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Local feature size

About: Local feature size is a research topic. Over the lifetime, 188 publications have been published within this topic receiving 10423 citations.


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Book
01 Jan 1997
TL;DR: In this article, an introduction to computational geometry focusing on algorithms is presented, which is related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
Abstract: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

4,805 citations

Journal ArticleDOI
TL;DR: A simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points that uses Voronoi vertices to remove triangles from the Delaunay triangulation is given.
Abstract: We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on a local feature size function, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We briefly describe an implementation of the algorithm and show example outputs.

631 citations

Journal ArticleDOI
TL;DR: Central to the method is a multi‐scale classification operator that allows feature analysis at multiplescales, using the size of the local neighborhoods as a discrete scale parameter, which significantly improves thereliability of the detection phase and makes the method more robust in the presence of noise.
Abstract: We present a new technique for extracting line-type features on point-sampled geometry. Given an unstructured point cloud as input, our method first applies principal component analysis on local neighborhoods to classify points according to the likelihood that they belong to a feature. Using hysteresis thresholding, we then compute a minimum spanning graph as an initial approximation of the feature lines. To smooth out the features while maintaining a close connection to the underlying surface, we use an adaptation of active contour models. Central to our method is a multi-scale classification operator that allows feature analysis at multiple scales, using the size of the local neighborhoods as a discrete scale parameter. This significantly improves the reliability of the detection phase and makes our method more robust in the presence of noise. To illustrate the usefulness of our method, we have implemented a non-photorealistic point renderer to visualize point-sampled surfaces as line drawings of their extracted feature curves.

520 citations

Proceedings ArticleDOI
07 Jun 1998
TL;DR: A simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points that uses Voronoi vertices to remove triangles from the Delaunay triangulation is given.
Abstract: We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on a local feature size function, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We briefly describe an implementation of the algorithm and show example outputs.

493 citations

Journal ArticleDOI
TL;DR: In this paper, a graph on a planar point set is constructed by sampling a smooth curve densely enough, and the graph on the samples is a polygonalization of the curve, with no extraneous edges.

386 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20212
20201
20192
20183
201715
20168