Proceedings ArticleDOI
Curve and surface smoothing without shrinkage
Gabriel Taubin
- pp 852-857
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TLDR
A new method for smoothing piecewise linear shapes of arbitrary dimension and topology is introduced, in fact a linear low-pass filter that removes high-curvature variations, and does not produce shrinkage.Abstract:
For a number of computational purposes, including visualization of scientific data and registration of multimodal medical data, smooth curves must be approximated by polygonal curves, and surfaces by polyhedral surfaces. An inherent problem of these approximation algorithms is that the resulting curves and surfaces appear faceted. Boundary-following and iso-surface construction algorithms are typical examples. To reduce the apparent faceting, smoothing methods are used. In this paper, we introduce a new method for smoothing piecewise linear shapes of arbitrary dimension and topology. This new method is in fact a linear low-pass filter that removes high-curvature variations, and does not produce shrinkage. Its computational complexity is linear in the number of edges or faces of the shape, and the required storage is linear in the number of vertices. >read more
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References
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Scale-space filtering
TL;DR: Scale-space filtering is a method that describes signals qualitatively, managing the ambiguity of scale in an organized and natural way.
Proceedings ArticleDOI
A signal processing approach to fair surface design
TL;DR: A very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology that is a linear time and space complexity algorithm and a very effective fair surface design technique.
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Fourier Descriptors for Plane Closed Curves
Charles T. Zahn,Ralph Roskies +1 more
TL;DR: It is established that the Fourier series expansion is optimal and unique with respect to obtaining coefficients insensitive to starting point and the amplitudes are pure form invariants as well as are certain simple functions of phase angles.