PointCNT: A One-Stage Point Cloud Registration Approach Based on Complex Network Theory
Abstract
:1. Introduction
- (1)
- An efficient, high-precision and end-to-end one-stage point cloud registration framework is proposed.
- (2)
- A deep learning network design method based on complex network theory is proposed, and a multipath feature extraction network based on the above method for point clouds is designed.
- (3)
- A self-supervised module is introduced to improve the feature extraction ability of the network.
- (4)
- GBSelf-attention and FBCorss-attention based on nonlocal neural networks are designed.
2. Related Work
2.1. Traditional Registration Methods
2.2. Learning-Based Two-Stage Registration Methods
2.3. Learning-Based One-Stage Registration Methods
3. PointCNT
3.1. Feature Extraction Module
3.2. Feature Embedding Module
3.2.1. GBSelf-Attention
3.2.2. Coordinate Embedding
3.2.3. Distance Embedding
3.3. Feature Fusion Module
3.4. Registration Module
3.5. Loss Function
4. Experiments and Results
4.1. Implementation Details
4.1.1. Dataset Used in the Experiments
4.1.2. Evaluation Metrics
4.2. Model Evaluation Experiment
4.2.1. Train and Test on Same Object Categories
4.2.2. Train and Test on Different Object Categories
4.2.3. Gaussian Noise Experiments
4.2.4. Partial Overlap Experiments
4.2.5. Effectiveness of PointCNT
4.3. Ablation Experiments
4.4. Effectiveness of ComKP-CNN
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
2D | Two-Dimensional |
3D | Three-Dimensional |
3DRegNet | Deep Neural Network for 3D Point Registration |
3Dsc | 3D Shape Context |
4PCS | 4-Points Congruent Sets |
ANNs | Artificial Neural Networks |
CAD | Computer-Aided Design |
ComKP-CNN | Complex Kernel Point Convolution Neural Network |
ConvBlock | KPConv Block |
DCP | Deep Closest Point |
DeepVCP | Deep Virtual Corresponding Points |
DGR | Deep Global Registration |
FBCross-attention | Feature-based Cross-attention |
FMR | Feature-Metric Registration |
FPFH | Fast Point Feature Histogram |
GBSelf-attention | Geometric-based Self-attention |
GeoTransformer | Geometric Transformer |
Go-ICP | A Globally Optimal Solution to 3D ICP Point-set Registration |
GPU | Graphic Processing Unit |
ICP | Iterative Closest Point |
KP-CNN | Kernel Point Convolution Neural Network |
KPConv | Kernel Point Convolution |
LiDAR | Light Detection and Ranging |
LK | Lucas–Kanade Algorithm |
MLP | Multilayer Perceptron |
NDT | Normal Distributions Transform |
PCA | Principal Component Analysis |
PCRNet | Point Cloud Registration Network using PointNet Encoding |
PFH | Point Feature Histogram |
PointCNT | A One-Stage Point Cloud Registration Approach Based on Complex |
Network Theory | |
PointDSC | Robust Point Cloud Registration using Deep Spatial Consistency |
