On Two Types Of Radial Orthogonal Moments

The technology of moments has widespread applications in image analysis, such as image reconstruction and compression, target object classifies, pattern recognition, figure watermark, machine vision and so on. Especially the application of orthogonal moments in image processing has been a hot spot at home and abroad. Y.L. Sheng proposed orthogonal Fourier-Mellin moments based on radial orthogonal polynomials in 1994, and illustrated that the number and position of zero point of radial polynomials respectively represent sampling frequency and sampling position on image. Obviously orthogonal moments solve the problem of sampling on image. Subsequently many scholars has studied the orthogonal moments function based on radial polynomials. Mukundan proposed the discrete Tchebichef moments which improve the precision and effect of reconstruction image greatly, as the moments did not require integral approximation and coordinate transformation existing in the analysis methods by discrete orthogonal moments. The performance of discrete Tchebichef moments on image processing was far superior to continuous orthogonal moments. On the basis of already existing theory of orthogonal moments, two kinds of radial orthogonal moments are introduced and applied to image reconstruction experiments in this paper.This paper proposes a kind of orthogonal polynomials with weighting function of x2m starting from the complexity of kernel function and the peak of orthogonal moments. Then some properties including orthogonality, norm and recurrence relation are proved by the methods of mathematical induction based on generating function. By combining the orthogonal polynomials with weighting function of x2 with Jacobi polynomials, a kind of alternate orthogonal polynomials is obtained.And the binary image reconstructing experiment by using the alternate orthogonal moments whose kernel functions are alternate orthogonal polynomials shows that alternate orthogonal moments have better reconstruction effect than Zernike moments.Starting from the structure of orthogonal moments, this paper presents a kind of discrete bi-Tchebichef moments by adopting discrete Tchebichef polynomials on both radial and circumferential direction to construct a two dimensional discrete orthogonal basis. The experiment of gray image reconstruction by using this discrete bi-Tchebichef moments shows that bi-Tchebichef moments have better reconstruction effect than Mukundan's methods from four aspects: reconstruction image, reconstruction error, moments computing time, and peak signal to noise ratio. What's more, the former methods avoid the phenomenon of snowflake television spots.