Exponential Splines and Minimal-Support Bases for Curve Representation
| Autor: | R. Delgado-Gonzalo P. Thévenaz M. Unser |
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| Rok vydání: | 2012 |
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| Zdroj: | Computer Aided Geometric Design |
| DOI: | 10.1016/j.cagd.2011.10 |
| Popis: | Our interest is to characterize the spline like integer shift invariant bases capable of reproducing exponential polynomial curves. We prove that any compact support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B spline with a compact support distribution. As a direct consequence of this factorization theorem we show that the minimal support basis functions of that subspace are linear combinations of derivatives of exponential B splines. These minimal support basis functions form a natural multiscale hierarchy which we utilize to design fast multiresolution algorithms and subdivision schemes for the representation of closed geometric curves. This makes them attractive from a computational point of view. Finally we illustrate our scheme by constructing minimal support bases that reproduce ellipses and higher order harmonic curves. |
| Databáze: | OpenAIRE |
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