## 2 Related Works  
The method proposed in this research for measuring the spool's angular position is a typical application of vision-based measurement (VBM), which is a rapidly developing technology due to the increasing affordability and capability of cameras and computing hardware/software [4]. A VBM system may apply machine learning [5], pattern recognition [6], template matching [7], or other algorithms to identify and obtain measurement results from a captured image or a video stream. Template matching is a basic and popular method applied in many fields, including transportation [8], civil infrastructure [9], textiles [10], medicine [11], security [12], office settings [13], industrial automation [14], and the semiconductor industry [15]. The functions of visual template-matching systems are varied, including measurement of angular [16] and planar [17] positions, rotation speed [18], target detection [19], visual tracking [20], and so forth. Existing template-matching algorithms can be roughly grouped into two categories: area-based matching and feature-point matching. Area-based matching methods, sometimes called correlation-like methods, match the template and source image by moving the template image one pixel per step in an exhaustive way, calculating a metric of the similarity between the template and the particular area of the source image after each move, and selecting the template location which has the maximum metric value. The metric is based on a correlation criteria, which generally contains (1) a cross-correlation (CC), such as CC, normalized cross-correlation (NCC) [21], or zero-normalized cross-correlation (ZNCC) [22]; (2) the sum of absolute differences (SAD) and its variants, like zero mean sum of absolute differences (ZSAD) or optimized sum of absolute difference (OSAD) [23]; and (3) the sum of squared differences (SSD) [24], normalized sum of squared differences (NSSD), or zero-normalized sum of squared differences (ZNSSD) [25]. Basic area-based matching methods are computationally time consuming; thus, multiple accelerating strategies have been developed. [PERSON] and [PERSON] [26] proposed a fast pattern-matching algorithm based on the NCC criterion by combining an adaptive multilevel partition with the winner-update scheme, and achieved efficient template searching. [PERSON] [27] presented a dimension-reducing algorithm to accelerate computation by calculating the SSD in horizontal and vertical directions separately. [PERSON] et al. [28] proposed a method named A-MNS, based on majority neighbor similarity (MNS) and the annulus projection transformation (APT). These methods were found to be effective for color-rich or strongly contrasting images, which are quite different from those in the present study. Feature-point matching is another template-matching algorithm with high efficiency and both geometric (rotation and scale) and photometric (brightness and exposure) invariance [29]. Instead of metric calculation for all the possible locations, feature points matching detects \"special\" points in the template and source, and then finds point correspondences based on their local appearance. Many kinds of features have been proposed in previous works, such as Harris, FAST (features from accelerated segment test), Hessian, SIFT (scale-invariant feature transform), SURF (speeded-up robust features), BRIEF (binary robust independent elementary features), and BRISK (binary robust invariant scalable keypoints) [30]. Furthermore, [PERSON] et al. put forward the KAZE algorithm, which exploits non-linear scale space through non-linear diffusion filtering [31]. They also presented Accelerated-KAZE (AKAZE) which improves the KAZE by constructing the non-linear scale spaces using a computationally efficient framework called fast explicit diffusion (FED) [32]. However, it was found to be unreliable to measure spool angular position directly using a template-feature-point-matching method due to the multiple similar structures and shapes on the spool that can easily cause mismatching in this case.