PointNetLK | Robust and Efficient Point Cloud Registration using PointNet |
PRNet | Partial Registration Network |
RANSAC | Random Sample Consensus |
ResBlock | Residual Blocks |
RGM | Robust Point Cloud Registration Framework Based on Deep Graph Matching |
RR | Registration Recall |
RRE | Relative Rotation Error |
RTE | Relative Translation Error |
SVD | Singular Value Decomposition |
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Method | Category | Proposed Year | Advantage | Disadvantage |
---|---|---|---|---|
ICP | Traditional Registration Method | 1992 | No need for a large amount of data for training. | Sensitive to the initial position of the point cloud and prone to falling into local optima. |
Go-ICP | 2016 | Adopting a global solution for higher registration accuracy. | Running speed is very slow. | |
DCP | Learning-based Two-stage Method | 2019 | Has good robustness to noise. | Not applicable for partial overlap. |
PointDSC | 2021 | High registration accuracy, suitable for partial overlap. | Slow running speed, requires additional algorithms to find corresponding points. | |
GeoTransformer | 2022 | High registration accuracy, suitable for partial overlap, without the need for additional algorithms to find corresponding points. | Slow running speed, registration accuracy constrained by key point matching. | |
PointNetLK | Learning-based One-stage Method | 2019 | Applying deep learning to point cloud registration for the first time. | Low registration accuracy, robustness and poor generalization. |
PCRNet | 2019 | Has good robustness to noise, is an end-to-end model, and runs fast. | The model has a simple structure and low registration accuracy. | |
FMR | 2020 | The unsupervised learning method is used to extract point cloud features, and the inverse synthesis algorithm is used to calculate the transformation matrix. | Poor registration performance when applied to point clouds with only partial overlap. |
DNN | Average Path Length | Clustering Coefficient | |
---|---|---|---|
DNN for images | VGG16 | 5.647 | 0 |
ResNet50 | 6.93 | 0 | |
DNN for point clouds | KP-CNN | 3.972 | 0 |
ComKP-CNN | 1.597 | 0.684 |
Initial Angle (°) | ICP | PointNetLK | PCRNet | FMR | DCP | GeoTransformer | PointDSC | PointCNT (Ours) | |
---|---|---|---|---|---|---|---|---|---|
RRE | 0 | 9.0583 | 0.0291 | 0.0867 | 0.0559 | 0.0484 | 0.0341 | 0.0574 | 0.0081 |
10 | 11.1343 | 3.1020 | 2.1663 | 1.5260 | 0.6368 | 0.6518 | 0.5333 | 0.5488 | |
20 | 12.0865 | 5.1491 | 3.1363 | 2.6720 | 2.1669 | 1.1784 | 1.0502 | 2.1426 | |
30 | 13.1300 | 6.0747 | 4.0494 | 3.1946 | 2.0129 | 2.0468 | 1.1013 | 2.5567 | |
40 | 16.0468 | 7.0898 | 6.0083 | 3.1537 | 2.6155 | 2.0655 | 1.5227 | 3.1776 | |
