Image analysis by discrete orthogonal Racah moments

Hongqing Zhu Zhu (1) , Huazhong Shu (1, 2) , Jun Liang (1) , Limin M. Luo (1, 2) , Jean-Louis Coatrieux (2, 3)

1 LIST - University of Science & Technology
2 CRIBS - Centre de Recherche en Information Biomédicale sino-français
3 LTSI - Laboratoire Traitement du Signal et de l'Image

Discrete orthogonal moments are powerful tools for characterizing image shape features for applications in pattern recognition and image analysis. In this paper, a new set of discrete orthogonal moments is proposed, based on the discrete Racah polynomials. In order to ensure numerical stability, the Racah polynomials are normalized, thus creating a set of weighted orthonormal Racah polynomials, to define the so-called Racah moments. This new type of discrete orthogonal moments eliminates the need for numerical approximations. The paper also discusses the properties of Racah polynomials such as recurrence relations and permutability property that can be used to reduce the computational complexity in the calculation of Racah polynomials. Finally, we demonstrate Racah moments' feature representation capability by means of image reconstruction and compression. Comparison with other discrete orthogonal transforms is performed, and the results show that the Racah moments are potentially useful in the field of image analysis.

Mots clés: Discrete orthogonal moments; Racah polynomials; Image reconstruction; Image compression; POLYNOMIALS; TRANSLATION; INVARIANTS; LATTICE

Domaines: Ingénierie biomédicale; Théorie des représentations [math.RT]; Traitement du signal et de l'image [eess.SP]; Complexité [cs.CC]; Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]

Hongqing Zhu Zhu, Huazhong Shu, Jun Liang, Limin M. Luo, Jean-Louis Coatrieux. Image analysis by discrete orthogonal Racah moments. Signal Processing, 2007, 87 (4), pp.687-708. ⟨10.1016/j.sigpro.2006.07.007⟩. ⟨inserm-00139088⟩