Ultrasound Probe Calibration Method of Single-Wire Phantom Using Levenberg-Marquardt Algorithm

Abstract

A freehand three-dimensional (3D) ultrasound system is a method of acquiring images using a 3D ultrasound probe or conventional two-dimensional (2D) ultrasound probe to give a 3D visualization of an object inside the body. Ultrasounds are used extensively in clinical applications since they are advantageous in that they do not bring dangerous radiation effects and have a low cost. However, a probe calibration method is needed to transform the coordinate position into a 3D visualization display, especially for image-guided intervention. The current ultrasound probe calibration system usually uses the numerical regression method for the N-wire phantom, which has problems in accuracy and reliability due to nonlinear point scattered ultrasound image data. Hence, a method for ultrasound probe positional calibration of single-wire phantom using the Levenberg-Marquardt algorithm (LMA) was proposed to overcome this weakness. This experiment consisted of an optical tracking system setup, a 2D ultrasound probe with marker, an ultrasound machine, and a single-wire object in a water container equipped with a marker. The position and orientation of the marker in a 2D ultrasound probe and the marker in the water container were tracked using the optical tracking system. A 2D ultrasound probe was equipped with a marker connected wirelessly using an optical tracking system to capture the single-wire object. The resulting sequences of 2D ultrasound images were reconstructed and visualized into 3D ultrasound images using three transformations, ultrasound beam to ultrasound probe’s marker, single-wire phantom position to container’s marker, and the 3D visualization transformation. The LMA was used to determine the best optimization parameters for determining the exact position and representing that 3D visualization. The experiment result showed that the lowest mean square error (MSE), rotation error, and translation error were 0.45 mm, 0.25°, and 0.3828 mm, respectively.