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Journal of Mathematical Imaging and Vision

, Volume 61, Issue 4, pp 555–570 | Cite as

A New Hybrid form of Krawtchouk and Tchebichef Polynomials: Design and Application

  • Sadiq H. AbdulhussainEmail author
  • Abd Rahman Ramli
  • Basheera M. Mahmmod
  • M. Iqbal Saripan
  • S. A. R. Al-Haddad
  • Wissam A. Jassim
Article
  • 212 Downloads

Abstract

In the past decades, orthogonal moments (OMs) have received a significant attention and have widely been applied in various applications. OMs are considered beneficial and effective tools in different digital processing fields. In this paper, a new hybrid set of orthogonal polynomials (OPs) is presented. The new set of OPs is termed as squared Krawtchouk–Tchebichef polynomial (SKTP). SKTP is formed based on two existing hybrid OPs which are originated from Krawtchouk and Tchebichef polynomials. The mathematical design of the proposed OP is presented. The performance of the SKTP is evaluated and compared with the existing hybrid OPs in terms of signal representation, energy compaction (EC) property, and localization property. The achieved results show that SKTP outperforms the existing hybrid OPs. In addition, face recognition system is employed using a well-known database under clean and different noisy environments to evaluate SKTP capabilities. Particularly, SKTP is utilized to transform face images into moment (transform) domain to extract features. The performance of SKTP is compared with existing hybrid OPs. The comparison results confirm that SKTP displays remarkable and stable results for face recognition system.

Keywords

Orthogonal polynomials Discrete orthogonal moments Energy compaction Localization property Face recognition system 

List of Abbreviation

COM

Continuous orthogonal moment

DCT

Discrete cosine transform

DKTT

Discrete Krawtchouk–Tchebichef transform

DTKT

Discrete Tchebichef–Krawtchouk transform

EC

Energy compaction

FR

Face Recognition

GM

Geometric moment

KP

Krawtchouk Polynomial

KTP

Krawtchouk–Tchebichef polynomial

OM

Orthogonal moment

OP

Orthogonal polynomial

SKTP

Squared Krawtchouk–Tchebichef polynomial

SKTT

Squared discrete Krawtchouk–Tchebichef transform

SVM

Support vector machine

TKP

Tchebichef–Krawtchouk polynomial

TP

Tchebichef polynomial

Notes

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer EngineeringUniversity of BaghdadBaghdadIraq
  2. 2.Department of Computer and Communication System EngineeringUniversiti Putra MalaysiaSerdangMalaysia
  3. 3.ADAPT Center, School of Engineering, Trinity College DublinUniversity of DublinDublin 2Ireland

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