Improved Geometric Calibration Method for Thermal Sensors Using the Hough Transform Algorithm

Abstract

Non-metric thermal sensors have been out of calibration in the laboratory for an extended period of time and require calibration to adjust for the interior orientation parameters and lens distortions. To generate photogrammetric products with the desired degree of geometric precision, it is important to identify the geometric calibration parameters of the non-metric sensor in order to minimize the relative orientation error and resolve the bundle adjustment. The purpose of this research is to present a novel method for geometric calibration of non-metric thermal sensors as a necessary preprocessing step before producing photogrammetric products with the desired geometric precision. To geometrically calibrate the non-metric thermal sensor, the proposed method employs a calibration pattern in the form of a rectangular plate composed of hollow circular targets with symmetrical placement geometry. Hollow circles induce temperature differences, improving the contrast and sharpness of the thermal calibration pattern. Due to the thermal sensors' low spatial resolution and low contrast, circular targets appear as an ellipse in the image. For this reason, in this study, the Hough Transform method is utilized to fit and extract the exact two-dimensional coordinates of the focal center of elliptical targets in the image space. The reason for this is that the Hough Transform employs the parameters of the ellipse to fit it and does not require the entire extraction of its circumferential lines. In the method utilized in this study, the Collinearity Equation is used to compute the geometric calibration elements of the thermal sensor. Various experiments were undertaken to evaluate the proposed approach. The results of these tests, which were performed based on the criterion of Mean Reprojection Error per Image, evaluated the accuracy of the geometric calibration as 0.03 pixels. Additionally, when the proposed method for re-projecting the target´s focal point to the calibration pattern is used in conjunction with the estimated calibration parameters, the mean error between the actual image coordinates and the actual ground coordinates of the targets is reduced to 0.28 pixels when compared to the method of the equation of conic sections.