Image Analysis By Discrete Radial Tchebichef Moments

The definition of the moment function and invariance of the image began from the 60's in last century. The moment and its function have been widely used in image processing and pattern recognition in various fields since Hu firstly put up with the moment's invariant theory in 1961.Geometric moment is the earliest moment, simple and convenient. But the Inadequacy thing is when in dealing with some complex image, the transformation is not very convenient. And with the order increasing, the phenomenon of instability in calculation and not easy to concentrate on analysis will appear.A distinctive feature of orthogonal moments is to describe the independent characteristics of the image, with minimum redundancy of information. because of its value range have certain requirements , the domain often be normalized before calculation.Current computational method of Image processing is numerical calculation, in a way of the discrete summation to approach the real integral operation. While the several given moment functions are all using a continuous integration form.Because Zernike moments have features like rotational invariance, low noise sensitivity, orthogonality and the minimum redundancy of information, they are widely applied in image engineering field.However, since the basis functions of the Zernike moments are continuous functions, large discretization error is unavoidably caused during the process of discretization.To solve this problem, discrete orthogonal Tchebichef moments are proposed by Mukundan, etc. then another radial Tchebichef moments which are defined in polar coordinates are proposed. Solve the discrete orthogonal moments defined in the Cartesian coordinate system is not easy to obtain rotation invariant problem. Mukundan's method adopted integer-point sampling which has defects of too many sampling points when the radius is small while the number of points are insurfficent when the radius is large and the efficiency of processing image is low.A square-to-circular image transformation is introduced to the image and make discrete vetor base which discrete radial Tchebichef polynomial orthgonal to discrete Fourier in circumferential direction constructing a kind of new discrete radial Tchebichef moments. The experimental results show that the suggested method is better than Mukundan's method when processing large image and eliminates snowflake in the process of image reconstruction. In order to enhance the effect of the image reconstruction,in this paper the section iterative method is proposed to reduce the error accumulation. Experimental results show that we can get better image reconstruction results.