2D and 3D Orthogonal Moments

Jan Flusser,

Jan Flusser

Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

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Tomáš Suk,

Tomáš Suk

Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

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Barbara Zitová,

Barbara Zitová

Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

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Book Author(s):Jan Flusser,

Jan Flusser

Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

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Tomáš Suk,

Tomáš Suk

Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

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Barbara Zitová,

Barbara Zitová

Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

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First published: 28 October 2016

https://doi.org/10.1002/9781119039402.ch7

Citations: 7

Summary

This chapter presents a survey of 2D and 3D orthogonal (OG) moments that are of importance in image analysis. Expressing orthogonal polynomials by means of hypergeometric functions may provide us with an insight into the complexity of the orthogonal polynomials. It explains the Yang's method in detail and gives a brief overview of polynomials and moments with reported applications in image analysis. The chapter reviews three approaches to the image reconstruction from moments, direct calculation, reconstruction in a Fourier domain, and reconstruction from OG moments. It presents an overview of 2D and 3D orthogonal moments with relevance to image analysis. Krawtchouk moments have become popular in image processing, because their kernel functions, Krawtchouk polynomials, can be made local by a proper setting of their parameters. Dual Hahn polynomials were obtained by interchanging the variable x and parameter n in the definition of Hahn polynomials.

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