Figure 1.
Flowchart of the automatic SORs reconstruction from point clouds.
Figure 1.
Flowchart of the automatic SORs reconstruction from point clouds.
Figure 2.
Two kinds of SORs. (a) A tall-thin type SOR and (b) a short-wide type SOR.
Figure 2.
Two kinds of SORs. (a) A tall-thin type SOR and (b) a short-wide type SOR.
Figure 3.
Rotation axis extraction for a short-wide SOR of a straw hat. (a) The point cloud of a straw hat with three axial directions, (b) Two parts of the point cloud divided by the plane according to axial direction 1, (c) Two parts of the point cloud divided by the plane according to axial direction 2, and (d) Two parts of the point cloud divided by the plane according to axial direction 3.
Figure 3.
Rotation axis extraction for a short-wide SOR of a straw hat. (a) The point cloud of a straw hat with three axial directions, (b) Two parts of the point cloud divided by the plane according to axial direction 1, (c) Two parts of the point cloud divided by the plane according to axial direction 2, and (d) Two parts of the point cloud divided by the plane according to axial direction 3.
Figure 4.
Circular contour fitting. (a) A point set of the top of a straw-hat, (b) Constructed TIN model, (c) Fitted circular contour by the RANSAC algorithm, and (d) Fitted circular contour only by the RANSAC algorithm.
Figure 4.
Circular contour fitting. (a) A point set of the top of a straw-hat, (b) Constructed TIN model, (c) Fitted circular contour by the RANSAC algorithm, and (d) Fitted circular contour only by the RANSAC algorithm.
Figure 5.
Original point-cloud (gray points) and the extracted projection profile of a straw hat (magenta points).
Figure 5.
Original point-cloud (gray points) and the extracted projection profile of a straw hat (magenta points).
Figure 6.
Schematic diagram of extracting the boundary X of the projection profile.
Figure 6.
Schematic diagram of extracting the boundary X of the projection profile.
Figure 7.
Overflow points processing. (a) The extracted point set of boundary X containing overflow points and (b) the processed point set of boundary X without overflow points.
Figure 7.
Overflow points processing. (a) The extracted point set of boundary X containing overflow points and (b) the processed point set of boundary X without overflow points.
Figure 8.
3D spatial data hyperfine modeling system.
Figure 8.
3D spatial data hyperfine modeling system.
Figure 9.
Reconstructed SOR of a cylinder. (a) A photo of the cylinder, (b) Original point cloud of the cylinder, (c) Reconstructed SOR of the cylinder by the curvature computation method, (d) Cross-section of the reconstructed SOR of the cylinder by the curvature computation method, (e) Reconstructed SOR of the cylinder by the proposed method, and (f) Cross-section of the reconstructed SOR of the cylinder by the proposed method.
Figure 9.
Reconstructed SOR of a cylinder. (a) A photo of the cylinder, (b) Original point cloud of the cylinder, (c) Reconstructed SOR of the cylinder by the curvature computation method, (d) Cross-section of the reconstructed SOR of the cylinder by the curvature computation method, (e) Reconstructed SOR of the cylinder by the proposed method, and (f) Cross-section of the reconstructed SOR of the cylinder by the proposed method.
Figure 10.
Reconstructed SOR of a frustum of a cone. (a) A photo of the frustum of a cone, (b) Original point cloud of the frustum of a cone, (c) Reconstructed SOR of the frustum of a cone by the curvature computation method, (d) Cross-section of the reconstructed SOR of the frustum of a cone by the curvature computation method, (e) Reconstructed SOR of the frustum of a cone by the proposed method, and (f) Cross-section of the reconstructed SOR of the frustum of a cone by the proposed method.
Figure 10.
Reconstructed SOR of a frustum of a cone. (a) A photo of the frustum of a cone, (b) Original point cloud of the frustum of a cone, (c) Reconstructed SOR of the frustum of a cone by the curvature computation method, (d) Cross-section of the reconstructed SOR of the frustum of a cone by the curvature computation method, (e) Reconstructed SOR of the frustum of a cone by the proposed method, and (f) Cross-section of the reconstructed SOR of the frustum of a cone by the proposed method.
Figure 11.
Reconstructed SOR of a vase. (a) A photo of the frustum of the vase, (b) Original point cloud of the vase, (c) Reconstructed SOR of the vase by the curvature computation method, (d) Cross-section of the reconstructed SOR of the vase by the curvature computation method, (e) Reconstructed SOR of the vase by the proposed method, and (f) Cross-section of the reconstructed SOR of the vase by the proposed method.
Figure 11.
