# A Global Structure and Adaptive Weight Aware ICP Algorithm for Image Registration

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## Abstract

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## 1. Introduction

- (1)
- This paper introduced a novel ICP variant, GSAW-ICP, incorporating a mathematical model of the global structure to account for the effects of deformation on both the normal vectors and the curvature of the object. The paper has also proposed two innovative metrics: (OAKV) Overlap Area Knockout Value, and (GT) Ground truth interior points, which were used to optimize the convergence strategy.
- (2)
- This paper introduced a loss measurement method based on the adaptive weight adjustment. The method was able to assign appropriate weights to outliers and overlapping values, as well as optimize the system performance under noise and outlier interference. The method improved the robustness of GSAW-ICP’s ability to estimate the gap between the ℓ2 cost and the robust M.
- (3)
- This paper presented a simulation and testing of the proposed method on the EPFL dataset and a reality measured dataset, before comparing it with the state-of-the-art algorithms. The paper has been organized as follows: Section 2 reviews the related work and the recent improvements of the ICP algorithm; Section 3 describes the solution process of GSAW-ICP and the mathematical model of the global structure; Section 4 explains the convergence criterion and the update iteration of GSAW-ICP, in addition to providing a feasibility analysis of the algorithm; Section 5 reports the experimental results and analysis for GSAW-ICP; and Section 6 concludes the paper. Figure 1 shows the technical flow chart of this paper, where the blue arrows indicate the method flow, and the yellow arrows highlight the novel contributions we made.

## 2. Related Work

## 3. Classical ICP Revisition

#### 3.1. Iterative Nearest Point

#### 3.2. Iterative Nearest Point

#### 3.3. Point Cloud Alignment Process

## 4. Loss Metrics for Adaptive Weight Adjustment

#### 4.1. Dealing with Outliers

#### 4.2. Update Iterative Process

- Update the rotation matrix:

- Update the translation vector:

- Update the adaptive weight vector:

