## 7 Performance Evaluation
### Experimental Results
Thus, when the number of matched features was less than five, the DSK was set to zero. The artwork that had the minimum number of nonzero DSK was selected as the identified artwork. Figure 17a shows the numbers of matched features between the artwork \"Mona Lisa\" and 360-degree images of 20 pieces of artwork displayed on the 79-inch monitor and located at a high distortion position. The octahedron-based rectilinear projection was applied to the 360-degree images. The number of matched features between the artwork _Mona Lisa_ and the 360-degree image that contained the same artwork was five, whereas the maximum number of matched features was six for the artwork _Cafe Terrace at Night_. However, the DSK between the artwork and the 360-degree image that contained the same artwork was 0.32 (in red circle), whereas the DSK between the artwork and the misidentified 360-degree image was 10.05, as shown in Figure 17b. Therefore, the misidentified results can be corrected and may further improve the identification precision for artwork that is located in the highly distorted position. Because SIFT performs best for precision, we show comparisons from before and after applying the DSK for the SIFT using the octahedron and dodecahedron-based methods. In Figure 18, the blue bars are the precision without using the DSK, and the red bars are the precision after applying the DSK. It is clear that the precision after using the DSK is larger than the precision without using the DSK for the H-distortion. Specifically, for the 79-inch monitor, the precision increases 20% and 15% for the octahedron and dodecahedron. For the L-distortion with the dodecahedron, there are no improvements in precision, whereas the precision increases approximately 5% for the octahedron. It is more efficient to combine the DSK with the octahedron. For the 79-inch monitor under the M-distortion using the dodecahedron, there is a decrease in precision after applying the DSK. Occasionally, when the 360-degree image contained the correct artwork, there were several false matches to irrelevant objects. Therefore, based on the mechanism of the DSK, there is a reduction in the similarity between two keypoint shapes. However, overall, the DSK enhances precision. Figure 17: Number of matched features and the DSK for the artwork _Mona Lisa_. (**a**) Number of matched features; (**b**) DSK. Based on the principle of the proposed approach, the features from the original artwork are extracted and stored in advance. Thus, to evaluate the computational complexity, we primarily focus on the feature extraction and matching times for the 360-degree images. Table 2 shows the average times (in seconds) for feature extraction and matching for one projected image. The SP and SH denote the pentagon and hexagon for the 32-hedron. The feature extraction time includes the time to generate a projected image. The extraction time is primarily based on the image size. Because the 360-degree image is large in size, the overall extraction speeds are not fast. Comparing the times for the different features reveals that the fastest feature is the FREAK, and the slowest is the SIFT. However, feature matching performs quickly for matching the projected image to an original artwork. Based on the amount of time for processing an entire polyhedron, the octahedron-based method performed better than the others.