DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction

The calibration of ultrasound probes is essential for three-dimensional ultrasound reconstruction and navigation. However, the existing calibration methods are often cumbersome and inadequate in accuracy. In this paper, a hybrid mathematical model, Dimensionality Reduction and Homography Transformation (DRHT), is proposed. The model characterizes the relationship between the image plane of ultrasound and projected calibration lines and homography transformation. The homography transformation, which can be estimated using the singular value decomposition method, reduces the dimensionality of the calibration data and could significantly accelerate the computation of image points in ultrasonic three-dimensional reconstruction. Experiments comparing the DRHT method with the PLUS library demonstrated that DRHT outperformed the PLUS algorithm in terms of accuracy (0.89 mm vs. 0.92 mm) and efficiency (268 ms vs. 761 ms). Furthermore, high-precision calibration can be achieved with only four images, which greatly simplifies the calibration process and enhances the feasibility of the clinical application of this model.