Image Processing Reference
In-Depth Information
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Fig. 5.21.
Deletion of unnecessary or redundant voxels in a line figure (see Algo-
rithms 5.19 and 5.20).
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Fig. 5.22.
Illustration of Algorithm 5.20 (corner elimination).
putational geometry (or digital geometry) [Goodman04]. It has been widely
applied in a variety of areas including physics, biology, and geography. It has
also become one of the inevitable tools in image pattern analysis and com-
puter graphics. Thus, an enormous volume of papers and topics have been
published that referred to Voronoi tessellation and relating problems. Voronoi
tessellation and its close relations have been called by different names, such
as: Voronoi polygon, Dirichlet tessellation (division), Delaunay triangulation,
Voronoi diagram.
Concepts of Voronoi tessellation and related topics are basically ap-
plicable to a digitized image. However, sometimes serious differences from
the continuous space are found in procedures to solve concrete problems
[Mase81, Toriwaki81, Toriwaki84, Toriwaki88]. Extension to a 3D image from
a 2D image is not di
cult in principle, but some complicated problems exist
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