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

被引：15

作者：

Kucukoglu, Irem ^{[1
]}

Simsek, Buket ^{[2
]}

Simsek, Yilmaz ^{[3
]}

机构：

[1] Alanya Alaaddin Keykubat Univ, Fac Engn, Dept Engn Fundamental Sci, TR-07425 Antalya, Turkey

[2] Akdeniz Univ, Fac Engn, Dept Elect Elect Engn, Antalya, Turkey

[3] Univ Akdeniz, Fac Sci, Dept Math, TR-07058 Antalya, Turkey

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 344卷

关键词：

Facial expression recognition; Machine learning; Bezier curve; Generating function; Statistical evaluations; Bernstein basis function; GENERATING-FUNCTIONS;

D O I：

10.1016/j.amc.2018.10.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：150 / 162

页数：13

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