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Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature

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  • Kucukoglu, Irem
  • Simsek, Buket
  • Simsek, Yilmaz

Abstract

In this paper, by using partial derivative formulas of generating functions for the multidimensional unification of the Bernstein basis functions and their functional equations, we derive derivative formulas and identities for these basis functions and their generating functions. We also give a conjecture and some open questions related to not only subdivision property of these basis functions, but also solutions of a higher-order special differential equations. Moreover, we provide an implementation for a real world problem of human facial expression recognition with the help of curvature of Bezier curves whose machine learning supported by statistical evaluations on feature vectors using in the aforementioned machine learning algorithm.

Suggested Citation

  • Kucukoglu, Irem & Simsek, Buket & Simsek, Yilmaz, 2019. "Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature," Applied Mathematics and Computation, Elsevier, vol. 344, pages 150-162.
    • Handle: RePEc:eee:apmaco:v:344-345:y:2019:i::p:150-162
    DOI: 10.1016/j.amc.2018.10.012
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    References listed on IDEAS

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    1. Yilmaz Simsek & Mehmet Acikgoz, 2010. "A New Generating Function of ( ) Bernstein-Type Polynomials and Their Interpolation Function," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, March.
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