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Digital-Discrete Method and Its Relations to Graphics and AI Methods

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Digital Functions and Data Reconstruction

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Abstract

As a practical method,digital-discrete data reconstruction uses both discrete and continuous methods for data interpolation and approximation. Today,a significant development in discrete mathematics is digital technology. Digital methods contain a flavor of graphical presentation and artificial intelligence. It is very interesting to explore the relationship between digital methods and graphical and intelligence methods. In this chapter,we introduce the subdivision method and the moving least squares method. These two methods are popular smooth data fitting methods in computer graphics. The subdivision method is an intuitive method for smooth shape design; the moving least squares method is a mesh-free method for data fitting. Our purpose is to provide a potential link from main stream techniques to digital functions. We also present the extension of digital functions to more general cases in artificial intelligence,especially in partial information searches and image segmentation. This expansion uses lambda-connectedness,which shares the same mathematical foundation as gradually varied functions. We include the algorithms for segmentations and fitting for image objects. This chapter also contains future research topics of the digital-discrete method.

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Acknowledgements

Many thanks to Dr. Peter Schroeder at Caltech for the online software on Chaikin’s method and the four point algorithm:http://www.multires.caltech.edu/teaching/demos/java/chaikin.htm.http://www.multires.caltech.edu/teaching/demos/java/4point.htm. Also thanks to Dr. Ken Joy at UC Davis for pointing out Chaikin’s work. Many thanks to Dr. Paul Chew at Cornell University for his software on Delaunay diagrams.http://www.cs.cornell.edu/home/chew/Delaunay.html.

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

    Li M. Chen

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Chen, L.M. (2013). Digital-Discrete Method and Its Relations to Graphics and AI Methods. In: Digital Functions and Data Reconstruction. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5638-4_12

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  • DOI: https://doi.org/10.1007/978-1-4614-5638-4_12

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-5637-7

  • Online ISBN: 978-1-4614-5638-4

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