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

Xuquan Ji, Yonghong Zhang, Huaqing Shang, Lei Hu, Xiaozhi Qi () and Wenyong Liu ()
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Xuquan Ji: School of Biological Science and Medical Engineering, Beihang University, Beijing 100083, China
Yonghong Zhang: School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China
Huaqing Shang: Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
Lei Hu: School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China
Xiaozhi Qi: Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
Wenyong Liu: School of Biological Science and Medical Engineering, Beihang University, Beijing 100083, China

Mathematics, 2025, vol. 13, issue 8, 1-17

Abstract: 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.

Keywords: ultrasound probe calibration; Dimensionality Reduction and Homography Transformation (DRHT); hybrid mathematical model; ultrasonic three-dimensional reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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