Moving Multiple Curves/Surfaces Approximation

With the development of modern scanning technology, the scanner is with higher accuracy. However, because of measurement error, it is still difficult to obtain exact point cloud data. So, it is necessary to do some research on denosing. Moving Multiple Curves/Surfaces Approximation is a new method for point cloud denoising. It can be used to separate mixed point data received from many different curves and surfaces and obtain relatively accurate data. This is a process of re-sampling.The paper mainly consists of three parts. We first present Moving Multiple Curves Approximation(MMCA) for plane curves. In order to elaborate the process of separating mixed point clouds using MMC A for plane curves, we consider the cases of s=2and s=4respectively, i.e. there will be two and four curves in a model. In the case of s=2, we focus on moving two straight lines and two parabolas approximation. For the sake of solving the two models, their corresponding models are converted to optimization models. In the case of s=4, the number of curves in a model is4. We also need to change the model to an optimal model. Both s=2and s=4, we present how to choose initial values and the details of implementation. According to the results of some examples, we will discover that it is effective for MMC A to separate mixed data received from multiple plane curves.We also propose Moving Multiple Surfaces Approximation (MMSA) for sur-faces in3D. Considering two pieces of mixed data from two surfaces, we provide MMS A with the model of s=2. Moving two planes approximation and moving two paraboloids approximation and their corresponding optimization models are presented. When a model is solved, we will get two target surfaces and then two target points are obtained. Using moving two planes approximation, we separate the exact and mixed data received from two planes and two spheres. By moving two paraboloids approximation, we deal with the exact and mixed data obtained from an elliptic paraboloid and its offset surface, hyperboloid paraboloid and its offset surface. The error estimation of the above eight cases are provided. Besides, we test the real data from the inner and outer walls of a part of cylindrical object and so on.Finally, we focus on the mixed data from space curves. In order to separate the mixed data, firstly, we need to establish a reference plane. Secondly, we project the related data points to the reference plane. Thirdly, we separate the projected points using the moving multiple curves approximation method. We will test some examples to show the effectiveness of our algorithm.