Reconstructed SOR of a vase. (a) A photo of the frustum of the vase, (b) Original point cloud of the vase, (c) Reconstructed SOR of the vase by the curvature computation method, (d) Cross-section of the reconstructed SOR of the vase by the curvature computation method, (e) Reconstructed SOR of the vase by the proposed method, and (f) Cross-section of the reconstructed SOR of the vase by the proposed method.
Figure 12.
Reconstructed SOR of a pillar of an ancient building. (a) An image of the pillar of an ancient building, (b) Original point cloud of the pillar of an ancient building, (c) Reconstructed SOR of the pillar of an ancient building by the curvature computation method, (d) Cross-section of the reconstructed SOR of the pillar of an ancient building by the curvature computation method, (e) Reconstructed SOR of the pillar of an ancient building by the proposed method, and (f) Cross-section of the reconstructed SOR of the pillar of an ancient building by the proposed method.
Figure 12.
Reconstructed SOR of a pillar of an ancient building. (a) An image of the pillar of an ancient building, (b) Original point cloud of the pillar of an ancient building, (c) Reconstructed SOR of the pillar of an ancient building by the curvature computation method, (d) Cross-section of the reconstructed SOR of the pillar of an ancient building by the curvature computation method, (e) Reconstructed SOR of the pillar of an ancient building by the proposed method, and (f) Cross-section of the reconstructed SOR of the pillar of an ancient building by the proposed method.
Figure 13.
Reconstructed SOR of a pot. (a) A photo of the frustum of the pot, (b) Original point cloud of the pot, (c) Reconstructed SOR of the pot by the curvature computation method, (d) Cross-section of the reconstructed SOR of the pot by the curvature computation method, (e) Reconstructed SOR of the pot by the proposed method, and (f) Cross-section of the reconstructed SOR of the pot by the proposed method.
Figure 13.
Reconstructed SOR of a pot. (a) A photo of the frustum of the pot, (b) Original point cloud of the pot, (c) Reconstructed SOR of the pot by the curvature computation method, (d) Cross-section of the reconstructed SOR of the pot by the curvature computation method, (e) Reconstructed SOR of the pot by the proposed method, and (f) Cross-section of the reconstructed SOR of the pot by the proposed method.
Figure 14.
Reconstructed SOR of a ceramic. (a) A photo of the frustum of the ceramic, (b) Original point cloud of the ceramic, (c) Reconstructed SOR of the ceramic by the curvature computation method, (d) Cross-section of the reconstructed SOR of the ceramic by the curvature computation method, (e) Reconstructed SOR of the ceramic by the proposed method, and (f) Cross-section of the reconstructed SOR of the ceramic by the proposed method.
Figure 14.
Reconstructed SOR of a ceramic. (a) A photo of the frustum of the ceramic, (b) Original point cloud of the ceramic, (c) Reconstructed SOR of the ceramic by the curvature computation method, (d) Cross-section of the reconstructed SOR of the ceramic by the curvature computation method, (e) Reconstructed SOR of the ceramic by the proposed method, and (f) Cross-section of the reconstructed SOR of the ceramic by the proposed method.
Figure 15.
Reconstructed SOR of a pillar of an ancient building. (a) Reconstructed SOR by the Delaunay-based SOR reconstruction method, (b) Reconstructed SOR by the Poisson SOR reconstruction method, (c) Reconstructed SOR by the RBF SOR reconstruction method, and (d) Reconstructed SOR by the proposed method.
Figure 15.
Reconstructed SOR of a pillar of an ancient building. (a) Reconstructed SOR by the Delaunay-based SOR reconstruction method, (b) Reconstructed SOR by the Poisson SOR reconstruction method, (c) Reconstructed SOR by the RBF SOR reconstruction method, and (d) Reconstructed SOR by the proposed method.
Figure 16.
Reconstructed SOR of a simple SOR with different sampling rate. (a) Reconstructed SOR with a sampling rate of 100%, (b) Reconstructed SOR with a sampling rate of 75%, (c) Reconstructed SOR with a sampling rate of 50%, and (d) Reconstructed SOR with a sampling rate of 50%.
Figure 16.
Reconstructed SOR of a simple SOR with different sampling rate. (a) Reconstructed SOR with a sampling rate of 100%, (b) Reconstructed SOR with a sampling rate of 75%, (c) Reconstructed SOR with a sampling rate of 50%, and (d) Reconstructed SOR with a sampling rate of 50%.
Figure 17.
Reconstructed SOR of a tall-thin SOR with different sampling rate. (a) Reconstructed SOR with a sampling rate of 100%, (b) Reconstructed SOR with a sampling rate of 75%, (c) Reconstructed SOR with a sampling rate of 50%, and (d) Reconstructed SOR with a sampling rate of 50%.
Figure 17.
