Results and Discussions When the inner surface of holes is qualified for calibration, the distortion correction of six kinds of endoscope images with different apertures is carried out with the regular pentagram of known size as the experimental object. The average measurement error of six groups of experiments is 1.95%, and the measurement accuracy is high. In the experimental group, the average standard deviation of the side length of the pentagram after correction is 9.07, which indicates that there is still a large difference in the correction effect in different directions. The main reason is that the accuracy of image center detection is not high enough. It shows that the proposed correction method has good universality. When the inner surface of the hole does not meet the calibration conditions, the simulated defects of the slot hole, the threaded hole, and the inner surface are taken as experimental objects, and the images are corrected. The average measurement error of the experiment is about 6.75%, which is higher than that of the hole with calibration conditions, but it still has great application value for the actual needs of the industrial field.

Holes are the most common form of parts in machining and manufacturing. Enterprises have been long suffered from the inner surface defect detection of holes, especially the measurement of inner surface size. With the development of image processing technology and miniaturization of imaging elements, inner surface defect detection based on endoscopic images has been widely used in mechanical manufacturing, aerospace, and other fields. When endoscopes are applied to detect the inner surface defects, the real inner surface is parallel to the main optical axis of the lens and exhibits a circular scattering distribution on the imaging plane, which is not conducive to identifying the contour and size of the defects. Aiming at the difficulty in measuring the inner surface defect size of the hole, this paper proposes an endoscope image correction method to realize the inner surface size measurement.

According to the mapping relationship between spatial coordinates and phase plane coordinates in the endoscopic imaging system, the endoscopic image distortion is divided into circumferential distortion and axial distortion. In the case of adding geometric constraints in the application scene, the parameters in the correction model are simplified to a central coordinate and a nonlinear parameter, which improves the correction accuracy of the edge region of the endoscope image. The Hough transform and difference expansion are adopted to process the endoscopic image to realize the circumferential correction, and the axial correction is performed by pixel calibration and nonlinear stretching of the circumferential corrected image. The paper utilizes the neural network algorithm to fit the axial correction function including the relative positions of pixels and apertures based on the calibration experiments of different apertures, thus overcoming the dependence of the axial correction on the calibration results. Additionally, the measurement of inner surface defects of holes without calibration conditions is obtained.

In this paper, a method for distortion correction and measurement of in-hole images based on the endoscopic imaging principle is proposed. The method of circumferential correction and axial correction is adopted to restore the endoscopic image to an orthographic image that conforms to the visual habit and measure the size. The feasibility of the method is verified by experiments and the factors affecting the detection accuracy are discussed. The specific conclusions are as follows. 1) The method based on image processing can effectively realize the endoscopic image correction and the defect measurement, and the accuracy is high. 2) The measurement method is not sensitive to the aperture, and the measurement accuracy is not affected by the test object, so the method has good applicability. 3) The coordinates of the image center and the axial distance growth function are the key parameters that affect the accuracy of image correction and defect measurement. For further improvement of detection accuracy, a textured calibration paper can be placed on the inner surface of the hole during the detection to improve the accuracy of circle center detection and axial distance growth function fitting. As the proposed correction method has good versatility and high accuracy, it can be used for automatic detection and intelligent detection of holes and pipelines.