# 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

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**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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**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