Multiresolution for curves and surfaces based on constraining wavelets

Abstract

We present a novel method for determining local multiresolution filters for a broad range of subdivision schemes. Our approach is based on constraining the wavelet coefficients such that the coefficients at even vertices can be computed from the coefficients of neighboring odd vertices. This constraint leads to an initial set of decomposition filters. To increase the quality of these initial filters, we use an optimization that reduces the size of the wavelet coefficients. The resulting multiresolution filters yield a biorthogonal wavelet system whose construction is similar to the lifting scheme. This approach is demonstrated in depth for cubic B-spline curves and Loop subdivision surfaces. Our filters are shown to perform comparably with existing filters.