Optimized dual interpolating subdivision schemes

This work investigates the non-stepwise interpolation property of the recently introduced class of dual interpolating subdivision schemes, and the “loss of memory” phenomenon that comes with it. New differences between schemes having an odd and an even dilation factors are highlighted. In particular, dual interpolating schemes having an odd dilation factor are proven to satisfy a 2-step interpolation property, while an even dilation factor corresponds to a completely non-stepwise interpolation process. These facts are exploited to define an optimized non-uniform level dependent implementation of dual interpolating schemes in order to overcome the computational drawback due to the “loss of memory”.