Open Access

ARTICLE

A Computational Modeling Approach for Joint Calibration of Low-Deviation Surgical Instruments

Bo Yang^1,2, Yu Zhou³, Jiawei Tian^4,*, Xiang Zhang², Fupei Guo², Shan Liu^5,*

1 School of Artificial Intelligence, Guangzhou Huashang College, Guangzhou, 511300, China
2 School of Automation, University of Electronic Science and Technology of China, Chengdu, 610054, China
3 Research Institute of AI Convergence, Hanyang University ERICA, Ansan-si, 15577, Republic of Korea
4 Department of Computer Science and Engineering, Hanyang University, Ansan-si, 15577, Republic of Korea
5 Department of Biomedical and Electrical Engineering, Marshall University, Huntington, WV 25755, USA

* Corresponding Authors: Jiawei Tian. Email: ; Shan Liu. Email:

(This article belongs to the Special Issue: Recent Advances in Signal Processing and Computer Vision)

Computer Modeling in Engineering & Sciences 2025, 145(2), 2253-2276. https://doi.org/10.32604/cmes.2025.072031

Received 18 August 2025; Accepted 23 October 2025; Issue published 26 November 2025

Abstract

Accurate calibration of surgical instruments and ultrasound probes is essential for achieving high precision in image guided minimally invasive procedures. However, existing methods typically treat the calibration of the needle tip and the ultrasound probe as two independent processes, lacking an integrated calibration mechanism, which often leads to cumulative errors and reduced spatial consistency. To address this challenge, we propose a joint calibration model that unifies the calibration of the surgical needle tip and the ultrasound probe within a single coordinate system. The method formulates the calibration process through a series of mathematical models and coordinate transformation models and employs a gradient descent based optimization to refine the parameters of these models. By establishing and iteratively optimizing a template coordinate system through modeling of constrained spherical motion, the proposed joint calibration model achieves submillimeter accuracy in needle tip localization. Building upon this, an N line based calibration model is developed to determine the spatial relationship between the probe and the ultrasound image plane, resulting in an average pixel deviation of only 1.2373 mm. Experimental results confirm that this unified modeling approach effectively overcomes the limitations of separate calibration schemes, significantly enhancing both precision and robustness, and providing a reliable computational model for surgical navigation systems that require high spatial accuracy without relying on ionizing radiation.

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Keywords

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