Multiresolution representation for curves based on ternary subdivision schemes

Subdivision offers a way to increase the resolution of models, while reverse subdivision possesses the opposite ability. Combining the two theories could realize the multiresolution (MR) representation of models. Based on two ternary subdivision schemes, we present the trial and refined filters and an algorithm to realize MR representation for curves, which has some difference compared with the work relating to binary schemes. And the filters yield biorthogonal wavelet systems which are the underlying theory fundament of curves MR. By experiments and numerical calculations, we demonstrate that by using the ternary methods one can accomplish the MR representation for curves and the low-resolution results obtained by reverse subdivision can approximate the original curves well. Besides, ternary methods need smaller number of decomposition times than binary methods to get low-resolution results at similar levels of resolution for the same original curve.