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On the Coupling of Decimation Operator with Subdivision Schemes for Multi-scale Analysis

  • Zhiqing KuiEmail author
  • Jean Baccou
  • Jacques Liandrat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)

Abstract

Subdivision schemes [5, 11] are powerful tools for the fast generation of refined sequences ultimately representing curves or surfaces. Coupled with decimation operators, they generate multi-scale transforms largely used in signal/image processing [1, 3] that generalize the multi-resolution analysis/wavelet framework [8]. The flexibility of subdivision schemes (a subdivision scheme can be non-stationary, non-homogeneous, position-dependent, interpolating, approximating, non-linear...) (e.g. [3]) is balanced, as a counterpart, by the fact that the construction of suitable consistent decimation operators is not direct and easy.

In this paper, we first propose a generic approach for the construction of decimation operators consistent with a given linear subdivision. A study of the so-called prediction error within the multi-scale framework is then performed and a condition on the subdivision mask to ensure a fast decay of this error is established. Finally, the cases of homogeneous Lagrange interpolatory subdivision, spline subdivision, subdivision related to Daubechies scaling functions (and wavelets) and some recently developed non stationary non interpolating schemes are revisited.

Keywords

Multi-scale analysis Decimation Subdivision 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Centrale Marseille, I2M, UMR 7353, CNRS, Aix-Marseille UniversityMarseilleFrance
  2. 2.Institut de Radioprotection et de Sûreté Nucléaire (IRSN)PSN-RES/SEMIA/LIMAR, CE CadaracheSaint Paul Les DuranceFrance

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