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Mathematical Techniques for Curve Fitting

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Structural Pattern Recognition

Part of the book series: Springer Series in Electrophysics ((SSEP,volume 1))

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Abstract

As we pointed out in the previous chapter, the brightness matrix of a picture must be transformed into a more compact mathematical structure before we can proceed with any pattern recognition analysis. Curve and surface fitting is a popular technique in many branches of engineering and computer science when large volumes of data must be described in a compact way. We describe a number of such techniques in this chapter. Sections 2.2–4 deal primarily with least integral square error approximations of functions of a single variable over their whole domain. Section 2.5 discusses uniform approximations (i.e., those minimizing the maximum pointwise error). Splines and piecewise approximations are introduced in Section 2.7 and their properties are investigated in Sections 2.8–12. Readers may prefer to skip this chapter, except possibly Section 2.6, on first reading and refer to it whenever its material is used in the sequel. Section 2.6 discusses some of the problems associated with the application of curve fitting techniques to pattern recognition and their relation to transforms.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Princeton University, 08540, Princeton, New Jersey, USA

    Theodosios Pavlidis PhD

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  1. Theodosios Pavlidis PhD
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© 1977 Springer-Verlag Berlin Heidelberg

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Pavlidis, T. (1977). Mathematical Techniques for Curve Fitting. In: Structural Pattern Recognition. Springer Series in Electrophysics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88304-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-88304-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-88306-4

  • Online ISBN: 978-3-642-88304-0

  • eBook Packages: Springer Book Archive

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