On Point-cloud Data Reconstruction Using RBF

Along with the great progress in 3D data measurement technique and device and 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 several problems such as surface reconstructing smoothing and blending. Because of the computation and storage complexity of RBF fitting, the speed of reconstruction and the scale of point-cloud data are restricted. On the base of the predecessors' work, this thesis presents some efficient algorithms for point-cloud data reconstruction. The major works involved are as follows:First of all, it summarizes the theory of RBF interpolation and the sufficient condition of the solvability of interpolation problem. 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.Secondly, based on octree space partition, a fast surface reconstruction method for point-cloud data using RBF is proposed. It partitions the point-cloud data space firstly and creates octree topologic structure accordingly. Then, at each cell of the octree partitions, a multi-order radial basis function that interpolates or approximates the data points which belong to the current cell is created. Due to the effective octree algorithm, the size of resulting matrix needed to be processed each time is reducedthat permits reconstructing of large-scale data sets in a reasonable time. Furthermore, the multi-order basis function has several advantages compared with the thin-plate basis function. The condition of the system matrix formed by the decreasing multi-order basis function is improved. Running time increases fairly linearly as more constraints are specified. The reconstructed surface is locally detailed, yet globally smooth, because the RBF that we use achieve multiple orders of smoothness. The relationship between the smoothness of surface and the values of parameters S and z is also analyzed.At the last, based on micro-genetic algorithm and RBF neural network, a novel approach for point-cloud data reconstruction is presented. It establishes a three-layered neural network. The weights between the output and the hidden layer are determined by training network using micro-genetic algorithm. The network is designed and used to reconstruct explicit and implicit surfaces. In the case of micro-genetic algorithm the "start and restart" procedure helps in avoiding the premature convergence and accelerating the convergence of network. Moreover, RBF neural network has better ability of fault-tolerance and functional approximation. The experimental results show that the RBF neural network is suitable for scattered data smooth interpolation and is efficient in repairing in-complete meshes.