Analysis And Research Of Image Moment In Polar Coordinate System

With the development of the field of information science,the application of image processing subjects in many fields has become more and more popular.It is closely related to many disciplines,including image processing,computer graphics,artificial intelligence,etc.,so realizing accurate and efficient decision-making has been a key research issue in digital image analysis.Extraction of image features and pattern recognition are two key steps in digital image analysis.Since Hu first introduced moments in pattern recognition tasks in 1962,as a kind of global invariant features,moments have been frequently used in various applications of computational vision.The existing image moments are divided into non-orthogonal moments and orthogonal moments according to whether their basis functions satisfy orthogonality.Since the basis functions of non-orthogonal moments such as geometric moments,central moments,and normalized moments are not orthogonal,it is difficult to reconstruct images with non-orthogonal moments.Furthermore,the image features calculated from non-orthogonal moments have high information redundancies,and are sensitive to noise,which degrades their classification performance and robustness to noise.In recent years the orthogonal moments have received extensive attentions due to their advantages over the non-orthogonal moments such as with less information redundancies and high tolerances to noise.They are divided into two categories including Cartesian orthogonal moments and circular orthogonal moments.The circular orthogonal moments defined in polar coordinates have attracted more attentions due to their obvious superiorities such as intrinsic rotation invariance and mirror invariance.This thesis proposes two novel kinds of circular orthogonal moments namely Laguerre circular orthogonal moment and Gegenbauer circular orthogonal moment.Their useful characteristics have been proved,and their performances on image reconstruction,pattern classification and tolerances to noise and image blurring are verifies through experiments.The experimental results demonstrate their superiorities to some representative circular orthogonal moments.The main contributions of this thesis are summarized as follows:(1)Based on Laguerre orthogonal polynomials,a new type of circular orthogonal moment named as Laguerre circular orthogonal moment has been proposed.Theoretical analysis demonstrates that the Laguerre circular orthogonal moment is invariant to image rotation and mirror.The experimental results show that the proposed moment yields a higher performance than that of the frequently-used moments i.e.Fourier-Mellin moments in terms of image reconstruction precision,classification accuracy and tolerance to various types of noise and image blurring,which can be used as an alternative type of global invariant features for image analysis.(2)Based on Gegenbauer polynomials,a new type of circular orthogonal moment named as Gegenbauer circular orthogonal moment has been proposed.Theoretical analysis demonstrates that the Gegenbauer circular orthogonal moment is invariant to image rotation and mirror.The experimental results show that the proposed moment outperforms over Fourier-Mellin and Bessel moments in terms of image reconstruction precision,classification accuracy and tolerance to various types of noise and image blurring.It can be used as an alternative type of global invariant features in relational applications of computational vision.