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 Transformat...
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| author | Xuquan Ji Yonghong Zhang Huaqing Shang Lei Hu Xiaozhi Qi Wenyong Liu |
| author_facet | Xuquan Ji Yonghong Zhang Huaqing Shang Lei Hu Xiaozhi Qi Wenyong Liu |
| author_sort | Xuquan Ji |
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| description | 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. |
| format | Article |
| id | doaj-art-943f19d486294c5491004ea0ea8ebdce |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-943f19d486294c5491004ea0ea8ebdce2025-08-20T02:18:04ZengMDPI AGMathematics2227-73902025-04-01138135910.3390/math13081359DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D ReconstructionXuquan Ji0Yonghong Zhang1Huaqing Shang2Lei Hu3Xiaozhi Qi4Wenyong Liu5School of Biological Science and Medical Engineering, Beihang University, Beijing 100083, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 100083, ChinaShenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 100083, ChinaShenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, ChinaSchool of Biological Science and Medical Engineering, Beihang University, Beijing 100083, ChinaThe 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.https://www.mdpi.com/2227-7390/13/8/1359ultrasound probe calibrationDimensionality Reduction and Homography Transformation (DRHT)hybrid mathematical modelultrasonic three-dimensional reconstruction |
| spellingShingle | Xuquan Ji Yonghong Zhang Huaqing Shang Lei Hu Xiaozhi Qi Wenyong Liu DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction Mathematics ultrasound probe calibration Dimensionality Reduction and Homography Transformation (DRHT) hybrid mathematical model ultrasonic three-dimensional reconstruction |
| title | DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction |
| title_full | DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction |
| title_fullStr | DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction |
| title_full_unstemmed | DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction |
| title_short | DRHT: A Hybrid Mathematical Model for Accurate Ultrasound Probe Calibration and Efficient 3D Reconstruction |
| title_sort | drht a hybrid mathematical model for accurate ultrasound probe calibration and efficient 3d reconstruction |
| topic | ultrasound probe calibration Dimensionality Reduction and Homography Transformation (DRHT) hybrid mathematical model ultrasonic three-dimensional reconstruction |
| url | https://www.mdpi.com/2227-7390/13/8/1359 |
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