## 5 Feature Extraction and Matching  
In 2015, five leading feature extraction algorithms, SIFT, SURF, BRIEF, BRISK, and FREAK, were used to generate keypoint descriptors of radiographs to classify assessments of bone age [4]. After comparing the five algorithms, SIFT performed the best in terms of precision. Although there were increased extraction speeds for the other feature algorithms, there were also decreases in precision. In 2016, a survey was administered to evaluate object recognition methods based on local invariant features from a robotics perspective [3]. The evaluation results concluded that the best performing keypoint descriptor was SIFT because it is robust in real-world conditions. This paper primarily focuses on identification precision rather than identification speed. In this section, instead of illustrating all of the feature algorithms, we provide a brief review of the  
Figure 7: Illustration of width and height of the viewing range for the dodecahedron. (**a**) Width and height of viewing range; (**b**) Cross section of the sphere. most representative algorithm, specifically, the SIFT feature extraction and matching methods. Before extracting features, we convert the color images into YIQ color space. The features are extracted from the Y components. SIFT transforms images into scale-invariant coordinates and generates many features. The number of features is important for recognition. For reliable identification, at least three features must be correctly matched to identify small objects [10]. A large number of robust keypoints can be detected in a typical image. The keypoint descriptors are useful because they are distinct and are obtained by assembling a vector of local gradients. SIFT is widely used for extracting rotation, scale, and translation-invariant features from images. With geometric transformation-invariant SIFT keypoints, object recognition has an increased performance for feature matching. Generally, the matching procedure for a keypoint occurs by finding its closest neighbor, which is the keypoint with the least amount of distance. However, an additional measure is used to discard features that have weak matches. The distance \(d_{1}\) between a keypoint and its closest neighbor is compared to the distance \(d_{2}\) between the keypoint and its second-closest neighbor. The second-closest match is an estimate of the density of false matches, specifically an incorrect match [10]. To achieve a reliably matched keypoint, the \(d_{1}\) must be significantly less than the \(d_{2}\). The comparison is simply defined as \(\tau\times d_{1}<d_{2}\). When the threshold \(\tau\) is set to 3, the matched results for artwork are better than those that use the default value of 1.5. However, we found that this additional measure does not provide adequate effects for all types of keypoints for identifying artwork in the 360-degree images. Although this approach is helpful to the SIFT, it is not suitable for the other features that are discussed in this paper. Thus, it is used in conjunction with SIFT and not combined with the other features for evaluating identification. Figure 8b shows a digital image of the original artwork _The Annunciation_, which has a size of 4057 \(\times\) 1840. Figure 8a shows an ordinary photograph of the artwork that has a size of 3264 \(\times\) 2448 and was taken from a 23-inch monitor. Figure 9a-g show the matched keypoints from the SIFT, SURF, MSER, BRISK, FAST, HOG, and FREAK descriptors. For the HOG and FREAK descriptors, the keypoints were detected using the FAST and BRISK methods. The features are well matched because they were extracted from common pictures that are not affected by stitching and projection. In the experimental results section, we show the matched results with 360-degree images. Figure 8: Original image and ordinary photograph of _The Annunciation_. (**a**) Ordinary photograph; (**b**) Original image. Figure 9: _Cont_. Figure 9: Matched keypoints for the seven types of features.