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- W257860868 abstract "Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the approximating subdivision operator $S$ in the analysis of the $S$ normal multi-scale transform, established in [7, Theorem 2.6], significantly disfavors the practical use of these transforms whenever $P_ell P$. We analyze in detail the normal multi-scale transform for planar curves based on B-spline subdivision scheme $S_p$ of degree $pge3$ and derive higher smoothness of the normal re-parameterization than in [7]. We show that further improvements of the smoothness factor are possible, provided the approximate normals are cleverly chosen. Following [10], we introduce a more general framework for those transforms where more than one subdivision operator can be used in the prediction step, which leads to higher detail decay rates." @default.
- W257860868 created "2016-06-24" @default.
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- W257860868 date "2013-11-18" @default.
- W257860868 modified "2023-09-27" @default.
- W257860868 title "B-spline normal multi-scale transforms for planar curves" @default.
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