## 4 The Proposed Method
### Fast Descriptor Matching
Step2: Compute feature descriptor for each located keypoint, if they are located in texture areas, then use Equations (11) and (12) to obtain robust description, otherwise, use binary test that defined in Equation (15) to describe the keypoints. Step3: Construct hash tables via Equation (20), the large set of JKD descriptors is distributed into many lattice cells independently. Step4: For \(\text{JKD}(k_{i})\) and \(\text{JKD}\big{(}k_{j}\big{)}\) the similarity can be measured by Equations (17) and 19. If those formulas are true, \(\text{JKD}(k_{i})\) and \(\text{JKD}\big{(}k_{j}\big{)}\) are considered matching. Step5: Repeat Step4 for any two keypoints in \(\left\{k_{1},k_{2},\cdots,k_{m}\right\}\) the resulting matching pairs is \(S=\left\{\left\langle k_{ij},k_{hc}\right\rangle\right|_{i}^{\prime},h\in[1,N]\right\}\). Step5: Repeat Step5: Repeat Step6 for any two keypoints in \(\left\{k_{1},k_{2},\cdots,k_{m}\right\}\) the resulting matching pairs is \(S=\left\{\left\langle k_{ij},k_{hc}\right\rangle\right|_{i}^{\prime},h\in[1,N]\right\}\). Step6: Repeat Step7: Repeat Step8: Repeat Step9: Repeat Step9: Repeat Step10: Repeat Step11: Repeat Step12: Repeat Step13: Repeat Step14: Repeat Step15: Repeat Step16: Repeat Step17: Repeat Step18: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step120: Repeat Step13: Repeat Step15: Repeat Step16 Repeat Step17: Repeat Step18: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step18: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step18: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step19: Repeat Step120

## 5 Experimental Results

The proposed SPFT is developed in C++, NVIDIA CUDA SDK 10.0 and OpenCV SDK 4.0, on a PC with Intel i7 CPU processor 3.40 GHz and 32.0 GB memory. We have evaluated the SPFT method on several challenging dataset, and have compared it with the state-of-the-art methods, including HPM [77], ROML [78], MODS [79], ENFT [35] and SuperPoint [80]. It should be noted that SuperPoint is deep learning-based approach to feature detection and descriptor computing, and is published on the European Conference on Computer Vision in 2018. ### Evaluation of Colosseum Dataset

We have evaluated the performance of the SPFT on the Colosseum dataset which is constructed by the authors of this paper. Samples of the Oxford benchmark are shown in Figure 6 where the lighting of every images is different to each other, and they also have many repeated features and structures. In the whole process of experiment, we use a standard evaluation metric to measure the performance for each method. The evaluation metric is defined as:

\[Precision=\frac{\#correct\ matches}{\#\text{{tentative\ matches}}} \tag{21}\]

where #_correct matches_ stands for the number of correct matches, #_tentative matches_ represents the number of raw matches, namely does not have any post-process steps such as RANSAC, cross-check and ratio-test. #### 5.1.1 Matching Precession

Figure 7 presents visualized results for each method, the green lines denotes correct matches. The HPM obtained the minimal number of feature correspondences. The number of feature correspondences from ROML is more than that of HPM. The number of feature correspondences of SuperPoint is the second place. The SPFT has the maximal number of feature correspondences. According to the common sense in the field of 3D reconstruction, the more the number of feature correspondences, the denser the point-cloud model from 3D reconstruction system. Thus, the SPFT can significantly increase the density of the reconstructed point-cloud model. Figure 6: Samples from Colosseum dataset.