50 | 20.1213 | 10.0190 | 8.0598 | 4.0932 | 4.1018 | 3.6256 | 1.8021 | 3.4471 | |
60 | 31.1141 | 16.1352 | 9.0943 | 6.0841 | 4.3775 | 4.0737 | 2.5845 | 4.0157 | |
70 | 37.1181 | 32.1661 | 13.0590 | 10.0162 | 7.1807 | 4.0254 | 3.0133 | 8.1355 | |
80 | 56.0147 | 58.1466 | 30.1745 | 42.0883 | 12.1429 | 5.1880 | 4.0809 | 12.1752 | |
RTE | 0 | 0.0752 | 0.0001 | 0.0001 | 0.0003 | 0.0003 | 0.0001 | 0.0002 | 0.0002 |
10 | 0.0702 | 0.0031 | 0.0031 | 0.0031 | 0.0020 | 0.0011 | 0.0002 | 0.0021 | |
20 | 0.0653 | 0.0041 | 0.0031 | 0.0021 | 0.0011 | 0.0020 | 0.0012 | 0.0021 | |
30 | 0.0661 | 0.0062 | 0.0041 | 0.0031 | 0.0018 | 0.0012 | 0.0010 | 0.0031 | |
40 | 0.0801 | 0.0080 | 0.0062 | 0.0050 | 0.0033 | 0.0018 | 0.0020 | 0.0037 | |
50 | 0.0903 | 0.0102 | 0.0090 | 0.0075 | 0.0043 | 0.0031 | 0.0017 | 0.0053 | |
60 | 0.1000 | 0.0202 | 0.0171 | 0.0121 | 0.0083 | 0.0047 | 0.0033 | 0.0083 | |
70 | 0.1201 | 0.0402 | 0.0251 | 0.0402 | 0.0111 | 0.0051 | 0.0042 | 0.0122 | |
80 | 0.1300 | 0.0701 | 0.0452 | 0.0601 | 0.0141 | 0.0102 | 0.0072 | 0.0140 |
Initial Angle (°) | ICP | PointNetLK | PCRNet | FMR | DCP | GeoTransformer | PointDSC | PointCNT (Ours) | |
---|---|---|---|---|---|---|---|---|---|
RRE | 0 | 9.0959 | 0.1845 | 0.1469 | 0.0092 | 0.0133 | 0.0554 | 0.1145 | 0.0278 |
10 | 11.0771 | 3.1107 | 3.1902 | 1.6782 | 0.7943 | 0.5084 | 1.1477 | 1.0007 | |
20 | 12.0457 | 5.6493 | 3.0634 | 2.6482 | 2.1269 | 1.1253 | 1.1978 | 2.3915 | |
30 | 13.0583 | 7.0153 | 5.1618 | 3.0255 | 2.3756 | 2.4167 | 1.3391 | 2.6777 | |
40 | 16.0784 | 8.1973 | 6.9155 | 3.2291 | 3.1534 | 3.0080 | 1.7222 | 3.0906 | |
50 | 20.0064 | 12.1962 | 9.0828 | 8.1173 | 4.0734 | 3.8179 | 2.1880 | 5.1831 | |
60 | 31.1160 | 17.0211 | 13.1846 | 15.0505 | 4.6581 | 4.0699 | 2.5154 | 5.3267 | |
70 | 37.1035 | 33.1767 | 20.1443 | 28.1324 | 8.1459 | 4.0913 | 3.5691 | 9.0556 | |
80 | 56.0563 | 62.0186 | 34.0484 | 39.1745 | 12.1727 | 6.1058 | 4.1685 | 13.0916 | |
RTE | 0 | 0.0749 | 0.0001 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
10 | 0.0699 | 0.0030 | 0.0029 | 0.0020 | 0.0020 | 0.0010 | 0.0000 | 0.0022 | |
20 | 0.0650 | 0.0041 | 0.0029 | 0.0019 | 0.0014 | 0.0021 | 0.0011 | 0.0020 | |
30 | 0.0659 | 0.0070 | 0.0050 | 0.0036 | 0.0018 | 0.0014 | 0.0009 | 0.0033 | |
40 | 0.0799 | 0.0090 | 0.0080 | 0.0044 | 0.0034 | 0.0016 | 0.0024 | 0.0037 | |
50 | 0.0901 | 0.0130 | 0.0119 | 0.0079 | 0.0050 | 0.0036 | 0.0017 | 0.0055 | |
60 | 0.1185 | 0.0251 | 0.0190 | 0.0150 | 0.0079 | 0.0050 | 0.0031 | 0.0110 | |
70 | 0.1150 | 0.0459 | 0.0300 | 0.0501 | 0.0130 | 0.0060 | 0.0045 | 0.0140 | |
80 | 0.1271 | 0.0750 | 0.0549 | 0.0701 | 0.0169 | 0.0120 | 0.0079 | 0.0181 |
Gaussian Standard Deviation | 0 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | |
---|---|---|---|---|---|---|---|
RRE | 0 | 0.0029 | 0.0123 | 0.0133 | 0.0125 | 0.0071 | 0.0002 |
