## 1 Introduction
The NCC metric is often used to manage the registration of images that differ only by a translation. If images are deformed by complex transformations, the template window cannot cover the same regions of interest in the template and the inspection images, so several studies have proposed modified NCC metrics to circumvent the image registration problem that is associated with complex transformations. To allow image matching that is invariant to rotation, a ring-projection transformation was proposed that transforms a 2D gray-level image into a rotation-invariant representation, as in a one-dimensional (1D) ring-projection space [PERSON] and [PERSON] (2016). [PERSON] and [PERSON] [PERSON] and [PERSON] (2016) further used the ring-projection to represent a target template in wavelet-decomposed sub-images. Specifically, they used only pixels with high wavelet coefficients at low levels of resolution to compute the NCC between two separate templates. [PERSON] and [PERSON] and [PERSON] (2016) also used a two-stage image-alignment method that first locates candidates by comparing the vector sums for ring-projection and then matches these candidates using Zernike moments. Table 1 summarizes the features, approaches, and disadvantages of image-alignment methods for each category of method. The feature-based category uses edge maps, points of interest, shape contours, and invariant descriptors as alignment features. The embedded approaches are the Hausdorff distance, feature correspondence, the Zernike moment, and measurement of dissimilarity. The disadvantage of the feature-based method is the alignment error that occurs when there is inaccurate feature extraction. The area-based category uses image templates as matching features and cross correlation or ring projection to register the images. However, computation time can be excessive for applications that involve complex image transformation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Features** & **Approaches** & **Disadvantages** \\ \hline \multirow{4}{*}{Feature-based} & Edge maps & Hausdorff distance & \\  & Interest point & Feature correspondence & \\  & Invariant descriptors & Zernike moment & \\  & Orientation code & Dissimilarity measurement & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A summary of the image alignment methods. Although there have been many studies of area-based image alignment techniques, relatively few concern ring-projection alignment, which is a special type of area-based method. This method transforms a 2D gray-level image into a rotation-invariant representation in one-dimensional (1D) ring-projection space [12]. [PERSON] [15] used the ring-projection technique to represent templates in multi-channel images using a method that rapidly selects candidates by computing the NCC between color ring-projection information. The rotation is then estimated by rotating the template. To reduce the computational complexity, an elimination strategy that quickly detects a similar candidate is used [16]. In this approach, the rotation invariant ring-projection transformation is used to describe the image. Two stage-matching methods have also been proposed in which the candidates are selected using the vector sums of the ring projection at the first stage. Only a single candidate then undergoes Zernike-moment template matching using rotation-invariant properties [14; 17]. Radial projection has also been shown to be applicable to template matching [18]. Radial projection transforms a 2D gray-level image into 1D space and the scale invariance is constructed in the form of radial lines. However, ring-projection descriptors are specific to rotation-invariant matching. The rotation angle between two corresponding shapes in different images can also not be estimated in order to perform image alignment as is necessary for industrial inspection.