Image analysis by discrete orthogonal dual Hahn moments

  • Authors:

  • Hongqing Zhu;Huazhong Shu;Jian Zhou;Limin Luo;J. L. Coatrieux

  • Affiliations:

  • Laboratory of Image Science and Technology, Department of Computer Science and Engineering, Southeast University, 210096 Nanjing, People's Republic of China;Laboratory of Image Science and Technology, Department of Computer Science and Engineering, Southeast University, 210096 Nanjing, People's Republic of China and Centre de Recherche en Information ...;Laboratory of Image Science and Technology, Department of Computer Science and Engineering, Southeast University, 210096 Nanjing, People's Republic of China;Laboratory of Image Science and Technology, Department of Computer Science and Engineering, Southeast University, 210096 Nanjing, People's Republic of China and Centre de Recherche en Information ...;INSERM U642, Laboratoire Traitement du Signal et de l'Image, Université de Rennes I, 35042 Rennes, France and Centre de Recherche en Information Biomédicale Sino-français (CRIBs), F ...

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2007

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Abstract

In this paper, we introduce a set of discrete orthogonal functions known as dual Hahn polynomials. The Tchebichef and Krawtchouk polynomials are special cases of dual Hahn polynomials. The dual Hahn polynomials are scaled to ensure the numerical stability, thus creating a set of weighted orthonormal dual Hahn polynomials. They are allowed to define a new type of discrete orthogonal moments. The discrete orthogonality of the proposed dual Hahn moments not only ensures the minimal information redundancy, but also eliminates the need for numerical approximations. The paper also discusses the computational aspects of dual Hahn moments, including the recurrence relation and symmetry properties. Experimental results show that the dual Hahn moments perform better than the Legendre moments, Tchebichef moments, and Krawtchouk moments in terms of image reconstruction capability in both noise-free and noisy conditions. The dual Hahn moment invariants are derived using a linear combination of geometric moments. An example of using the dual Hahn moment invariants as pattern features for a pattern classification application is given.