#### 4.3. Update Iterative Process

## 5. Experimental Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Giancola, S.; Zarzar, J.; Ghanem, B. Leveraging Shape Completion for 3D Siamese Tracking. In Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA, 15–20 June 2019; pp. 1359–1368. [Google Scholar] [CrossRef][Green Version]
- Rusinkiewicz, S. A symmetric objective function for ICP. ACM Trans. Graph.
**2019**, 38, 1–7. [Google Scholar] [CrossRef] - Besl, P.J.; McKay, N.D. A method for registration of 3-D shapes. In Proceedings of the Sensor Fusion IV: Control Paradigms and Data Structures, Boston, MA, USA, 30 April 1992; pp. 239–256. [Google Scholar]
- Huang, X.; Mei, G.; Zhang, J.; Abbas, R. A comprehensive survey on point cloud registration. arXiv
**2021**, arXiv:2103.02690. [Google Scholar] - Pottmann, H.; Huang, Q.-X.; Yang, Y.-L.; Hu, S.-M. Geometry and convergence analysis of algorithms for registration of 3D shapes. Int. J. Comput. Vis.
**2006**, 67, 277–296. [Google Scholar] [CrossRef] - Chen, Y.; Medioni, G. Object modelling by registration of multiple range images. Image Vis. Comput.
**1992**, 10, 145–155. [Google Scholar] [CrossRef] - Pottmann, H.; Leopoldseder, S.; Hofer, M. Registration without ICP. Comput. Vis. Image Underst.
**2004**, 95, 54–71. [Google Scholar] [CrossRef] - Li, J.; Hu, Q.; Zhang, Y.; Ai, M. Robust symmetric iterative closest point. ISPRS J. Photogramm. Remote Sens.
**2022**, 185, 219–231. [Google Scholar] [CrossRef] - Zhang, J.; Yao, Y.; Deng, B. Fast and robust iterative closest point. IEEE Trans. Pattern Anal. Mach. Intell.
**2021**, 44, 3450–3466. [Google Scholar] [CrossRef] [PubMed] - Bouaziz, S.; Tagliasacchi, A.; Pauly, M. Sparse iterative closest point. In Computer Graphics Forum; Blackwell Publishing Ltd.: Oxford, UK, 2013; Volume 32, pp. 113–123. [Google Scholar]
- Guo, Y.; Zhao, L.; Shi, Y.; Zhang, X.; Du, S.; Wang, F. Adaptive weighted robust iterative closest point. Neurocomputing
**2022**, 508, 225–241. [Google Scholar] [CrossRef] - Li, J.; Hu, Q.; Ai, M. GESAC: Robust graph enhanced sample consensus for point cloud registration. ISPRS J. Photogramm. Remote Sens.
**2020**, 167, 363–374. [Google Scholar] [CrossRef] - Wang, W.; de Gusmao, P.P.B.; Yang, B.; Markham, A.; Trigoni, N. Radarloc: Learning to relocalize in fmcw radar. In Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi’an, China, 30 May–5 June 2021; IEEE: Piscataway, NJ, USA, 2021; pp. 5809–5815. [Google Scholar]
- You, Y.; Lou, Y.; Li, C.; Cheng, Z.; Li, L.; Ma, L.; Lu, C.; Wang, W. Keypointnet: A large-scale 3d keypoint dataset aggregated from numerous human annotations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 13–19 June 2020; pp. 13647–13656. [Google Scholar]
- Yuan, T.W.; Lu, Y.N.; Shi, Z.K.; Zhang, Z. Research on a Non-Rigid 3D Shape Retrieval Method Based on Global and Partial Description. In Fuzzy Systems and Data Mining II; IOS Press: Amsterdam, The Netherlands, 2016; pp. 562–569. [Google Scholar]
- Li, J.; Lee, G.H. Usip: Unsupervised stable interest point detection from 3d point clouds. In Proceedings of the IEEE/CVF international conference on computer vision, Cambridge, MA, USA, 20–23 June 2019; pp. 361–370. [Google Scholar]
- Rusu, R.B.; Blodow, N.; Beetz, M. Fast point feature histograms (FPFH) for 3D registration. In Proceedings of the 2009 IEEE international conference on robotics and automation, Kobe, Japan, 12–17 May 2009; IEEE: Piscataway, NJ, USA, 2009; pp. 3212–3217. [Google Scholar]
