm)			Centers of mass distance (mm)
	Max.	Avg.	95%
Tumor A	2.50 ± 0.40	0.85 ± 0.14	1.77 ± 0.31	1.77 ± 0.35
Tumor B	2.41 ± 0.28	0.74 ± 0.12	1.56 ± 0.18	1.55 ± 0.25
Tumor C	2.68 ± 0.36	0.88 ± 0.18	1.90 ± 0.29	1.79 ± 0.39
Average	2.53 ± 0.36	0.83 ± 0.16	1.75 ± 0.30	1.71 ± 0.35

Table 2. Dice score.

Tumor ID	A	B	C
Average Dice	0.66 ± 0.05	0.81 ± 0.03	0.68 ± 0.06
Tumor volume (cc)	0.36	1.56	0.38
Equivalent diameter (mm)	8.83	14.39	8.99

Table 3. Mean and standard deviation absolute rigid transformation parameters (euler angles and translation vector) between multi-sweep ultrasound reconstructions and ground truth CT of the phantom.

α (deg)	β (deg)	γ (deg)	tx (mm)	ty (mm)	tz (mm)	residual (mm)
0.75 ± 0.60	0.66 ± 0.51	0.26 ± 0.25	0.95 ± 0.56	1.65 ± 1.33	1.79 ± 1.31	0.37 ± 0.19