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Geometric Search and Geometric Processing

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Digital and Discrete Geometry

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Abstract

In this chapter, we focus on cutting edge problems in geometric data processing. These problems have common properties and usually can be summarized as generally as: Given a set of n data points \(x_1,...,x_n\) in m-dimensional space,R m, how do we find the geometric structures of the sets or how do we use the geometric properties in real data processing? Geometric data representation, image segmentation, and object thinning are some of the most successful applications of discrete and digital geometry. Along with the fast development of wireless networking, geometric search, especially R-tree technology, has become a central method for quickly identifying and retrieving a geometric location. 3D thinning is one of the best applications developed through digital geometry by preserving topological structures while reducing pixels or voxels. The classic methods of geometric pattern recognition such as the k-means and k-nearest neighbor algorithms are also included. The newest topic in BigData and data science is concerned with these methods.

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Notes

  1. 1.

    VerticalNews reported a patent application by Canon Inc with the description on this. http://www.spclab.com/research/lambda/VerticalNewsReportsRelatedChen91a.pdf http://www.spclab.com/research/lambda/VerticalNewsReportsRelatedChen91a.pdf.

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Authors and Affiliations

  1. University of the District of Columbia, Washington, District of Columbia, USA

    Li M. Chen

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  1. Li M. Chen
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Correspondence to Li M. Chen .

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© 2014 Springer International Publishing Switzerland

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Chen, L. (2014). Geometric Search and Geometric Processing. In: Digital and Discrete Geometry. Springer, Cham. https://doi.org/10.1007/978-3-319-12099-7_12

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  • DOI: https://doi.org/10.1007/978-3-319-12099-7_12

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