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. & COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

This study examines the non-stepwise interpolation property and memory loss phenomenon of the recently introduced dual interpolating subdivision schemes. It identifies new differences between schemes with odd and even dilation factors, showing that odd dilation factors have a 2-step interpolation property, while even dilation factors result in completely non-stepwise interpolation processes. These findings are utilized to develop an optimized non-uniform level dependent implementation of dual interpolating schemes to overcome the computational drawback caused by memory loss.