A Set Of Discrete And Continuous Orthogonal Moments Of Invariants In Image Analysis

Moments, which is used to describe general characteristics of the object, has been widely used in image processing field and other applications. Since1961Hu introduced the moment invariant, based on this theory related researchers put forward a series of moment invariant using different methods. They made a great contribution in image recognition, target classification, azimuth estimation, image coding and rebuild areas. There are some widely used moments like orthogonal moment and discrete moment, for example, Tchebichef moment, orthogonal Fourier-Mellin, Zernike moment, Legendre moment and Krawtchouk moment etc. This paper is also around these moments to construct image invariants, which are used for image recognition and classification experiments.Firstly, two new affine invariants are introduced for object recognition using discrete orthogonal Tchebichef moments. Then using Krawtchouk moment construct a new scale invariant. The scale invariant is derived from Krawchouk polynomials directly. So no numerical approximation is involved in deriving the moments. Lastly two sets of invariants which are invariant to convolution with circularly symmetric point spread function (PSF) are introduced for object recognition and image classification using orthogonal Fourier-Mellin moments and quaternion Fourier-Mellin moments, respectively.Also Radon transformation and polar Fourier transform are introduced, mainly about their properties. These properties showed that it can be well used to image processing. In this paper we get image rotation invariant using the combination of Radon transform and Fourier-Mellin moments. Using above methods, a lot of experiments were introduced and showed these invariants have better performance, better anti-noise ability, therefore more suitable for image processing.