Reconstructed SOR of a tall-thin SOR with different sampling rate. (a) Reconstructed SOR with a sampling rate of 100%, (b) Reconstructed SOR with a sampling rate of 75%, (c) Reconstructed SOR with a sampling rate of 50%, and (d) Reconstructed SOR with a sampling rate of 50%.
Figure 18.
Reconstructed SOR of a short-wide SOR with different sampling rate. (a) Reconstructed SOR with a sampling rate of 100%, (b) Reconstructed SOR with a sampling rate of 75%, (c) Reconstructed SOR with a sampling rate of 50%, and (d) Reconstructed SOR with a sampling rate of 50%.
Figure 18.
Reconstructed SOR of a short-wide SOR with different sampling rate. (a) Reconstructed SOR with a sampling rate of 100%, (b) Reconstructed SOR with a sampling rate of 75%, (c) Reconstructed SOR with a sampling rate of 50%, and (d) Reconstructed SOR with a sampling rate of 50%.
Table 1.
Relative deviations of the three rotation axes from axial directions 1, 2, and 3 after quaternion rotation.
Table 1.
Relative deviations of the three rotation axes from axial directions 1, 2, and 3 after quaternion rotation.
Axial Direction | Number of Points M | Number of Points N | Number of Points M-N | Relative Deviation |
---|
1 | 21,668 | 15,620 | 6048 | 0.613 |
2 | 21,668 | 10,966 | 10,702 | 0.02 |
3 | 21,668 | 6043 | 15,625 | 1.586 |
Table 2.
Parameters comparison for the two reconstructed simple SORs between the curvature computation method and the proposed method.
Table 2.
Parameters comparison for the two reconstructed simple SORs between the curvature computation method and the proposed method.
Objects | Parameters | Curvature Computation Method | Proposed Method | Percentage Improvement |
---|
Cylinder | RMS (mm) | 0.42 | 0.29 | 30.1% |
Time (ms) | 2151 | 1039 | 51.7% |
Frustum of a cone | RMS (mm) | 0.56 | 0.29 | 41.1% |
Time (ms) | 1928 | 1001 | 48.1% |
Table 3.
Parameters comparison for the two reconstructed tall-thin SORs between the curvature computation method and the proposed method.
Table 3.
Parameters comparison for the two reconstructed tall-thin SORs between the curvature computation method and the proposed method.
Objects | Parameters | Curvature Computation Method | Proposed Method | Percentage Improvement |
---|
Vase | RMS (mm) | 0.35 | 0.24 | 31.4% |
Time (ms) | 2450 | 1835 | 25.1% |
Pillar | RMS (mm) | 0.43 | 0.30 | 30.2% |
Time (ms) | 1836 | 1349 | 26.5% |
Table 4.
Parameters comparison for the two reconstructed short-wide SORs between the curvature computation method and the proposed method.
Table 4.
Parameters comparison for the two reconstructed short-wide SORs between the curvature computation method and the proposed method.
Objects | Parameters | Curvature Computation Method | Proposed Method | Percentage Improvement |
---|
Pot | RMS (mm) | 0.51 | 0.21 | 58.8% |
Time (ms) | 4020 | 3012 | 25.1% |
Ceramic | RMS (mm) | 0.33 | 0.23 | 30.3% |
Time (ms) | 1548 | 1113 | 28.1% |
Table 5.
Parameters comparison for the reconstructed SOR of a pillar of an ancient building by the Delaunay-based method, Poisson method, RBF method, and the proposed method.
Table 5.
Parameters comparison for the reconstructed SOR of a pillar of an ancient building by the Delaunay-based method, Poisson method, RBF method, and the proposed method.
Parameters | Delaunay | Poisson | RBF | Proposed Method |
---|
RMS (mm) | 0.06 | 0.58 | 0.45 | 0.30 |
Time (ms) | 1936 | 1489 | 1523 | 1349 |
Table 6.
Accuracy comparison of the reconstructed SORs with different sampling rates for a simple SOR, a tall-thin SOR, and a short-wide SOR.
Table 6.
Accuracy comparison of the reconstructed SORs with different sampling rates for a simple SOR, a tall-thin SOR, and a short-wide SOR.
| Sampling Rate | 100% | 75% | 50% | 25% |
---|
Simple SOR | Number of points | 148,400 | 111,300 | 74,200 | 37,100 |
RMS (mm) | 0.28 | 0.88 | 3.9 | 4.5 |
Tall-thin SOR | Number of points | 36,114 | 27,085 | 18,057 | 9028 |
RMS (mm) | 0.32 | 0.85 | 3.77 | 4.81 |
Short-wide SOR | Number of points | 10,131 | 7598 | 5065 | 2532 |
RMS (mm) | 0.26 | 0.81 | 4.47 | 5.54 |