Numerical Stability Analysis On Orthogonal Moments Of Image

R.Mukundan, in the study of using Tchebichef moments to analysis image, proposed that in the calculation process of high order moments,the impact of various error factors will cause the calculated moments to be distorted and even divergent, resulting in the image can not be accurately reconstructed. But what lead to the error of the moment calculation, in recent years, there being no relevant research. Zemike moment‘s basis function is a continuous function. In the calculation process of it, we need to carry on the coordinate transformation and integral approximation about it, which will bring a great discrete error. In recent years, several discrete orthogonal moments, such as Tchebichef moments, Hahn moments and Kawtchouk moments are proposed. Discrete orthogonal moment having no discrete error, its calculation accuracy is only related to the high order numerical error and it does not need the integral approximation and the spatial coordinate transformation to be better than the continuous moment.This paper discusses the numerical stability of orthogonal image moments to solve the causes of transmission error of orthogonal moments. Orthogonal polynomials is the kernel function of orthogonal image moments.In the calculation process of features of orthogonal moments which based on the three term recurrence formula, due to the limitation of computer system’s byte, the truncation error generated by the system,resulting in some orthogonal polynomials’ s computation is stable, while others are divergent,thus lead to the instability of orthogonal mome numerical value when the discrete higher order orthogonal polynomials are calculated. In order to find the general rules of discrete high-order orthogonal polynomial’s three recursive calculation stability. This paper is based on discrete control theory. Three recursive formulas of orthogonal polynomials are transformed into the variable coefficient differential equations of order k, that is, the zero input response of the discrete linear time varying system is discussed. In view of the difficulty of the stability of the discrete linear time varying system, there is no complete theoretical system to determine whether the system is stable or unstable. In this paper, based on the Lee Yap Andrianof theorem, the original state equation is transformed into an equivalent equation of state by a rotation matrix and a diagonal matrix by using the SVD decomposition of the matrix, and deduces two new instability criterion. We successfully find the root cause of the classical Tchebichef and Krawtchouk polynomials instability, and the validity of the proposed criterion is verified by experiments.