Manuscript received March 1, 2025; revised April 16, 2025; accepted August 1, 2025; published December 19, 2025.

Abstract—This paper investigates a two-Dimensional (2-D) coordinate calibration method, specifically, the quadratic transformation for machine vision systems integrated with robot arms. The objective is to establish a precise relationship between image coordinates and the world coordinate system, enabling data from the world coordinates to be used for robot arm manipulation. The calibration process was performed using a pattern target featuring 13 black circles along the OX-direction and 12 black circles along the OY-direction, each with a radius of 10 mm. The distances between the centers of the circles were 22 mm in the OX-direction and 16 mm in the OY-direction. Image processing and machine vision techniques were employed to determine the image coordinates of these calibration points. The calibration results showed that the positive maximum deviation is 0.656 mm and 0.648 mm in the OX-direction and OYdirection, respectively. The negative maximum deviation is −0.690 mm and −0.660 mm in the OX-direction and OYdirection, respectively. The experimental results demonstrate that the proposed method is both effective and accurate in determining object positions within real-world coordinates, supporting precise robot arm manipulation.

Keywords—coordinate calibration, image processing, machine vision, two Dimension (2-D), robot arm

Cite: Ngoc-Vu Ngo, "Study of 2-D Coordinate Calibration Method for Machine Vision Systems Using Regression Analysis," Journal of Image and Graphics, Vol. 13, No. 6, pp. 645-650, 2025.

Copyright © 2025 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC-BY-4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.