31 research outputs found
Six-Point Subdivision Schemes with Cubic Precision
This paper presents 6-point subdivision schemes with cubic precision. We first derive a relation between the 4-point interpolatory subdivision and the quintic B-spline refinement. By using the relation, we further propose the counterparts of cubic and quintic B-spline refinements based on 6-point interpolatory subdivision schemes. It is proved that the new family of 6-point combined subdivision schemes has higher smoothness and better polynomial reproduction property than the B-spline counterparts. It is also showed that, both having cubic precision, the well-known Hormann-Sabin’s family increase the degree of polynomial generation and smoothness in exchange of the increase of the support width, while the new family can keep the support width unchanged and maintain higher degree of polynomial generation and smoothness
Semi-regular Dubuc-Deslauriers wavelet tight frames
In this paper, we construct wavelet tight frames with n vanishing moments for
Dubuc-Deslauriers 2npoint semi-regular interpolatory subdivision schemes. Our
motivation for this construction is its practical use for further regularity
analysis of wide classes of semi-regular subdivision. Our constructive tools
are local eigenvalue convergence analysis for semi-regular Dubuc-Deslauriers
subdivision, the Unitary Extension Principle and the generalization of the
Oblique Extension Principle to the irregular setting by Chui, He and
St\"ockler. This group of authors derives suitable approximation of the inverse
Gramian for irregular Bspline subdivision. Our main contribution is the
derivation of the appropriate approximation of the inverse Gramian for the
semi-regular Dubuc-Deslauriers scaling functions ensuring n vanishing moments
of the corresponding framelets