10 | 0.5095 | 0.4869 | 0.5851 | 0.7079 | 0.6462 | 0.6709 | |
20 | 2.0118 | 2.1917 | 2.1138 | 2.3090 | 2.2119 | 2.3873 | |
30 | 2.5086 | 2.5101 | 2.6973 | 2.6055 | 2.7947 | 2.6089 | |
40 | 3.0057 | 3.4008 | 3.1896 | 3.5051 | 3.4001 | 3.1924 | |
50 | 3.3896 | 3.6013 | 3.6986 | 3.4945 | 3.7084 | 3.7896 | |
60 | 3.9989 | 4.2122 | 4.3876 | 4.1903 | 4.4972 | 4.5954 | |
70 | 7.9855 | 8.3915 | 8.1942 | 8.4931 | 8.7858 | 8.6007 | |
80 | 11.9947 | 13.0138 | 13.0043 | 13.4954 | 13.1888 | 13.7911 | |
RTE | 0 | 0.0000 | 0.0001 | 0.0000 | 0.0001 | 0.0000 | 0.0001 |
10 | 0.0020 | 0.0020 | 0.0017 | 0.0021 | 0.0021 | 0.0024 | |
20 | 0.0019 | 0.0022 | 0.0025 | 0.0024 | 0.0024 | 0.0026 | |
30 | 0.0029 | 0.0029 | 0.0035 | 0.0038 | 0.0036 | 0.0036 | |
40 | 0.0036 | 0.0039 | 0.0036 | 0.0037 | 0.0040 | 0.0042 | |
50 | 0.0051 | 0.0053 | 0.0054 | 0.0054 | 0.0055 | 0.0056 | |
60 | 0.0082 | 0.0084 | 0.0083 | 0.0083 | 0.0083 | 0.0084 | |
70 | 0.0119 | 0.0118 | 0.0130 | 0.0133 | 0.0125 | 0.0135 | |
80 | 0.0143 | 0.0155 | 0.0150 | 0.0152 | 0.0161 | 0.0161 |
Model | RRE (°) | RTE | RR (%) | Time (s) |
---|---|---|---|---|
ICP | 17.3752 | 0.0253 | 82.3 | 0.12 |
PointNetLK | 17.3752 | 0.0253 | 82.3 | 0.12 |
PCRNet | 9.5863 | 0.0229 | 85.7 | 0.16 |
FMR | 8.8724 | 0.0183 | 88.2 | 0.08 |
DCP | 4.7283 | 0.0067 | 95.2 | 0.21 |
GeoTransformer | 3.6878 | 0.0042 | 97.1 | 0.23 |
PointDSC | 3.4586 | 0.0036 | 97.3 | 0.24 |
PointCNT (Ours) | 4.5128 | 0.0064 | 96.4 | 0.15 |
Dataset | RRE (°) | RTE (cm) | RR (%) |
---|---|---|---|
3DMatch | 0.3258 | 7.3854 | 93.6 |
KITTI | 0.2614 | 7.9368 | 97.2 |
CK | SS | CE | DE | FB | MP | AP | RQ | RM | RRE (°) | RTE | RR (%) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
baseline | ✓ | ✓ | 6.7322 | 0.0135 | 85.9 | |||||||
CK | ✓ | ✓ | ✓ | 5.3264 | 0.0083 | 89.3 | ||||||
SS | ✓ | ✓ | ✓ | 5.7217 | 0.0087 | 87.4 | ||||||
CE | ✓ | ✓ | ✓ | 5.6429 | 0.0086 | 87.6 | ||||||
DE | ✓ | ✓ | ✓ | 5.8141 | 0.0088 | 86.9 | ||||||
FB | ✓ | ✓ | ✓ | 5.5833 | 0.0085 | 88.1 | ||||||
MP | ✓ | ✓ | 6.0135 | 0.0090 | 86.6 | |||||||
RQ | ✓ | ✓ | 6.1078 | 0.0091 | 86.4 | |||||||
SS+CE+DE+FB+MP+RQ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.8463 | 0.0075 | 94.1 | |||
CK+CE+DE+FB+MP+RQ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.7234 | 0.0067 | 95.2 | |||
CK+SS+DE+FB+MP+RQ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.7832 | 0.0070 | 94.8 | |||
CK+SS+CE+FB+MP+RQ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.7138 | 0.0066 | 95.3 | |||
CK+SS+CE+DE+MP+RQ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.8195 | 0.0073 | 94.4 | |||
CK+SS+CE+DE+FB+AP+RQ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.6618 | 0.0069 | 95.6 | ||
CK+SS+CE+DE+FB+MP+RM | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.6576 | 0.0068 | 95.8 | ||