- Zeng, A.; Song, S.; Nießner, M.; Fisher, M.; Xiao, J.; Funkhouser, T. 3dmatch: Learning local geometric descriptors from rgb-d reconstructions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA, 21–26 July 2017; pp. 1802–1811. [Google Scholar]
- Brogaard, R.Y.; Ravn, O.; Boukas, E. Absolute localisation in confined spaces using deep geometric features. Electron. Lett.
**2021**, 57, 621–623. [Google Scholar] [CrossRef] - Xie, S.; Gu, J.; Guo, D.; Qi, C.R.; Guibas, L.; Litany, O. Pointcontrast: Unsupervised pre-training for 3d point cloud understanding. In Proceedings of the Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, 23–28 August 2020; Proceedings, Part III 16; Springer International Publishing: Cham, Switzerland, 2020; pp. 574–591. [Google Scholar]
- Ao, S.; Hu, Q.; Yang, B.; Markham, A.; Guo, Y. Spinnet: Learning a general surface descriptor for 3d point cloud registration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA, 20–25 June 2021; pp. 11753–11762. [Google Scholar]
- Lowe, D.G. Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis.
**2004**, 60, 91–110. [Google Scholar] [CrossRef] - Zhong, Y. Intrinsic shape signatures: A shape descriptor for 3D object recognition. In Proceedings of the 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, Kyoto, Japan, 27 September–4 October 2009; IEEE: Piscataway, NJ, USA, 2009; pp. 689–696. [Google Scholar]
- Chernozhukov, V.; Chetverikov, D.; Demirer, M.; Duflo, E.; Hansen, C.; Newey, W.; Robins, J. Double/debiased machine learning for treatment and structural parameters. Econom. J.
**2018**, 21, C1–C68. [Google Scholar] [CrossRef][Green Version] - Granger, S.; Pennec, X. Multi-scale EM-ICP: A fast and robust approach for surface registration. In Proceedings of the Computer Vision—ECCV 2002: 7th European Conference on Computer Vision, Copenhagen, Denmark, 28–31 May 2002; Proceedings, Part IV 7; Springer: Berlin/Heidelberg, Germany, 2002; pp. 418–432. [Google Scholar]
- Singh, R.; Pal, B.C.; Jabr, R.A. Statistical representation of distribution system loads using Gaussian mixture model. IEEE Trans. Power Syst.
**2009**, 25, 29–37. [Google Scholar] [CrossRef][Green Version] - Li, J.; Hu, Q.; Ai, M. Point cloud registration based on one-point ransac and scale-annealing biweight estimation. IEEE Trans. Geosci. Remote Sens.
**2021**, 59, 9716–9729. [Google Scholar] [CrossRef] - Chum, O.; Matas, J.; Kittler, J. Locally optimized RANSAC. In Proceedings of the Pattern Recognition: 25th DAGM Symposium, Magdeburg, Germany, 10–12 September 2003; Proceedings 25; Springer: Berlin/Heidelberg, Germany, 2003; pp. 236–243. [Google Scholar]
- Liu, Z.; Chen, Z.; Xie, S.; Zheng, W.-S. TransGrasp: A Multi-Scale Hierarchical Point Transformer for 7-DoF Grasp Detection. In Proceedings of the 2022 International Conference on Robotics and Automation (ICRA), Philadelphia, PA, USA, 23–27 May 2022; IEEE: Piscataway, NJ, USA, 2022; pp. 1533–1539. [Google Scholar]
- Rousseeuw, P.J.; Hubert, M. Anomaly detection by robust statistics. Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
**2018**, 8, e1236. [Google Scholar] [CrossRef][Green Version] - Tsai, R.Y. An efficient and accurate camera calibration technique for 3D machine vision. Proc. IEEE Conf. Comput. Vis. Pattern Recognit.
**1986**, 1986, 364–374. [Google Scholar] - Geiger, A.; Lenz, P.; Stiller, C.; Urtasun, R. Vision meets robotics: The kitti dataset. Int. J. Robot. Res.
**2013**, 32, 1231–1237. [Google Scholar] [CrossRef][Green Version]

