Research On Image Reconstruction Method Based On Image Moment In Cartesian Coordinate System

With the development of social informatization level trend growing, image processing-related intelligent application is more extensive and profound impact on people’s daily lives. Image geometric invariant descriptor is an important issue in the field of image recognition. Image moments, as a kind of global feature descriptors, have been widely used in many image processing fields such as image reconstruction, image recognition, data compression and digital watermarking etc, due to their good stability under geometric distortion and decent noise robustness. This paper addressed the issue of image geometric invariant descriptor and paid attention to the orthogonal moment based methods.The main research work and innovation points are summarized as follows:(1) Firstly, the latest development and research on image moments such as the geometric moments, Legendre moments, Gaussian-Hermite moments, Tchebichef moments, Krawtchouk moments and Hahn moments were summarized. Their recent related works have been detailed. We also analyzed and compared experimentally the continuous and discrete orthogonal moments defined in Cartesian coordinates in terms of image reconstruction, image representation noise robustness and computational cost. With those results, Image moment theory constantly enriches.(2) Secondly, based on the unbiased finite impulse response (UFIR) polynomial, we present a novel kind of image discrete orthogonal moments-UFIR moments. They are free of the numerical integration error associated with continuous orthogonal moments. Since the domain of these polynomials matches the discrete domain of the image accurately, the transformation of the image coordinate space is not required in calculations of these moments. This property makes the moments superior to the continuous orthogonal moments in terms of image reconstruction accuracy. Compared with the existing discrete orthogonal moments the proposed moments do not involve any factorial calculation, consequently, yield higher calculation accuracy and efficiency. In addition, there is no need for parameter selection, and so the UFIR discrete orthogonal moments are adapt for blind analysis of images. In order to reduce their computational costs and representation errors further, the computational aspects of the moments using the recursive property are discussed as well. Experimental results show the superiority of these moments.(3) Finally, we also put forward a kind of image reconstruction method based on image grid concept which is essentially conducted on orthogonal-space’s subspace. The classical discrete orthogonal moments such as Krawtchouk moments, Hahn moments and UFIR moments are considered and their image reconstruction performances are improved significantly via our orthogonal-space’s subspace reconstruction method especially in high-order cases. Furthermore, we prove theoretically the orthogonality of the subspace in an orthogonal space, and concluded that the smooth portion of the orthogonal polynomial has no performance contribution to image reconstruction while its dramatic portion yields obvious contribution with the premise that the dramatic numerical changes must be within a certain scope, otherwise, serious distortion will arise in reconstructed image in case of using high-order moments.