# Hash Indexing-Based Image Matching for 3D Reconstruction
## 4 Experimental Results
### Evaluation on the EdgeFoci Dataset  
The EdgeFoci dataset [65] is a benchmark for evaluating the performance of local feature detectors and descriptors. It consists of nine sequences and each sequence has a variant number of images. The samples of the EdgeFoci dataset are provided in Figure 5, they are Boat, Graffiti, Light, Dame, Obama, Painted Ladies, Rushmore, and Yosemite, respectively. The partially matching results are provided in Figure 6 where the BFM has the most incorrect matches. The RatioTest can reject some outliers from the matching collection produced by the BFM. The ENFT has more robustness than that of the BFM and KNN + RatioTest due to the use of a two-pass matching strategy. The HashMatch can generate the most accurate feature correspondences via Haar wavelet encoding. In the case of Notre Dame, it has symmetric structures and repeated features. The BFM produced the highest number of feature correspondences for Notre Dame, but there are too many incorrect matches in the collection of generated feature correspondences. The KNN + RatioTest also has outliers because its performance suffers from the constant threshold. If a big threshold is used by the KNN, it may produce more feature correspondences than that of the KNN with a small threshold but have more incorrect matches. Otherwise, The KNN with a small threshold can reject more incorrect feature correspondence; however, it can also reject some correct ones. Although the ENFT can filter many outliers from the collection of the initial feature correspondences by the two-pass matching strategy, a few incorrect matches also exist. However, the HashMatch has the best performance among the compared methods, providing the highest number of correct feature correspondences.  
In addition to the qualitative analysis, we also provided the statistical results (number of correct feature correspondences) for the compared methods. The results are listed in Table 1, where the higher the number of correct feature correspondences, the better the performance of the corresponding method. As the stated before, the KNN + RatioTest has the worst performance and the least amount of feature correspondences. The HashMatch has the highest number of feature correspondences (only inliers) on the whole dataset, demonstrating excellent performance. Finally, for each sequence, we recorded the computational time taken by the HashMatch. These times are depicted in Figure 7. The HashMatch can match ten thousand local features in a small amount of time. Moreover, we also provide the computational time for each method in Figure 8, where it can be seen that our proposed HashMatch has the fastest speed. To this end, both qualitative and quantitative results have proven the excellent performance of the HashMatch.  
Figure 5: Image pairs from the EdgeFoci dataset.  
Figure 6: Matching results for Image pairs from the EdgeFoci dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**Sequence**} \\ \cline{2-9}  & **Boat** & **Graffiti** & **Light** & **Notre Dame** & **Obama** & **Painted Ladies** & **Rushmore** & **Yosemite** \\ \hline KNN + RatioTest & 95 & 70 & 501 & 70 & 21 & 39 & 17 & 23 \\ ENFT [61] & 141 & 96 & 698 & 89 & 25 & 80 & 23 & 28 \\ MODS [62] & 101 & 83 & 564 & 142 & 42 & 47 & 18 & 32 \\ RepMatch [32] & 117 & 120 & 721 & 137 & 60 & 69 & 35 & 41 \\ CODE [63] & 98 & 109 & 706 & 110 & 58 & 53 & 29 & 47 \\ D2D + KNN [64] & 167 & 203 & 792 & 89 & 81 & 90 & 42 & 59 \\ R2D2 + KNN [15] & 130 & 178 & 807 & 120 & 90 & 83 & 53 & 62 \\ HashMatch (Ours) & 558 & 378 & 1263 & 307 & 328 & 407 & 286 & 613 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical results (correct matches) of the EdgeFoci dataset.  
Figure 7: Computational times taken by the HashMatch on the Edge Foci dataset. These times consist of two parts, namely, feature detection time and feature matching time.