**Figure 10.**The relationship between the root mean squared error of the registration effect and the signal-to-noise ratio. From (

**a**–

**d**), the number of iterations increases by 10, while (

**a**) has 50 iterations.

**Figure 11.**The relationship between the root mean squared error of the registration effect and the signal-to-noise ratio. From (

**a**–

**d**), the noise interference increases by 5 db in sequence, while (

**a**) has a noise interference of 0 db.

Algorithm | Num | Dataset 1 | Dataset 2 | Dataset 3 | Dataset 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Center Coordinates | Dis (m) | DER (%) | Center Coordinates | Dis (m) | DER (%) | Center Coordinates | Dis (m) | DER (%) | Center Coordinates | Dis (m) | DER (%) | ||

ICP | 1 | (2.136, 37.054) | 0.644 | 5.04 | (2.768, 42.473) | 3.317 | 15.89 | (6.309, 50.831) | 0.621 | 3.69 | (−1.811, 39.733) | 1.082 | 7.89 |

2 | (3.002, 35.207) | 1.38 | 10.81 | (2.613, 36.703) | 2.002 | 9.59 | (4.193, 45.645) | 1.373 | 8.17 | (−0.732, 35.737) | 3.029 | 22.34 | |

3 | (6.199, 41.047) | 0.421 | 3.30 | (7.632, 47.041) | 0.558 | 2.67 | (5.706, 39.449) | 0.337 | 2.01 | (2.740, 38.105) | 0.927 | 6.84 | |

AA-ICP | 1 | (1.636, 35.959) | 1.013 | 7.93 | (2.459, 41.404) | 2.483 | 11.89 | (6.304, 49.974) | 0.336 | 2.00 | (−2.178, 39.789) | 0.824 | 6.07 |

2 | (3.990, 37.417) | 1.116 | 8.74 | (3.031, 35.781) | 2.740 | 13.13 | (3.565, 44.726) | 0.313 | 1.86 | (−0.487, 35.942) | 2.718 | 20.5 | |

3 | (6.331, 41.545) | 0.135 | 1.06 | (7.264, 46.621) | 0.788 | 3.77 | (5.891, 38.915) | 0.902 | 5.36 | (2.664, 38.137) | 0.992 | 7.32 | |

Sparse ICP | 1 | (1.697, 35.626) | 1.352 | 10.59 | (0.166, 40.232) | 0.144 | 0.69 | (6.550, 49.360) | 0.883 | 5.25 | (−2.910, 39.365) | 0.230 | 1.69 |

2 | (3.170, 37.434) | 1.30 | 10.18 | (3.875, 38.937) | 0.566 | 2.71 | (3.221, 45.164) | 0.534 | 3.18 | (−0.423, 36.913) | 1.962 | 14.47 | |

3 | (6.250, 41.242) | 0.227 | 1.78 | (7.603, 46.798) | 0.725 | 3.47 | (5.817, 39.178) | 0.630 | 3.75 | (2.735, 38.065) | 0.894 | 6.60 | |

Robust ICP | 1 | (1.487, 36.552) | 0.411 | 3.22 | (0.412, 40.083) | 0.358 | 1.71 | (6.617, 48.378) | 1.867 | 11.11 | (−3.056, 39.482) | 0.416 | 3.07 |

2 | (3.839, 36.024) | 0.289 | 2.26 | (3.631, 37.058) | 1.415 | 6.78 | (3.301, 46.799) | 2.167 | 12.89 | (−0.273, 38.682) | 1.476 | 10.89 | |

3 | (6.222, 41.278) | 0.189 | 1.48 | (6.441, 45.726) | 1.850 | 8.86 | (5.438, 39.942) | 0.226 | 1.34 | (3.226, 38.306) | 1.022 | 7.54 | |

GSAW-ICP | 1 | (1.387, 36.852) | 0.157 | 1.23 | (0.312, 40.483) | 0.156 | 0.75 | (6.221, 50.131) | 0.306 | 1.82 | (−2.856, 39.012) | 0.213 | 1.57 |

2 | (3.839, 36.324) | 0.016 | 0.13 | (3.665, 38.581) | 0.155 | 0.75 | (3.157, 44.775) | 0.179 | 1.07 | (0.073, 38.182) | 1.03 | 7.60 | |

3 | (6.322, 41.578) | 0.150 | 1.17 | (7.321, 47.519) | 0.157 | 0.75 | (5.677, 39.523) | 0.258 | 1.53 | (3.226, 38.506) | 1.221 | 9.01 |

**Table 2.**Comparison of running results between GSAW-ICP and several typical registration algorithms.

Algorithm | Evaluation Index (Overlap Area Knockout Value) | ||||
---|---|---|---|---|---|

