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

KÜÇÜKOĞLU İ., Simsek B., ŞİMŞEK Y.

APPLIED MATHEMATICS AND COMPUTATION, cilt.344, ss.150-162, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 344
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.amc.2018.10.012
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.150-162
  • Anahtar Kelimeler: Facial expression recognition, Machine learning, Bezier curve, Generating function, Statistical evaluations, Bernstein basis function, GENERATING-FUNCTIONS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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. (C) 2018 Elsevier Inc. All rights reserved.