In order to improve fitting accuracy of free-form surface, an improved method for the currently recognized NURBS free-form surface based on discrete stationary wavelet transform is proposed. Firstly, the elevation image of the free-form surface point cloud and the elevation sequence of the elevation image are obtained by using the grid method. Then, feature points of the free-form surface are extracted by the discrete stationary wavelet transform. Finally, using the extracted feature points, high accuracy NURBS free-form surface is realized. Compared with the conventional NURBS method and the NURBS method based on dual-tree complex wavelet transform, the experimental results showed that the root mean squared errors of fitting results of free-form surface were deduced 77.64% and 23.16%, respectively. Therefore, the proposed method has satisfactory fitting precision.INDEX TERMS 3D measurement, reverse engineering, discrete stationary wavelet transform, NURBS free-form surface.

In order to further improve the accuracy and speed of the present commonly used NURBS surface method, an improved method for NURBS surface based on particle swarm optimization BP neural network is proposed. Firstly, node vectors of the data points are calculated by using the parametrization method of accumulating chord length. Then, prediction model of node vectors is constructed by using the particle swarm optimization BP neural network, and the experiment is presented to justify the feasibility and veracity of constructed prediction model. Finally, using the predicted node vectors, a fast and highprecision NURBS surface is realized. The results showed that the root mean squared error of fitting result of surface was deduced 84.05% and the run time was deduced 92.42% compared with the traditional NURBS method. Therefore, the proposed method is a fast and high-precise NURBS surface fitting method.

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