Bimba | Children | Dragon | Angle | Bunny | |

ICP | 25.3 | 32.4 | 27.4 | 28.3 | 33.6 |

ICP-l | 23.2 | 26.1 | 25.1 | 26.8 | 30.2 |

AA-ICP | 27.7 | 24.6 | 26.3 | 27.1 | 39.4 |

Sparse ICP | 21.6 | 17.2 | 20.1 | 22.9 | 24.3 |

Fast ICP | 13.2 | 14.6 | 12.8 | 17.6 | 18.4 |

Robust ICP | 16.9 | 16.4 | 13.5 | 15.8 | 19.9 |

Symmetric ICP | 15.7 | 13.1 | 15.3 | 18.2 | 21.5 |

GSAW-ICP | 11.1 | 10.7 | 12.8 | 15.3 | 18.9 |

**Table 3.**Comparison of running results between GSAW-ICP and several typical registration algorithms.

Algorithm | Evaluation Index (Ground Truth Interior Points) | ||||
---|---|---|---|---|---|

Bimba | Children | Dragon | Angle | Bunny | |

ICP | 14.62 | 20.31 | 18.28 | 17.24 | 21.27 |

ICP-l | 15.71 | 21.56 | 17.89 | 13.51 | 22.14 |

AA-ICP | 18.92 | 23.64 | 23.51 | 20.01 | 26.41 |

Sparse ICP | 16.21 | 21.28 | 20.37 | 18.29 | 22.41 |

Fast ICP | 19.27 | 26.83 | 28.41 | 21.25 | 30.58 |

Robust ICP | 19.89 | 25.89 | 28.22 | 22.18 | 28.89 |

Symmetric ICP | 18.26 | 22.17 | 26.19 | 21.16 | 28.75 |

GSAW-ICP | 19.58 | 27.12 | 27.81 | 22.71 | 29.61 |

**Table 4.**Comparison of running results between GSAW-ICP and several typical registration algorithms.

Algorithm | Average Ranking | ||
---|---|---|---|

OAKV | GT | Mean | |

ICP | 7.6 | 7.6 | 7.6 |

ICP-l | 6.2 | 7.2 | 6.7 |

AA-ICP | 7.2 | 5.2 | 6.2 |

Sparse ICP | 5 | 6.2 | 5.6 |

Fast ICP | 2 | 2 | 2 |

Robust ICP | 3.2 | 2.2 | 2.7 |

Symmetric ICP | 3.4 | 4.4 | 3.9 |

GSAW-ICP | 1.2 | 1.8 | 1.5 |

**Table 5.**Comparison of running results between GSAW-ICP and several typical registration algorithms.

Algorithm | Evaluation Index | |||
---|---|---|---|---|

0.02ADD | 0.05ADD | 0.1ADD | Mean | |

ICP | 26.23 | 66.38 | 89.21 | 60.61 |

ICP-l | 32.51 | 72.41 | 91.52 | 65.48 |

GSAW -ICP | 33.27 | 71.62 | 92.86 | 65.92 |

+ARC-Welsh | 35.81 | 75.74 | 93.71 | 68.42 |

+Surface | 42.61 | 78.47 | 95.72 | 72.27 |

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## Share and Cite

**MDPI and ACS Style**

Cao, L.; Zhuang, S.; Tian, S.; Zhao, Z.; Fu, C.; Guo, Y.; Wang, D.
A Global Structure and Adaptive Weight Aware ICP Algorithm for Image Registration. *Remote Sens.* **2023**, *15*, 3185.
https://doi.org/10.3390/rs15123185

**AMA Style**

Cao L, Zhuang S, Tian S, Zhao Z, Fu C, Guo Y, Wang D.
A Global Structure and Adaptive Weight Aware ICP Algorithm for Image Registration. *Remote Sensing*. 2023; 15(12):3185.
https://doi.org/10.3390/rs15123185

**Chicago/Turabian Style**

Cao, Lin, Shengbin Zhuang, Shu Tian, Zongmin Zhao, Chong Fu, Yanan Guo, and Dongfeng Wang.
2023. "A Global Structure and Adaptive Weight Aware ICP Algorithm for Image Registration" *Remote Sensing* 15, no. 12: 3185.
https://doi.org/10.3390/rs15123185