CK+SS+CE+DE+FB+MP+RQ (Ours) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 4.5128 | 0.0064 | 96.4 |
Initial Angle | 20° | 40° | 60° | 80° | ||||
---|---|---|---|---|---|---|---|---|
Metrics | RRE (°) | RTE | RRE (°) | RTE | RRE (°) | RTE | RRE (°) | RTE |
Using ComKP-CNN | 2.4273 | 0.0026 | 3.2351 | 0.0041 | 4.6168 | 0.0085 | 13.8413 | 0.0162 |
Using KP-CNN | 2.5185 | 0.0031 | 3.5017 | 0.0048 | 4.8912 | 0.0097 | 14.376 | 0.0177 |
Using self-supervised modeule | 2.4273 | 0.0026 | 3.2351 | 0.0041 | 4.6168 | 0.0085 | 13.8413 | 0.0162 |
No self-supervised modeule | 2.5032 | 0.0029 | 3.4926 | 0.0045 | 4.8128 | 0.0092 | 14.1734 | 0.0169 |
Using coordinate embedding | 2.4273 | 0.0026 | 3.2351 | 0.0041 | 4.6168 | 0.0085 | 13.8413 | 0.0162 |
No coordinate embedding | 2.4984 | 0.0028 | 3.4586 | 0.0044 | 4.8326 | 0.0091 | 14.0128 | 0.0168 |
Using distance embedding | 2.4273 | 0.0026 | 3.2351 | 0.0041 | 4.6168 | 0.0085 | 13.8413 | 0.0162 |
No distance embedding | 2.4815 | 0.0029 | 3.4125 | 0.0044 | 4.8402 | 0.0091 | 13.9821 | 0.0166 |
Using FBCross-attention | 2.4273 | 0.0026 | 3.2351 | 0.0041 | 4.6168 | 0.0085 | 13.8413 | 0.0162 |
No FBCross-attention | 2.5148 | 0.003 | 3.4824 | 0.0046 | 4.8621 | 0.0094 | 14.2675 | 0.0172 |
Using max pooling | 2.4273 | 0.0026 | 3.2351 | 0.0041 | 4.6168 | 0.0085 | 13.8413 | 0.0162 |
Using average pooling | 2.4637 | 0.0028 | 3.3861 | 0.0043 | 4.8236 | 0.0087 | 13.9643 | 0.0165 |
PointNetLK | PCRNet | FMR | DCP | GeoTransformer | PointDSC | ||
---|---|---|---|---|---|---|---|
Without ComKP-CNN | RRE (°) | 17.3752 | 9.5863 | 8.8724 | 4.7283 | 3.6878 | 3.4586 |
RTE | 0.0253 | 0.0229 | 0.0183 | 0.0067 | 0.0042 | 0.0036 | |
RR (%) | 82.3 | 85.7 | 88.2 | 95.2 | 97.1 | 97.3 | |
With ComKP-CNN | RRE (°) | 14.8463 | 7.8362 | 7.2156 | 3.6748 | 3.1163 | 3.0376 |
RTE | 0.0221 | 0.0204 | 0.0168 | 0.0055 | 0.0037 | 0.0034 | |
RR (%) | 86.6 | 87.8 | 90.4 | 96.3 | 97.7 | 97.9 |
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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Wu, X.; Wei, X.; Xu, H.; Li, C.; Hou, Y.; Yin, Y.; He, W. PointCNT: A One-Stage Point Cloud Registration Approach Based on Complex Network Theory. Remote Sens. 2023, 15, 3545. https://doi.org/10.3390/rs15143545
Wu X, Wei X, Xu H, Li C, Hou Y, Yin Y, He W. PointCNT: A One-Stage Point Cloud Registration Approach Based on Complex Network Theory. Remote Sensing. 2023; 15(14):3545. https://doi.org/10.3390/rs15143545
Chicago/Turabian StyleWu, Xin, Xiaolong Wei, Haojun Xu, Caizhi Li, Yuanhan Hou, Yizhen Yin, and Weifeng He. 2023. "PointCNT: A One-Stage Point Cloud Registration Approach Based on Complex Network Theory" Remote Sensing 15, no. 14: 3545. https://doi.org/10.3390/rs15143545