基于L型靶标的相机标定及文物二维数字化

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

摘要/Abstract

摘要：

在可移动文物的二维数字化保护与研究中，需要提供文物正摄图及文物外形尺寸。相机标定不仅能校正成像畸变，还能提高精度。仿真分析表明，相机标定精度取决于靶标占视场大小，L型靶标具有和矩形靶标相近的精度。因此，提出基于L型靶标的相机标定方法及文物外形尺寸计算方法，设计了具有方向标志的L型靶标及靶点匹配方法，可根据文物成像视场选取合适靶标范围进行标定，保证了标定精度。由于设计的靶标不遮挡文物，且能同步完成相机标定与文物正摄图采集工作，精准获取相机内外参数，通过三维坐标数据实现文物尺寸的高精度计算。实验结果表明，L型靶标的靶点识别和匹配方法准确，相机标定参数能够有效校正文物图像畸变，不同文物的外形尺寸测量精度均优于0.2 mm，较比例尺方法精度提高超过一个数量级，能为可移动文物二维数字化记录和保护提供重要技术支持。

关键词: 相机标定, L型靶标, 图像畸变校正, 文物外形尺寸

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

中图分类号:

K87
TP391.41

赵敏, 王妞娜, 严潼颖, 朱凌建. 基于L型靶标的相机标定及文物二维数字化[J]. 图学学报, 2026, 47(2): 423-431.

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.

图/表 16

图1 针孔成像模型

Fig. 1 Pinhole imaging model

图2 靶标形状和靶点分布图((a) 矩形靶标；(b) L型靶标)

Fig. 2 Target shape and target distribution map ((a) Rectangular target distribution;(b) L-shaped target distribution)

图3 不同靶标形状对相机的标定精度影响

Fig. 3 The influence of different target shapes on the calibration accuracy of the camera

图4 靶标大小对标定结果的影响

Fig. 4 The influence of target size on calibration results

表1 靶标形状及大小对标定精度的影响

Table 1 The influence of target shape and size on calibration accuracy

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

图5 L型靶标结构

Fig. 5 L-type target structure

图6 靶点识别流程

Fig. 6 Feature dots identification process

图7 靶点匹配流程

Fig. 7 Feature dots matching process

图8 特征靶点坐标系

Fig. 8 Characteristic target coordinate system

图9 靶点识别和匹配((a) 正摄图；(b) 相机反转拍摄)

Fig. 9 Target identification and matching ((a) Orthographic image; (b) Camera reverse shooting)

图10 基于L型靶标的文物正摄图((a) 原图像；(b) 去畸变图像)

Fig. 10 Orthophoto of artifacts based on L-shaped target ((a) Original image; (b) De-distorted image)

表2 相机标定结果

Table 2 Camera calibration results

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

图11 文物正摄图

Fig. 11 Orthophoto image of artifacts

表3 不同方法计算文物外形尺寸结果

Table 3 Results of external dimensions calculation of artifacts by different methods

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

图12 不同类型文物((a) 文物盒；(b) 釉彩瓶)

Fig. 12 Different types of artifacts ((a) Artifacts box; (b) Glazed color bottle)

表4 不同类型文物外形尺寸测量结果

Table 4 Measurement results of different artifacts’ dimensions

文物	外形参数	实际值/mm	测量值 L/mm	误差 E/mm
文物盒	长	281.292	281.436	0.144
	宽	201.413	201.299	0.114
	高	121.108	121.229	0.121
釉彩瓶	高	255.285	255.421	0.136
	腹部直径	122.932	122.868	0.064
	最宽	140.088	140.213	0.125
	底部直径	96.009	95.961	0.048

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