| Since Hu first introduced the moment invariant in 1961, moments and moment functions have been widely used in the fields of image analysis and pattern recognition.Zernike moments have the orthogonality property and good rotation invariance, which has been extensive researched and developmented. However, Zernike moment basis function as a continuous function, large errors will be generated in the calculation process, so discrete orthogonal moments have been proposed in recent years,, such as the Tchebichef moments, Hahn moments and Krawtchouk moments and so on. Krawtchouk moments can be extracted local features of the image at different locations, which is superior to other two kinds of discrete moments, but the numerical divergence of its high-order moments makes it impossible to accurately rebuild large image.In this paper, we briefly introduce and evaluate various forms of moments and introduced a series of algorithm accuracy evaluation system, A error propagation model of Krawtchouk moments is proposed and the mechanism of the error propagation has been analyzed. In order to accurately compute Krawtchouk polynomials, a piecewise recursive algorithm based GMP bignum library, which is useful for the arbitrary parameter p, has been present. The experiment prove that the propose method can effectively restrain and control the accumulation error of the high-order Krawtchouk moments to a certain extent, and finally eliminate the degradation of reconstruction images.Meanwhile,Krawtchouk moments do not have a natural geometric invariance (rotation, scaling and translation), which limit the application of Krawtchouk moments to some extent. A rectangle-to-circle image transformation is introduced to the image and make discrete vetor base which discrete radial Krawtchouk polynomial orthgonal to discrete Fourier in circumferential direction constructing a kind of new discrete radial Krawtchouk moments. The experimental results show that the proposed Krawtchouk moments are invariant... |
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