## 3 Results and Discussion
### Quantitative Evaluation and Comparison
#### 3.2.2 Comparison with Other MVS Algorithms  
Next, we quantitatively compare the proposed algorithm with other MVS algorithms. The data sets of _house model_ and _volleyball_ were selected for this purpose, since their ground truths and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Mean Complete** & **Mean Accuracy** & **Med Complete** & **Med Accuracy** \\ \hline SFM & 1.12 & 0.36 & 0.29 & 0.18 \\ Proposed & 1.00 & 0.28 & 0.28 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation results (mm) for _volleyball_ with different initial sparse seed extraction methods. Figure 8: Dense 3D point clouds of _volleyball_ expanded from sparse seed points extracted by the SFM and proposed methods. Each row from left to right: ground truth, dense points following the SFM method, dense points following the proposed method. The first row presents the entire images and the second row presents enlarged details within the green rectangles of the first row. Figure 7: Sparse seed points of _volleyball_ extracted by the SFM method and the proposed method. Each row from left to right: sparse seed points extracted by the SFM method, sparse seed points extracted by the proposed method. The second row presents the enlarged details of the corresponding red rectangles in the first row. reconstructed 3D point clouds by the DAISY algorithm [12], PMVS algorithm [16], and MRF algorithm [10] are provided by the DTU benchmarks [1; 2]. As shown in the first column of Figure 9, the point cloud reconstructed by the proposed algorithm looks clean and complete. Tiny structures such as the small antenna and chimney on the roof were clearly reconstructed. Even in the enlarged views shown in the second and third columns, the proposed algorithm provided rich details with high quality, very close to the ground truth. In contrast, as can be seen from the enlarged views in the second and the third columns, the 3D point clouds reconstructed by DAISY lost some distinctive structures; 3D point clouds reconstructed by PMVS contained many tiny faults; and 3D point clouds reconstructed by MRF consisted of extremely dense points deviating obviously away from the ground truth, resulting in low accuracy. The quantitative evaluation results for accuracy and completeness of _house model_ are listed in Table 4. The evaluation was performed for the same volumes, manually cut out from the ground truth and all reconstructed dense points where the ground truth was complete (the regions in the red rectangles in the first column in Figure 9). From Table 4, it can be seen that, for _house model_, the mean accuracy of the proposed algorithm, 0.28 mm, was the same as that of the DAISY algorithm and the mean complete of the proposed algorithm, 0.41 mm, was much better than the 0.54 mm of the DAISY algorithm and 0.45 mm of the PMVS algorithm. Although the MRF algorithm had the highest completeness, its accuracy was very low. The numbers of 3D points for _house model_ produced  
Figure 9: The ground truth and reconstructed 3D point clouds of _house model_. From top row to bottom row: ground truth, 3D points as reconstructed by DAISY, PMVS, MRF, and the proposed algorithm. The second column shows enlarged views of the corresponding green rectangles in the same row of the first column, whereas the third column shows enlarged views of the corresponding red rectangles in the same row of the second column. by DAISY, PMVS, MRF and the proposed algorithm were 1,000,782, 2,490,988, 21,918,711 and 2,029,048, respectively. These numbers reflect in some way the completeness of the algorithms. The ground truth and reconstructed 3D point clouds of _volleyball_ are shown in Figure 10. As shown in the first column, the 3D point cloud reconstructed by the proposed algorithm appears most complete. Even in the enlarged views in the second and the third columns, it still looks smooth and continuous, very close to the ground truth.