Reconstruction of parametric curves and surfaces using an adaptive basis function network

A robust technique for reconstructing curves and surfaces from measured data points is an important tool for recovering the geometry of an object in many engineering applications, such as computer vision, computer-aided design and reverse engineering. Typically, the digitized data points are first segmented into numerous curve segments or surface regions according to the natural geometry of the object. A low-order mathematical model is then reconstructed for each region and these regions are attached, or "stitched" together to represent the complete original object.; In this thesis, a new approach called the adaptive basis function network is developed and investigated for the curve and surface fitting process. The new algorithm is based on the notion of functional approximation by neural networks. The approach employs a two-layer neural network architecture to perform a weighted summation of nonlinear Bernstein or B-spline basis functions. The control points of the Bernstein or B-spline basis functions are defined as the weights of the network and determined using a least square learning algorithm. The learning rate can be adjusted in the learning process in order to accelerate the convergence speed and reduce the error. Once the learning phase is complete, the control points can de used for surface patch reconstruction by any CAD/CAM system that utilizes parametric modeling techniques. The adaptive basis function network approach has been successfully applied to reconstruct a variety of the curves and surfaces. The proposed method improves the computational time and accuracy of the results over traditional matrix manipulation techniques. Further research will focus on joining several curve segments and surface patches for complete model reconstruction.