Journal of Geodesy and Geoinformation Science ›› 2021, Vol. 4 ›› Issue (4): 34-45.doi: 10.11947/j.JGGS.2021.0403

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A New Photogrammetric Inspection Method for National Flags with Pentagrams

Ting On CHAN1,3(),Wei LANG1,2(),Tingting CHEN1,2,Zhiquan LIU3,Qianying ZHAO3,Chuyao LIAO1,Lupan ZHANG3   

  1. 1. School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China
    2. China Regional Coordinated Development and Rural Construction Institute, Sun Yat-sen University, Guangzhou 510275, China
    3. Guangdong Provincial Key Laboratory of Urbanization and Geo-simulation, School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2021-02-28 Accepted:2021-08-30 Online:2021-12-20 Published:2021-12-30
  • Contact: Wei LANG;
  • About author:Ting On CHAN (1981—),male, PhD, engaged in scientific and engineering research which includes laser scanning, photogrammetry, environmental monitoring, etc.E-mail:
  • Supported by:
    Science and Technology Program of Guangzhou, China(202102080287)


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