24 October 2016 A point cloud modeling method based on geometric constraints mixing the robust least squares method
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The appearance of 3D laser scanning technology has provided a new method for the acquisition of spatial 3D information. It has been widely used in the field of Surveying and Mapping Engineering with the characteristics of automatic and high precision. 3D laser scanning data processing process mainly includes the external laser data acquisition, the internal industry laser data splicing, the late 3D modeling and data integration system. For the point cloud modeling, domestic and foreign researchers have done a lot of research. Surface reconstruction technology mainly include the point shape, the triangle model, the triangle Bezier surface model, the rectangular surface model and so on, and the neural network and the Alfa shape are also used in the curved surface reconstruction. But in these methods, it is often focused on single surface fitting, automatic or manual block fitting, which ignores the model's integrity. It leads to a serious problems in the model after stitching, that is, the surfaces fitting separately is often not satisfied with the well-known geometric constraints, such as parallel, vertical, a fixed angle, or a fixed distance. However, the research on the special modeling theory such as the dimension constraint and the position constraint is not used widely. One of the traditional modeling methods adding geometric constraints is a method combing the penalty function method and the Levenberg-Marquardt algorithm (L-M algorithm), whose stability is pretty good. But in the research process, it is found that the method is greatly influenced by the initial value.

In this paper, we propose an improved method of point cloud model taking into account the geometric constraint. We first apply robust least-squares to enhance the initial value’s accuracy, and then use penalty function method to transform constrained optimization problems into unconstrained optimization problems, and finally solve the problems using the L-M algorithm. The experimental results show that the internal accuracy is improved, and it is shown that the improved method for point clouds modeling proposed by this paper outperforms the traditional point clouds modeling methods.
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JIanping Yue, JIanping Yue, Yi Pan, Yi Pan, Shun Yue, Shun Yue, Dapeng Liu, Dapeng Liu, Bin Liu, Bin Liu, Nan Huang, Nan Huang, } "A point cloud modeling method based on geometric constraints mixing the robust least squares method", Proc. SPIE 10006, Lidar Technologies, Techniques, and Measurements for Atmospheric Remote Sensing XII, 100060M (24 October 2016); doi: 10.1117/12.2241758; https://doi.org/10.1117/12.2241758

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