Surface recovery by using regularization theory and its application to multiresolution analysis

In this paper, a surface recovery method using multiresolution wavelet transform is proposed. For representing 3D surface shapes, 4th order B-spline functions with uniform knots are introduced as scaling functions of spline wavelets. In order to estimate the surface function, a regularization problem is solved by an iterative algorithm. The estimated surface function can, be decomposed into an approximate surface function at the lowest resolution and the corresponding wavelet components. Consequently, by reducing the noise components which the wavelet components include, the surface recovery method can give an accurate estimation of the surface function. Through several experiments, both the robustness to noises and the edge-preserving property in recovering the surface have been confirmed