Homography matrix estimation method based on adaptive genetic algorithm

Abstract

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.

Keywords

camera calibration / intrinsic camera parameters / calibration board / homography matrix / reprojection error / Zhang’s calibration

References

[1] YANG S C, WEN J, WU S W, et al. Camera calibration with active standard Gaussian stripes for 3D measurement. Measurement, 2024, 233: 114793.

[2] ROMANO R, MAGGI D, HIROSE T, et al. Impact of lane keeping assist system camera misalignment on driver behavior. Journal of Intelligent Transportation Systems, 2021, 25(2): 157-169.

[3] BELL J J, MICARONI V, STRANO F, et al. Testing the impact of Remotely Operated Vehicle (ROVs) camera angle on community metrics of temperate mesophotic organisms: a 3D model-based approach. Ecological Informatics, 2023, 76: 102041.

[4] YU Y W, WANG K, DU L Q, et al. Matching point pair optimization registration method for point cloud model. Optics and Precision Engineering, 2023, 31(4): 503-516.

[5] LEE J, PARK E, YOO S. Multi-scale local implicit keypoint descriptor for keypoint matching//2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, June 17-24, 2023, Vancouver, BC, Canada. New York: IEEE, 2023: 6145-6154.

[6] DUAN Y, YU Y L, LIANG M Y. A weighted camera calibration algorithm with global solution of homography. Optics & Laser Technology, 2024, 174: 110585.

[7] FISCHLER M A, BOLLES R C. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Readings in Computer Vision, 1987: 726-740.

[8] CHUM O, MATAS J. Matching with PROSAC-progressive sample consensus//2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 20-25, 2005, San Diego, CA, USA. New York: IEEE, 2005: 220-226.

[9] WANG Y, WANG J Y, DU W H, et al. Point cloud plane fitting algorithm based on least square median. Laser & Optoelectronics Progress, 2023, 60(4): 247-254.

[10] LAI H J, MENG X Y, XIAO S D, et al. Homography matrix estimation optimization algorithm based on RANSAC. Transducer and Microsystem Technologies, 2023, 42(8): 135-138.

[11] ZHAO C Y, ZHAO H C. Accurate and robust feature-based homography estimation using HALF-SIFT and feature localization error weighting. Journal of Visual Communication and Image Representation, 2016, 40: 288-299.

[12] HORVÁTH L, RICE G, ZHAO Y Q. Change point analysis of covariance functions: a weighted cumulative sum approach. Journal of Multivariate Analysis, 2022, 189: 104877.

[13] TORR P H S, ZISSERMAN A. MLESAC: a new robust estimator with application to estimating image geometry. Computer Vision and Image Understanding, 2000, 78(1): 138-156.

[14] RAHDAN A, BOLANDI H, ABEDI M. Design of on-board calibration methods for a digital Sun sensor based on Levenberg-Marquardt algorithm and Kalman filters. Chinese Journal of Aeronautics, 2020, 33(1): 339-351.

[15] YAN N, MEI Y P, YANG T, et al. RTHEN: Unsupervised deep homography estimation based on dynamic attention for repetitive texture image stitching. Displays, 2024, 82: 102670.

[16] VADIGI S, SETHI K, MOHANTY D, et al. Federated reinforcement learning based intrusion detection system using dynamic attention mechanism. Journal of Information Security and Applications, 2023, 78: 103608.

[17] WANG X Q. Research on image stitching technology based on deep learning. Beijing: Beijing University of Posts and Telecommunications, 2023.

[18] ZHANG Z, KANG J H, SUN Z F, et al. An optimization measurement method of laser sensor based on perspective projection model. Optics Communications, 2022, 506: 127582.

[19] XIONG K, HE X R, WANG C X, et al. Calibration method of fisheye camera for high-precision collimation measurement. Infrared and Laser Engineering, 2024, 53(2): 117-127.

[20] YIN Y H, GAO D, DENG K N, et al. Vision-based autonomous robots calibration for large-size workspace using ArUco map and single camera systems. Precision Engineering, 2024, 90: 191-204.

[21] WANG Y P, CUI X W, LI Y. Research on radar grid coordinates and optical pixel coordinate mapping method based on unisometric transformation. Journal of Signal Processing, 2023, 39(7): 1233-1242.

[22] HUANG L, ZHANG Q C, ASUNDI A. Camera calibration with active phase target: improvement on feature detection and optimization. Optics Letters, 2013, 38(9): 1446-1448.

[23] XU Y J, GAO F, ZHANG Z H, et al. A calibration method for non-overlapping cameras based on mirrored absolute phase target. The International Journal of Advanced Manufacturing Technology, 2019, 104(1): 9-15.

[24] MAHMOUDINAZLOU S, KWON C. A hybrid genetic algorithm for the Min-max multiple traveling salesman problem. Computers & Operations Research, 2024, 162: 106455.

[25] MEI Z, GONG J C, GAO Y C, et al. Integrated optimization of structure and control systems based on a modified adaptive multi-population genetic algorithm. Journal of Central South University (Science and Technology), 2024, 55(2): 799-809.

[26] ZHANG Z. Flexible camera calibration by viewing a plane from unknown orientations//7th IEEE International Conference on Computer Vision, September 20-27, 1999, Kerkyra, Greece. New York: IEEE. 1999: 666-673.