The Research On Curving Surface Reconstruction Method Based On Radial Basis Function

With the rapid development of the three-dimensional equipment and technology,the method for modeling of carving surface becomes more and more widely and directly. Based on the characteristics of the carving surface, we put forward an method which according to the radial basis functions for the modeling of carving surface. We proposed that applying to two different kind of data to realize this method.The first object which we study is the cloud data. With the increasing requirement of reality, real-time in computer graphics, reconstruction of point-cloud data has become one of the fundamental problems in CAD, CG as well as CV. As one of the important point-cloud data interpolation tools, the implicit representation of objects shapes with RBF offers a unified framework for the surface reconstruction work. The other object we study is digital image. Through our work we successfully realize its surface reconstruction which apply an new method for our curving production. Major works involved are as follows:Firstly, Based on regularization techniques, a unified RBF approach, that allows the surface to exactly interpolate the data and approximate the noisy data, is presented. The approach creates a single implicit function by summing together several weighted radial basis functions., based on quaternary tree space partition, a fast surface reconstruction method for point-cloud data using RBF is proposed. It is partitions the point-cloud data space firstly. Then, at each cell of the tree, a multi-quadric radial basis function that interpolates or approximates the data points which belong to the current cell is created. Due to the effective algorithm, the size of resulting matrix needed to be processed each time is reduced that permits reconstructing of large-scale data sets in a reasonable time. Compare to the cubic function, multi-quadric function can appear a better performance. Running time increases fairly linearly as more constraints are specified. The reconstructed surface is locally detailed, yet globally smooth.Secondly, on the base of the main reconstruction methods, we seem the image as scattered data in 3D, with the focal division method, we successfully realize the reconstruction on image by use of the second Gaussian radial basis function.we also do much work on the smoothing on combination of the curves. All of the research and experiment show that our work on this two methods are helpful to improve the efficiency of surface reconstruction.