## Maolin Xu* , Jiaxing Wei* and Hongling Xiu*## |

ID | Deviation (mm) | ||
---|---|---|---|

x coordinate | y coordinate | z coordinate | |

1 | -0.002 | 0.004 | -0.007 |

2 | 0.006 | -0.003 | 0.003 |

3 | 0.008 | -0.007 | 0.007 |

4 | 0.002 | 0.006 | 0.006 |

5 | 0.004 | 0.007 | -0.008 |

6 | 0.002 | 0.011 | 0.001 |

As we can be learned from Table 1, the maximum deviations of x, y, and z coordinates are 8 mm, 11 mm, and 8 mm, respectively. Therefore, it can be easily concluded that the three-axis error is stable in the coordinate system conversion of point clouds.

However, it’s not enough to validate the conversion results by three-axis error. In this paper, three-term error is used to further validate the accuracy of point clouds conversion, including plane error, elevation error and three-dimensional error. The equations of three-term error is defined as follows:

The plane error:

The elevation error:

The three-dimensional error:

The plane, elevation and three-dimensional errors obtained by Eqs. (20)-(22) are 11.6 mm, 8.0 mm, and 13.6 mm, respectively. The above accuracy of point clouds conversion reflected by three-term error is equivalent to the accuracy of the single-base-station RTK, which demonstrates the applicability of our proposed new method.

Through the basic Rodrigues rotation method, the coordinates of point clouds at four stations are converted to engineering coordinate system. The basic Rodrigues rotation method proposed in this paper does not involve the drawback of large angle initialization, only the rotation angles of point clouds need to be calculated. Therefore, the new method has not only realized the coordinate system conversion of point clouds, but also achieved the seamless splicing of point clouds. More importantly, due to the conversion accuracy made in this study is relatively high, the further point clouds modelling would be more accurate.

To further validate the reliability of the basic Rodrigues rotation model proposed in this paper, we adopt the ICP method to splice the point clouds, and select the FARO target points to convert the coordinate system. Besides, it should also be highlighted that the use of ICP method is also within the MAPTEK software. The ICP method mainly looks for the feature points of similar area, minimizes the difference of two neighbored point clouds to complete the splicing of point clouds.

In general, ICP method involves global splicing and requires to select the location of initial point clouds. As a consequence, the iterative process increases the time of point clouds splicing. After the four-station point clouds splicing, the coordinates of four FARO target points are taken for coordinate system conversion. It should be noted that the selection of four FARO target points is the same as basic Rodrigues rotation method, and the remaining six target points are also used for accuracy analysis. The there-axis error of ICP method is presented in Table 2.

Table 2 indicates that the maximum deviations of x, y, and z coordinates are 16 mm, 19 mm, and 15 mm, respectively. Compared with the basic Rodrigues rotation method, there is an obviously increase in three-axis error produced by ICP method. In addition, the three-term error of ICP method is calculated by Eqs. (20)-(22). The plane, elevation and three-dimensional errors of ICP method are 21.3 mm, 13.7 mm, and 25.3 mm, respectively. The plane and three-dimensional errors of ICP method are larger than our new method, and the elevation error is equivalent to our new method. The reason lays in the scanner used in this paper has high accuracy in angle and distance measurement, which results in the similarity in elevation error of two methods.

By comparing with ICP method for point clouds splicing and coordinate system conversion, the basic Rodrigues rotation method achieves the splicing and coordinate system conversion of point clouds simultaneously. Therefore, the basic Rodrigues rotation method reduces the error of manually selection of feature points, and the conversion accuracy has significant improvement. The comparison of ICP method and basic Rodrigues rotation method in the same software platform also suggests that the time of basic Rodrigues rotation method is 1/3 of ICP method, so the basic Rodrigues rotation method is more efficient. Consequently, we can conclude that the basic Rodrigues rotation method has better stability than ICP method.

The purpose of this paper is to propose a simple model to achieve the coordinate system conversion of point clouds. Due to the coordinate system conversion of point clouds is a basic work before point clouds semantic recognition and three-dimensional reconstruction, the subject has become more meaningful in various scientific fields. The basic Rodrigues rotation model proposed in this paper has advantages of need not linearization, simplicity and efficiency. Besides, the new method also performs superiority in high accuracy and seamless splicing by experimental comparison.

In this paper, we use the method of manual selection to determine the scanning coordinates of feature points. Manual selection undoubtedly increases the error of coordinate extraction and reduces the automation of workflow, which is a potential limitation needs to be further improved.

We will focus on the automatic identification of feature points, because the machine learning has always been a characteristic issue in big data field. Therefore, our next work is to achieve the automation of point clouds coordinate conversion. Besides, the feature recognition is not limited to the conversion of coordinate system, it has a widely applications in change detection and intelligent travel.

He is currently a professor of University of Science and Technology Liaoning, Anshan, China. His research interest includes mine monitoring and measurement data processing. He is currently a graduate student (master’s degree) of University of Science and Technology Liaoning, Anshan, China. His research interest includes data processing and application of point clouds.

He is currently a professor of University of Science and Technology Liaoning, Anshan, China. His research interest includes mine monitoring and measurement data processing. He is currently a graduate student (master’s degree) of University of Science and Technology Liaoning, Anshan, China. His research interest includes data processing and application of point clouds. She is currently a graduate student (master’s degree) of University of Science and Technology Liaoning, Anshan, China. Her research interest includes remote sensing image processing and application.

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