Summary
While human intelligence can easily grasp the shapes in a scene from the information acquired by the eyes, this task is far from trivial for computers. This chapter surveys recent advances in the curve reconstruction problem, in which polygonal curves that approximate underlying curves of unknown shape are constructed from given sample points from the curves. In recently developed algorithms for this purpose, a powerful mathematical tool, called the Voronoi diagram, plays a main role for extracting the shape from the sample points. The aim of this chapter is to survey the algorithms, offering an intuitive view about the role that Voronoi diagram plays.
In the last decade, great advances were brought about since a concept called ε-sample was introduced. This enabled us to sample an underlying curve in variable density according to its local feature size. This chapter intuitively explains the mechanism by which algorithms can handle ε-samples. Another recent topic is the introduction of the optimization technique which has been applied to many other practical problems. This chapter briefly reviews how this technique is applied to the curve reconstruction problem.
Another important application of the curve reconstruction problem is to extract the “skeleton” structure of a target figure: The Voronoi edges dual to the Delaunay edges not used in the reconstruction is known to approximate the medial axis of the figure. As reported the Chapter 7 of this book, this technique is a fundamental tool for some GIS applications such as automated feature extraction from digitized maps.
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Hiyoshi, H. (2009). Intelligent Solutions for Curve Reconstruction Problem. In: Gavrilova, M.L. (eds) Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence. Studies in Computational Intelligence, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85126-4_6
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