Image Analysis by Discrete Orthogonal Hahn Moments

Orthogonal moments are recognized as useful tools for object representation and image analysis. It has been shown that the recently developed discrete orthogonal moments have better performance than the conventional continuous orthogonal moments. In this paper, a new set of discrete orthogonal polynomials, namely Hahn polynomials, are introduced. The related Hahn moment functions defined on this orthogonal basis set are investigated and applied to image reconstruction. In experiments, the Hahn moments are compared with the other two discrete orthogonal moments: Chebyshev and Krawtchouk moments. The simulation results show that the Hahn moment-based reconstruction method is superior to the other two discrete orthogonal moment-based methods.

[1]  J. Arvesú,et al.  Some discrete multiple orthogonal polynomials , 2003 .

[2]  A. Ronveaux,et al.  Difference equations for the co-recursive rth associated orthogonal polynomials of the Dq-Laguerre-Hahn class , 2003 .

[3]  Raveendran Paramesran,et al.  Image analysis by Krawtchouk moments , 2003, IEEE Trans. Image Process..

[4]  R. Mukundan,et al.  Some computational aspects of discrete orthonormal moments , 2004, IEEE Transactions on Image Processing.

[5]  V. B. Uvarov,et al.  Special Functions of Mathematical Physics: A Unified Introduction with Applications , 1988 .

[6]  Roland T. Chin,et al.  On Image Analysis by the Methods of Moments , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  C. Hamitouche,et al.  A moment-based three-dimensional edge operator , 1990, IEEE Transactions on Biomedical Engineering.

[8]  Chee-Way Chong,et al.  A comparative analysis of algorithms for fast computation of Zernike moments , 2003, Pattern Recognit..

[9]  Xiaoli Yang,et al.  A comparative study of Fourier descriptors and Hu's seven moment invariants for image recognition , 2004, Canadian Conference on Electrical and Computer Engineering 2004 (IEEE Cat. No.04CH37513).

[10]  Renato Alvarez-Nodarse,et al.  The dual Hahn q -polynomials in the lattice ? and the q -algebras ? and ? , 1996 .

[11]  Jan Flusser,et al.  Pattern recognition by affine moment invariants , 1993, Pattern Recognit..

[12]  Alfred M. Bruckstein,et al.  Comments on: 'Robust Line Fitting in a Noisy Image by the Method of Moments' , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  R. S. Costas-Santos,et al.  Factorization method for difference equations of hypergeometric type on nonuniform lattices , 2001, 1003.5279.

[14]  Huazhong Shu,et al.  A new fast method for computing Legendre moments , 2000, Pattern Recognit..

[15]  Mihran Tucceryan,et al.  Moment-based texture segmentation , 1994 .

[16]  Rene F. Swarttouw,et al.  The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report Fac , 1996, math/9602214.

[17]  Iván Area,et al.  Classical orthogonal polynomials: dependence on parameters , 2000 .

[18]  Li-Min Luo,et al.  A modified moment-based edge operator for rectangular pixel image , 1994, IEEE Trans. Circuits Syst. Video Technol..

[19]  Miroslaw Pawlak,et al.  On Image Analysis by Moments , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Boris A Kupershmidt.  q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev , 2003 .

[21]  Hon-Son Don,et al.  3-D Moment Forms: Their Construction and Application to Object Identification and Positioning , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  R. Mukundan,et al.  Discrete vs. Continuous Orthogonal Moments for Image Analysis , 2001 .

[23]  R. C. Papademetriou,et al.  Reconstructing with moments , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol. III. Conference C: Image, Speech and Signal Analysis,.

[24]  Alvaro R. De Pierro,et al.  Analysis for the reconstruction of a noisy signal based on orthogonal moments , 2002, Appl. Math. Comput..

[25]  Sim Heng Ong,et al.  Image Analysis by Tchebichef Moments , 2001, IEEE Trans. Image Process..

[26]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[27]  Nico M. Temme,et al.  The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis , 2000 .

[28]  S. Panchanathan,et al.  Image Indexing Using Moments and Wavelets , 1996, 1996. Digest of Technical Papers., International Conference on Consumer Electronics.

[29]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[30]  Wolfram Koepf,et al.  On a structure formula for classical q -orthogonal polynomials , 2001 .

[31]  Huazhong Shu,et al.  Image analysis by discrete orthogonal Racah moments , 2007, Signal Process..

[32]  J. Arvesú,et al.  On the Connection and Linearization Problem for Discrete Hypergeometric q-Polynomials , 2001 .

[33]  G. Talenti.  Recovering a function from a finite number of moments , 1987 .

[34]  Mihran Tuceryan,et al.  Moment-based texture segmentation , 1994, Pattern Recognit. Lett..