C. Local Feature Matching

After the feature descriptors extracted by SURF-BRISK are 512-bit binary bit strings consisting of 0 and 1, the Hamming distance is used to measure similarity. Assuming that there are two descriptors of *S*<sup>1</sup> and *S*2, the Hamming distance is determined as

$$D\_{kl}(S\_1, S\_2) = \sum\_{i=1}^{512} (\mathbf{x}\_i \otimes y\_i),\tag{9}$$

where *S1* = *x1x1* ... *x512, S2* = *y1y2* ... *y512, x, y* and the value of x and y is 0 or 1. The smaller the value of *D*kd, the higher the matching rate, and vice versa. Therefore, the matching point pairs are obtained using the nearest-neighbor Hamming distance in the matching process.

Here, three descriptors, SURF, BRISK, and SURF-BRISK, are compared. Two tile images have been chosen for matching tests to compare the real-time and matching rate of these descriptors, as shown in Table 1 and Figure 5. Obviously, the SURF algorithm has the most matching points, the BRISK algorithm has the fastest matching, and the SURF-BRISK algorithm combines the advantages of both. The algorithm is faster than SURF and gets more matching points than BRISK.

**Table 1.** Detection times of different descriptors. Brisk: binary robust invariant scalable keypoints.


**Figure 5.** Matching results of different algorithms: (**a**) SURF; (**b**) BRISK; (**c**) SURF-BRISK.
