Using Eigenvalues of Covariance Matrices for Automated Visual Inspection of Microdrills

Abstract

This paper proposes a translation, rotation, and template-free automated visual inspection scheme that detects microdrill defects using the eigenvalues of covariance matrices. We first derived the colour images of microdrills and extracted the boundary of the first facets. Then, the smaller eigenvalues of the covariance matrices of given regions of support were calculated for boundary representation, and they were thresholded to separate the boundaries into segments. The least square linear regression method was used to fit the segments into linear equations. Eventually, the defects were detected by three inspection rules that measure five features of microdrills including: gap distance, parallel, and enclosed angles, accordingly. The proposed scheme was implemented in C++ with a graphical user interface environment. Fifteen microdrills, digitized without alignment, were used to verify the proposed inspection process. Experimental results show that the proposed scheme reliably achieves the inspection of microdrills.

Optimizing Region of Support for Boundary-Based Corner Detection: A Statistic Approach

“…1 (with 0%, 10%, 20%, 30%, and 40% noise) for optimum k. that when the noise intensity is getting bigger, the optimum length of region of support is getting larger. This result is agree with the observations made by Tien and Yeh [15] that larger regions of support can be used to eliminate noise. Figure 6 depicts the detected corners of each noisy boundary in Fig.…”

“…Figure 1 simulates the influence of noise on a perfect image (a Chinese character generated by TrueType font size 240) of size 249 × 305 pixels by adding 10%, 20%, 30%, and 40% salt-andpepper noise, respectively; the corresponding boundaries are also disturbed by the added noise. As pointed out by Tien and Yeh [15], a larger region of support should be used to effectively eliminate the noise. However, as shown in Table 1, the average length of region of support determined by these two methods is getting shorter while the noise is getting more severe.…”

Dominant point detection for planar data

“…The authors claimed that the L S data points with sharper angles have larger S than smoother ones. The S of a corner point is usually a local maximum among the S of the points on the boundary segment [13]. According to Yahya [14], S is not only affected by the sharpness of curves but also by the size of support.…”

Revision of Using Eigenvalues of Covariance Matrices in Boundary-Based Corner Detection

“…Others use morphological operators to extract corners [5]. Boundary-based corner detectors, segmenting objects from an image first and then locating the discontinuities on the object boundaries [6]- [13], have been widely applied to spline curve fitting [14], [15], automated visual inspection [16]- [19], image segmentation [20]- [22], object recognition [23], etc.…”

“…Based on extensive tests, they found that small eigenvalues have good performance on detection and localization of corners for curved objects under different rotation and scale changes [12]. Since then, many studies have applied the small eigenvalues to detect corners directly [15], [16], [18], [21]. In addition, some others studies were also inspired by Tsai et al's small eigenvalues approach [6], [7], [13], [14], [17], [19], [22], [23].…”