Camera calibration and 2D digitalization of artifacts based on L-shaped target

doi:10.11996/JG.j.2095-302X.2026020423

Abstract

Abstract:

In the 2D digital conservation and research of movable artifacts, it is essential to provide orthographic images of the relics as well as their external dimensions. Camera calibration not only corrects imaging distortion but also enhances precision. Simulation analysis indicates that the accuracy of camera calibration depends on the proportion of the field of view occupied by the target, and an L-shaped target achieves a similar level of accuracy to the rectangular target. Therefore, a camera calibration method based on an L-shaped target and a calculation method for the external dimensions of artifacts were proposed. An L-shaped target with directional markers and a target point matching method were designed, enabling the selection of an appropriate target range for calibration according to the imaging field of view of the relics, thus ensuring calibration accuracy. Since the designed target did not block the relics, camera calibration and the acquisition of orthographic images of the relics could be conducted simultaneously. The internal and external parameters of the camera were obtained accurately, and high-precision calculations of the relics’ dimensions were realized using3D coordinate data. Experimental results demonstrated that the target-point recognition and matching method for L-shaped targets was accurate, that the camera calibration parameters effectively corrected image distortion in cultural relics, and that the measurement accuracy for the external dimensions of various relics consistently was below 0.2 mm, representing an improvement of over one order of magnitude compared to the scale method. The proposed approach provided significant technical support for the 2D digitization and preservation of movable cultural relics.

Key words: camera calibration, L-shaped target, image distortion correction, artifacts external dimensions

CLC Number:

K87
TP391.41

ZHAO Min, WANG Niuna, YAN Tongying, ZHU Lingjian. Camera calibration and 2D digitalization of artifacts based on L-shaped target[J]. Journal of Graphics, 2026, 47(2): 423-431.

Figures/Tables 16

References 19

[1]	谭冰钰, 薛艳敏, 钦松. 中国石窟文物数字化技术方法研究综述[J]. 图学学报, 2025, 46(3): 479-490. DOI
	TAN B Y, XUE Y M, QIN S. Review of digital technology methods for grottoes cultural relics in China[J]. Journal of Graphics, 2025, 46(3): 479-490 (in Chinese). DOI
[2]	刘欢. 对考古绘图方法的认识与比较[J]. 文物鉴定与鉴赏, 2022(18): 134-137.
	LIU H. Understanding and comparison of archaeological drawing methods[J]. Identification and Appreciation to Cultural Relics, 2022(18): 134-137 (in Chinese).
[3]	兰静. 考古文物绘图轮廓线提取及绘图流程研究[J]. 文物鉴定与鉴赏, 2022(11): 174-176.
	LAN J. Research on contour extraction and drawing process of archaeological relics drawing[J]. Identification and Appreciation to Cultural Relics, 2022(11): 174-176 (in Chinese).
[4]	马鸿藻. 考古器物绘图[M]. 北京: 北京大学出版社, 2008: 11.
	MA H Z. Drawing of archaeological objects[M]. Beijing: Peking University Press, 2008: 11 (in Chinese).
[5]	朱善银, 兪佑植. Picman图像分析技术在文物保护中的应用[J]. 文物鉴定与鉴赏, 2019(12): 94-95.
	ZHU S Y, YU Y Z. The application of Picman image analysis technology in cultural relics protection[J]. Identification and Appreciation to Cultural Relics, 2019(12): 94-95 (in Chinese).
[6]	林旭东, 张旭. 基于透视畸变矫正的高精度相机标定方法[J]. 激光与光电子学进展, 2023, 60(16): 1615004.
	LIN X D, ZHANG X. Accurate camera calibration method based on perspective distortion correction[J]. Laser & Optoelectronics Progress, 2023, 60(16): 1615004 (in Chinese).
[7]	ZHANG Z. A flexible new technique for camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(11): 1330-1334. DOI URL
[8]	WANG K, LIU C H, SHEN S J. Geometric calibration for cameras with inconsistent imaging capabilities[J]. Sensors, 2022, 22(7): 2739. DOI URL
[9]	郑冬梅, 宋文爱. 相机标定关键设备对标定精度的影响分析[J]. 图学学报, 2017, 38(2): 236-240. DOI
	ZHENG D M, SONG W A. Influence analysis of key equipments for camera calibration accuracy[J]. Journal of Graphics, 2017, 38(2): 236-240 (in Chinese). DOI
[10]	赵敏, 李晓港, 苏泽鹏, 等. 基于定向分层靶标的相机参数标定[J]. 光学学报, 2022, 42(16): 1612004.
	ZHAO M, LI X G, SU Z P, et al. Camera parameter calibration based on directional layered target[J]. Acta Optica Sinica, 2022, 42(16): 1612004 (in Chinese). DOI URL
[11]	WENG J, COHEN P, HERNIOU M. Camera calibration with distortion models and accuracy evaluation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(10): 965-980. DOI URL
[12]	王海, 杨延竹, 李恒. 摄像机畸变中心及畸变系数标定方法[J]. 机械设计与制造, 2024(8): 38-43.
	WANG H, YANG Y Z, LI H. Camera distortion coefficient and calibration method of distortion center[J]. Machinery Design & Manufacture, 2024(8): 38-43 (in Chinese).
[13]	ZHOU C M, ZHONG P F, LIU L, et al. Subpixel corner detection algorithm based on the plane chessboard[J]. Journal of Physics: Conference Series, 2024, 2741: 012008. DOI
[14]	陈泽勇, 吴丽君, 李乙. 应用于相机标定的亚像素棋盘角点检测[J]. 网络安全与数据治理, 2025, 44(4): 46-51.
	CHEN Z Y, WU L J, LI Y. Subpixel checkerboard corner detection for camera calibration[J]. Cyber Security and Data Governance, 2025, 44(4): 46-51 (in Chinese).
[15]	HARRIS C G, STEPHENS M. A combined corner and edge detector[C]// Proceedings of the Alvey Vision Conference. Manchester: Alvey Vision Club, 1988: 1-6.
[16]	康朝海, 洪立, 任伟建, 等. 基于亚像素边缘检测和圆心修正补偿的高精度相机标定方法[J]. 激光与光电子学进展, 2024, 61(8): 0811006.
	KANG C H, HONG L, REN W J, et al. High-precision camera calibration method based on subpixel edge detection and circularity correction compensation[J]. Laser & Optoelectronics Progress, 2024, 61(8): 0811006 (in Chinese).
[17]	陈圣峰, 陈兵, 刘坚. 基于边缘方向投影的棋盘格角点亚像素细化[J]. 光学学报, 2022, 42(8): 0815001.
	CHEN S F, CHEN B, LIU J. Checkerboard corners sub-pixel refinement based on edge direction projection[J]. Acta Optica Sinica, 2022, 42(8): 0815001 (in Chinese). DOI URL
[18]	国家文物局. WW/T 0114-2023 可移动文物二维数字化采集与加工[S]. 北京: 文物出版社, 2023.
	National Cultural Heritage Administration. WW/T 0114-2023 Two-dimensional digital acquisition and processing of movable cultural relics[S]. Beijing: Cultural Relics Press, 2023 (in Chinese).
[19]	中华人民共和国国家文物局. WW/T 0017-2013 馆藏文物登录规范[S]. 北京: 文物出版社, 2013.
	National Cultural Heritage Administration. WW/T 0017-2013 Specification for registration of cultural relics in the collection of cultural institutions[S]. Beijing: Cultural Relics Press, 2013 (in Chinese).

