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Homography matrix estimation method based on adaptive genetic algorithm.

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Title: Homography matrix estimation method based on adaptive genetic algorithm.
Alternate Title: 基于自适应遗传算法的单应性矩阵估计方法.
Authors: Cheng, QIAN1, Zhifeng, ZHU1 zzf@ahut.edu.cn, Ke, YANG1, Tao, ZHANG1, Guotai, JI1
Source: Journal of Measurement Science & Instrumentation. Dec2025, Vol. 16 Issue 4, p558-568. 11p.
Subjects: Camera calibration, Genetic algorithms, Matrices (Mathematics), Estimation theory, Image registration, Calibration
Abstract (English): In camera calibration, accurate estimation of homography matrix between the world coordinates of the calibration board and its image coordinates is a key step in high-precision calibration of intrinsic camera parameters. The existing homography matrix estimation methods have problems such as dependence on thresholds, low computational efficiency, and initial model or sorting quality affecting results. In this paper, a homography matrix estimation method based on adaptive genetic algorithm was proposed. Firstly, a new circular grid calibration board was designed and the strategy of first sampling of data sets was optimized. Secondly, a mathematical model for the estimated homography matrix was established according to the adaptive genetic algorithm. Thereby the optimal homography matrix between the calibration board and its image was obtained. Finally, the intrinsic camera parameters were calculated based on Zhang’s calibration method. The experimental results show that compared with the results of three traditional estimation methods RANSAC, PROSAC, and LMEDS, the reprojection error of the images by our estimation method is reduced by about 4.11%—7.85%, 11.94%— 16.91%, and 10.19%—17.82%, respectively; and the average running time of the algorithm decreases by about 25.85%—37.47%, 11.99%—22.71%, and 46.50%—53.35%, respectively. In addition, the homography matrix estimation method in this paper was applied to camera calibration. The results show that compared with the traditional estimation method, the average accuracy of the camera during the calibration process increases by about 5.48%, 15.06%, and 11.47%, respectively; and the average calibration efficiency of the camera is improved by about 10.13%, 5.71%, and 14.26%, respectively. The homography matrix estimation method proposed in this paper not only obtained reliable results, but also had certain value and significance in improving the estimation accuracy and calculation efficiency in camera calibration. [ABSTRACT FROM AUTHOR]
Abstract (Chinese): 在相机标定中, 精确估计标定板世界坐标与其图像坐标之间的单应性矩阵是相机内参数高精度标定的关键步骤。现有的 单应性矩阵估计方法存在依赖阈值、计算效率低、初始模型或排序质量影响结果等问题。本文提出了一种基于自适应遗传算法的 单应性矩阵估计方法。首先, 设计了一种新型的圆形网格标定板, 并优化了匹配点对数据集初次抽样的策略。然后, 根据自适应 遗传算法建立估计单应性矩阵的数学模型, 从而获得标定板与其图像之间的最优单应性矩阵。最后, 结合张氏标定法计算出相机 内参数。实验结果表明: 基于自适应遗传算法的估计方法与传统的估计方法 RANSAC、 PROSAC 和 LMedS 相比, 图像的重投影 误差分别降低约 4. 11% −7. 85%, 11. 94% −16. 91%, 10. 19% −17. 82%。算法的平均运行时间分别减少约 25. 85% −37. 47%, 11. 99% −22. 71%, 46. 50% −53. 35%。另外, 将本文的单应性矩阵估计方法应用于相机的标定过程中, 对比结果显示: 该方法相 比 较 于 传 统 方 法, 相 机 在 标 定 过 程 中 的 平 均 精 度 分 别 提 高 约 5. 48%, 15. 06%, 11. 47%。 相 机 的 平 均 标 定 效 率 分 别 提 升 约 10. 13%, 5. 71%, 14. 26%。本文提出的单应性矩阵估计方法不仅能够得到可靠的结果, 而且对提升相机标定过程中的估计精度 和计算效率方面具有一定的价值和意义。 [ABSTRACT FROM AUTHOR]
Copyright of Journal of Measurement Science & Instrumentation is the property of Journal of Measurement Science & Instrumentation and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Homography matrix estimation method based on adaptive genetic algorithm.
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  Data: 基于自适应遗传算法的单应性矩阵估计方法.
