Numerical Computation-Based Position Estimation for QR Code Object Marker: Mathematical Model and Simulation

Providing position and orientation estimations from a two-dimensional (2D) image is challenging, as such images lack depth information between the target and the automation system. This paper proposes a numerical-based monocular positioning method to determine the position and orientation of a singl...

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Vydané v:Computation Ročník 10; číslo 9; s. 147
Hlavní autori: Teoh, Mooi Khee, Teo, Kenneth T. K., Yoong, Hou Pin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.08.2022
Predmet:
3D positioning
Apexes
Augmented reality
Automation
Calibration
Cameras
Codes
Estimation theory
Image processing
Localization
machine vision
Markers
Mathematical models
Methods
Numerical analysis
numerical method
Numerical models
Orientation
pinhole imaging
Pinholes
pose estimation
Position measurement
QR code marker
Robots
Rotation
Simulation
Vision systems
Malaysia
ISSN:2079-3197, 2079-3197
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Shrnutí:Providing position and orientation estimations from a two-dimensional (2D) image is challenging, as such images lack depth information between the target and the automation system. This paper proposes a numerical-based monocular positioning method to determine the position and orientation of a single quick response (QR) code object marker. The three-dimensional (3D) positional information can be extracted from the underdetermined system using the QR code’s four vertices as positioning points. This method uses the fundamental principles of the pinhole imaging theory and similar triangular rules to correspond the QR code’s corner points in a 3D environment to the 2D image. The numerical-based model developed with suitable guessing parameters and correct updating rules successfully determines the QR code marker’s position. At the same time, an inversed rotation matrix determines the QR code marker’s orientation. Then, the MATLAB platform simulates the proposed positioning model to identify the maximum rotation angles detectable at various locations using a single QR code image with the known QR code’s size and the camera’s focal length. The simulation results show that the proposed numerical model can measure the position and orientation of the tilted QR code marker within 30 iterations with great accuracy. Additionally, it can achieve no more than a two-degree angle calculation error and less than a five millimeter distance difference. Overall, more than 77.28% of the coordinate plane simulated shows a converged result. The simulation results are verified using the input value, and the method is also capable of experimental verification using a monocular camera system and QR code as the landmark.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2079-3197
2079-3197
DOI:10.3390/computation10090147