Image Analysis Based On Purely Discrete Orthogonal Moments

In the process of image processing,the image moment is used as an effective method to describe the global invariant descriptors of the image,such as orthogonal moment and non-orthogonal moment.Non-orthogonal moments,such as geometric moments,have superior properties such as geometric invariance,but there is information redundancy,which is not conducive to image reconstruction and limits its application extension.Orthogonal moments,such as Zernike moment,orthogonal Fourier-Mellin moment,Bessel-Fourier moment,because of the orthogonality of its projection function,can carry out accurate image reconstruction,but the definition domain is continuous,the orthogonal moments calculated by using the zeroth order approximation method,are generally suffer from the numerical integration errors.Therefore,in the calculation of moments,we need to transform the coordinate domain,transform the square image function definition in the Cartesian coordinate into the unit circle of the polar coordinate domain,which will produce the geometrical error and can affect the performance of the calculation precision and recognition of the moment.The existing orthogonal moments can be divided into Cartesian orthogonal moments and polar coordinate orthogonal moments according to the definition of coordinate domain.The orthogonal moments defined in the polar coordinate domain have rotation invariance due to its own characteristics.In this paper,we propose a series of improvement methods for the numerical integration error and geometrical error existing in the current circularly orthogonal moments,and the main work content and innovation are as follows:(1)Based on Chebyshev function,a new circularly orthogonal moment is proposed in this paper.The moment is defined in the entire polar coordinate domain,unlike the existing circularly orthogonal moment,the definition is the unit circle,which needs to convert definition domain of the image,so there is no geometrical error.For a given moment calculation order n,the radial projection function is smoother and the oscillation frequency is lower,and the numerical integration error is highly robust compared with the existing circularly orthogonal moments.Therefore,this moment can be used for more accurate image reconstruction and better performance in image classification.(2)A novel category of circularly moments named as purely discrete circularly orthogonal moments is proposed.For a given digital image,we design a method to transform the image into its discrete polar coordinate space.Based on unbiased finite impulse response discrete orthogonal polynomials,the purely discrete circularly orthogonal moment is defined in the discrete polar coordinate domain.Since the definition of the proposed circularly orthogonal moment does not relate to the double integration,it is free of the numerical integration error.This makes the proposed orthogonal moments have better performance than the existing circularly orthogonal moments in preserving the useful information of the image and image reconstruction accuracy.The experimental data show that the proposed moments have better performance than the existing circularly orthogonal moments in image reconstruction and image classification,and have high robustness to common image noises such as salt and pepper noise,Gaussian noise and image smoothing distortion.(3)Describe a method for secure palmprint recognition,in which the service provider does not have direct access to the image information content,and the image information is accessed completely in the form of encryption.Firstly,the chaotic encryption algorithm is introduced into the space domain,and then a new pure discrete circular orthogonal moment is proposed,which is used to extract the invariant feature independent from the cryptographic secret key from the encrypted palmprint image to access and identify information.The experimental data show that the proposed palmprint recognition method has certain superiority in the classification accuracy and the calculation cost for the encrypted palmprint image and the plaintext palmprint image.Therefore,the proposed method has some potential in the privacy protection of palmprint images.