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  Data: <searchLink fieldCode="AR" term="%22Cheng%2C+QIAN%22">Cheng, QIAN</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Zhifeng%2C+ZHU%22">Zhifeng, ZHU</searchLink><relatesTo>1</relatesTo><i> zzf@ahut.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ke%2C+YANG%22">Ke, YANG</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Tao%2C+ZHANG%22">Tao, ZHANG</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Guotai%2C+JI%22">Guotai, JI</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Measurement+Science+%26+Instrumentation%22">Journal of Measurement Science & Instrumentation</searchLink>. Dec2025, Vol. 16 Issue 4, p558-568. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Camera+calibration%22">Camera calibration</searchLink><br /><searchLink fieldCode="DE" term="%22Genetic+algorithms%22">Genetic algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Image+registration%22">Image registration</searchLink><br /><searchLink fieldCode="DE" term="%22Calibration%22">Calibration</searchLink>
– Name: Abstract
  Label: Abstract (English)
  Group: Ab
  Data: In camera calibration, accurate estimation of homography matrix between the world coordinates of the calibration board and its image coordinates is a key step in high-precision calibration of intrinsic camera parameters. The existing homography matrix estimation methods have problems such as dependence on thresholds, low computational efficiency, and initial model or sorting quality affecting results. In this paper, a homography matrix estimation method based on adaptive genetic algorithm was proposed. Firstly, a new circular grid calibration board was designed and the strategy of first sampling of data sets was optimized. Secondly, a mathematical model for the estimated homography matrix was established according to the adaptive genetic algorithm. Thereby the optimal homography matrix between the calibration board and its image was obtained. Finally, the intrinsic camera parameters were calculated based on Zhang’s calibration method. The experimental results show that compared with the results of three traditional estimation methods RANSAC, PROSAC, and LMEDS, the reprojection error of the images by our estimation method is reduced by about 4.11%—7.85%, 11.94%— 16.91%, and 10.19%—17.82%, respectively; and the average running time of the algorithm decreases by about 25.85%—37.47%, 11.99%—22.71%, and 46.50%—53.35%, respectively. In addition, the homography matrix estimation method in this paper was applied to camera calibration. The results show that compared with the traditional estimation method, the average accuracy of the camera during the calibration process increases by about 5.48%, 15.06%, and 11.47%, respectively; and the average calibration efficiency of the camera is improved by about 10.13%, 5.71%, and 14.26%, respectively. The homography matrix estimation method proposed in this paper not only obtained reliable results, but also had certain value and significance in improving the estimation accuracy and calculation efficiency in camera calibration. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (Chinese)
  Group: Ab
  Data: 在相机标定中, 精确估计标定板世界坐标与其图像坐标之间的单应性矩阵是相机内参数高精度标定的关键步骤。现有的 单应性矩阵估计方法存在依赖阈值、计算效率低、初始模型或排序质量影响结果等问题。本文提出了一种基于自适应遗传算法的 单应性矩阵估计方法。首先, 设计了一种新型的圆形网格标定板, 并优化了匹配点对数据集初次抽样的策略。然后, 根据自适应 遗传算法建立估计单应性矩阵的数学模型, 从而获得标定板与其图像之间的最优单应性矩阵。最后, 结合张氏标定法计算出相机 内参数。实验结果表明: 基于自适应遗传算法的估计方法与传统的估计方法 RANSAC、 PROSAC 和 LMedS 相比, 图像的重投影 误差分别降低约 4. 11% −7. 85%, 11. 94% −16. 91%, 10. 19% −17. 82%。算法的平均运行时间分别减少约 25. 85% −37. 47%, 11. 99% −22. 71%, 46. 50% −53. 35%。另外, 将本文的单应性矩阵估计方法应用于相机的标定过程中, 对比结果显示: 该方法相 比 较 于 传 统 方 法, 相 机 在 标 定 过 程 中 的 平 均 精 度 分 别 提 高 约 5. 48%, 15. 06%, 11. 47%。 相 机 的 平 均 标 定 效 率 分 别 提 升 约 10. 13%, 5. 71%, 14. 26%。本文提出的单应性矩阵估计方法不仅能够得到可靠的结果, 而且对提升相机标定过程中的估计精度 和计算效率方面具有一定的价值和意义。 [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Measurement Science & Instrumentation is the property of Journal of Measurement Science & Instrumentation and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.62756/jmsi.1674-8042.2025054
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        Text: English
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      – SubjectFull: Genetic algorithms
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      – SubjectFull: Matrices (Mathematics)
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      – SubjectFull: Estimation theory
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      – SubjectFull: Image registration
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      – SubjectFull: Calibration
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      – TitleFull: Homography matrix estimation method based on adaptive genetic algorithm.
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              M: 12
              Text: Dec2025
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