靶标	Std(f)/mm	Std(u₀) /pixel	Std(v₀) /pixel	Std(k₁)	Std(k₂)
L型靶标 240×240	0.038	7.72	7.87	0.028 8	0.432 6
矩形靶标240×240	0.034	5.55	4.21	0.025 2	0.398 4
L型靶标360×360	0.018	1.86	2.48	0.006 8	0.042 7

靶标	Std(f)/mm	Std(u₀) /pixel	Std(v₀) /pixel	Std(k₁)	Std(k₂)
L型靶标 240×240	0.038	7.72	7.87	0.028 8	0.432 6
矩形靶标240×240	0.034	5.55	4.21	0.025 2	0.398 4
L型靶标360×360	0.018	1.86	2.48	0.006 8	0.042 7

相机型号	焦距f /mm	主点(u₀, v₀) /pixel	径向畸变系数		切向畸变系数		重投影误差 ε/pixel
相机型号	焦距f /mm	主点(u₀, v₀) /pixel	k₁	k₂	p₁	p₂	重投影误差 ε/pixel
Sony	55.30	(3 182.1, 2 268.2)	-0.054 0	0.661 0	0.001 8	-0.008 8	0.16
Sony	19.13	(3 121.9, 2 092.0)	-0.025 0	0.038 0	0.000 1	-0.000 7	0.12
Canon	54.39	(1 302.9, 872.5)	-0.498 5	9.789 3	-0.001 2	-0.001 2	0.18

相机型号	焦距f /mm	主点(u₀, v₀) /pixel	径向畸变系数		切向畸变系数		重投影误差 ε/pixel
相机型号	焦距f /mm	主点(u₀, v₀) /pixel	k₁	k₂	p₁	p₂	重投影误差 ε/pixel
Sony	55.30	(3 182.1, 2 268.2)	-0.054 0	0.661 0	0.001 8	-0.008 8	0.16
Sony	19.13	(3 121.9, 2 092.0)	-0.025 0	0.038 0	0.000 1	-0.000 7	0.12
Canon	54.39	(1 302.9, 872.5)	-0.498 5	9.789 3	-0.001 2	-0.001 2	0.18

视场	文物参数	实际值/mm	测量值L/mm			误差E/mm
视场	文物参数	实际值/mm	I	II	III	I	II	III
部分靶标	高	197.492	197.594	199.866	199.053	0.102	2.374	1.161
部分靶标	瓶口	112.477	112.526	113.371	112.902	0.035	0.894	0.425
全部靶标	高	197.492	197.323	201.785	199.381	0.169	4.263	2.034
全部靶标	瓶口	112.477	112.539	113.814	113.122	0.062	1.337	0.635