Earticle

초록

영어

The continuous orthogonal polynomials, such as Zernike and pseudo-Zernike, are often used as an expansion of corneal height data. However, the use of continuous polynomials has some limitations due to the discretization. It is because that the integrals are usually approximated by discrete summations, and this process not only leads to numerical errors, but also severely affects some analytical properties such as rotation invariance, orthogonality, etc. To overcome these drawbacks, this paper presents a methodology for decomposing corneal height data into discrete orthogonal Tchebichef polynomials. Tchebichef polynomials, which are a product of angular functions and radial Tchebichef polynomials, are orthogonal in the discrete coordinate. Therefore, the approximation error caused by discretization can be avoided, and the analytical property can be well preserved. Examples of modeling corneal elevation are provided for simulation corneas, real normal corneas, and real abnormal corneas. The experimental results show that the proposed discrete Tchebichef polynomials have better surface representation capability than Zernike polynomials or pseudo-Zernike polynomials, and have more robust fitting for the level of noise found in current videokeratoscopes, so that they can be used as an alternative to fit the corneal surface.

목차

Abstract
 1. Introduction
 2. Background
  2.1. Zernike polynomials
  2.2. Pseudo-Zernike polynomials
 3. Modeling corneal surfaces with discrete Tchebichef polynomials
 4. Experimental results and discussions
 5. Conclusions
 References

키워드

저자

• Hongqing Zhu [ Department of Electronics and Communications Engineering, East China University of Science and Technology ]
• Min liu [ Department of Electronics and Communications Engineering, East China University of Science and Technology ]
• Huazhong Shu [ Lab of Image Science and Technology, School of Computer Science and Engineering, Southeast University ]
• Jin Zhang [ Lab of Image Science and Technology, School of Computer Science and Engineering, Southeast University ]
• Hui Zhang [ Lab of Image Science and Technology, School of Computer Science and Engineering, Southeast University ]

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Signal Processing, Image Processing and Pattern Recognition

• 간기

  격월간

• pISSN

  2005-4254

• 수록기간

  2008~2016

• 십진분류

  KDC 505 DDC 605