A New Photogrammetric Inspection Method for National Flags with Pentagrams

doi:10.11947/j.JGGS.2021.0403

Abstract

Abstract:

National flags are very important symbols of countries. They represent the countries’s authority and dignity of a country. However, there are some occasions where the flags were produced incorrectly(or as frauds) but still hung officially without a formal inspection. In this paper, we propose a photogrammetric inspection method for hanging national flags of China, for which only one single image is required to perform the inspection. The proposed method allows automatic estimation of the relative positions and orientation of the pentagrams, so exposure of inappropriate flags can be identified avoided. The method invokes a novel 2D geometric model of a pentagram (five-pointed star)to constrain an adjustment to estimate the camera’s exterior orientation parameters based on a single image of a statically hung flag. Conventional error parameters such as the radial distortion parameters are integrated into the pentagram model to form a calibration process to reduce the 3D reconstruction errors. Once the camera and the distortion parameters are estimated, the relative positions, orientations, and dimensions of all the five pentagrams can be readily computed with independent pentagram fitting so the flag quality can be verified using the national standard. More than 20 different hanging flags were captured to verify the proposed method. The results indicate that the method is flexible and accurate, with an accuracy of 1.1mm for the position/dimension, and 0.2° for the orientation on average. Since the method is based on the proposed geometric model of the pentagram, it can be readily adapted to form another system to verify other countries’ national flags containing more than one pentagram.

Key words: photogrammetry; camera calibration; pentagram; flag inspection

Ting On CHAN,Wei LANG,Tingting CHEN,Zhiquan LIU,Qianying ZHAO,Chuyao LIAO,Lupan ZHANG. A New Photogrammetric Inspection Method for National Flags with Pentagrams[J]. Journal of Geodesy and Geoinformation Science, 2021, 4(4): 34-45.

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	Before IOP calibration	After IOP calibration
Largest x image residual /mm/pix	1.35e-03/10.32	9.95e-04/7.61
Largest y image residual /mm/pix	1.77e-03/13.56	1.08e-03/8.26
RMSE/mm/pix	7.56e-04/5.79	5.70e-04/4.36

	Without APs	With APs
Average RMSE of Dataset 1 /mm/pix	4.86e-4/3.72	2.45e-4/1.87
Average RMSE of Dataset 2 /mm/pix	4.19e-4/3.21	3.47e-4/2.65
Average RMSE of Datasets 1 & 2/mm/pix	4.56e-4/3.49	2.91e-4/2.23

Positions and orientations	Position errors/m	Orientation errors/(°)	Dimension errors/m
1	0.0014	0.07	0.0011
2	0.0018	0.28	0.0008
3	0.0009	0.35	0.0014
4	0.0011	0.084	0.0002

	No. of flag
Pass	19
Failed	2

Small star	Position errors/m	Orientation errors/(°)	Dimension errors/m
1	0.001	0.482	0.001
2	0.002	1.355	0.002
3	0.004	1.077	0.002
4	0.003	0.016	0.001