3D shapes modeling which has hierarchical structure based on B-spline surfaces with non-uniform knots

A method for 3D shapes modeling which has hierarchical structure is proposed. For representing 3D surface shapes, 4th order non-uniform rational B-spline functions with controllable knots are employed as the surface model. Consequently, a multiresolution representation technique based on multiresolution wavelet transform can be implemented with the corresponding B-wavelets. The surface models at each resolution level are obtained by performing a decomposition algorithm, after the surface model at the highest level is estimated. In order to estimate the surface model as accurately as possible, a regularization problem is solved by an iterative algorithm. Through several experiments using real data of range images, the effectiveness of the proposed method was confirmed.