## 7 Performance Evaluation
### Experimental Results
The position of the artwork in Figure 14a is a little closer to the South Pole than the position of the artwork in Figures 12a and 13a. There are no matched features. In Figure 14b,c, there are a few false matches after shifting the artwork towards the south. These three matched results suggest that the probability of a false match will increase when the artwork is shifted further away from the Equator, because there is an increase in distortion. Based on the previous experiments, it is clear that the features are difficult to match directly using the 360-degree image when the artwork is positioned away from the Equator. To improve the feature matching, we used the proposed polyhedron-based rectilinear projection to divide and project the  
Figure 14: Matched results for the 23-inch monitor for three types of distortions. (**a**) Matched results for low distortion; (**b**) Matched results for middle distortion; (**c**) Matched results for high distortion. Figure 13: Matched results for the 32-inch monitor for three types of distortions. (**a**) Matched results for low distortion; (**b**) Matched results for middle distortion; (**c**) Matched results for high distortion. 360-degree image into several images. We applied this method to several of the 360-degree images that were previously shown. Figure 15a shows a projected image of Figure 12c using the 32-hedron. There are four correctly matched features. Figure 15b shows a projected image of Figure 13b using the octahedron. Although there are four matched features, one is a false match. Figure 15c shows a projected image of Figure 14b using the dodecahedron. There are three correctly matched features and an almost matched feature. The feature matching is improved from the no match results to at least three correct matches. Clearly, there are significant improvements in feature matching. After matching the features from the artwork, the precision of the artwork identification is automatically computed based on the matched results without artificial participation. An experiment to compare precision was conducted with the following goals: (1) to evaluate the effects of the number and sizes of the polygons on precision; (2) to evaluate the effects of the DSK on precision; and (3) to determine whether the proposed method increases the precision of the artwork identification. First, we evaluated precision based on the number of matched features. Each of the divided \(n\) images from a 360-degree image was matched to the original artwork images. The maximum number of matched features among the \(n\) images represented the similarity between the 360-degree image and the original artwork. The original artwork with the maximum number was selected as the identified artwork. Precision was computed by dividing the number of correctly identified artwork by the total number of artwork. Figure 16a-u show the precision of the artwork identification for seven types of features: SIFT, SURF, FAST, BRISK, MSER, HOG, and FREAK. The \(x\)-axis denotes the level of distortion,  
Figure 15: Projected images using the three types of polyhedrons. (**a**) A projected image using the 32-hedron; (**b**) A projected image using the octahedron; (**c**) A projected image using the dodecahedron. which is represented by high (H), middle (M), and low (L), and is based on the distance between the artwork and the Equator. The \(y\)-axis denotes the percentage of precision. The acronyms N, O, D, and S denote no-projection, octahedron, dodecahedron, and 32-hedron (soccer ball). Figure 16: _Cont._  
Comparing the precisions for the blue line N from the seven features, it is clear that the SIFT is the most robust feature for remedying distortion of the 360-degree image. The precision for identifying artwork that was located at the position of L-distortion without using the proposed method for the 79-inch monitor (79-SIFT-N-L) is 95%, which is the highest value for directly matching the features of 360-degree images to those from the original images.