Generic Jacobi-Fourier Moment And Quasi Fourier-Mellin Transform

The invariant feature extraction is an important part of pattern recognition,which is of great significance in practical application and theoretical research.Although Jacobi-Fourier orthogonal moment has many excellent performances,but the robustness to noise and reconstruction performance of it need to be further improved;On the other hand,the traditional Fourier-Mellin transform can only be used to extract similar invariant features rather than general affine invariant features.Therefore,the traditional Jacobi-Fourier moment and FourierMellin transform are improved to extract invariant features.The main contributions include:The generic Jacobi-Fourier is proposed.Orthogonal moments of image have the properties of numerical stability and convenient to reconstruction,while Jacobi-Fourier moment is the generation of traditional orthogonal moments.Orthogonal Fourier-Mellin moment and Zernike moment are the special case of Jacobi-Fourier moment.However,the radial function in traditional Jacobi-Fourier moment is only integer order polynomial.In this paper,the radial function in traditional Jacobi-Fourier moment is extended to general function so that the generic Jacobi-Fourier moment is proposed which includes the traditional Jacobi-Fourier moment.The experimental results show that the generic Jacobi-Fourier moment is more robust to noise and has better performance of reconstruction under the condition of selecting appropriate parameters.The quasi Fourier-Mellin transform is proposed to extract the affine invariants.Traditional Fourier-Mellin transform is robust to noise and invariant to scaling and rotation so that it has been widely used in many fields.Whereas rotation and scaling are only features of similar transformation.Images of the same object taken from different viewpoints often suffer from geometric distortions.Affine transform is a reasonable approximation for these distortions.In this paper,we consider modifying the traditional Fourier-Mellin transform to extract affine invariant features.To eliminate the shearing in affine transform,two factors are proposed and embedded into Fourier-Mellin transform.The quasi Fourier-Mellin transform is proposed.The factors are equivalent to the traditional whitening transformation,which can eliminate the shearing in affine transformation without tedious calculation.Furthermore,the quasi FourierMellin descriptor is proposed based on quasi Fourier-Mellin transform.The descriptor can be used to extract affine invariants of images directly.The experimental results verify that quasi Fourier-Mellin descriptor is invariant to affine transform.It also shows that quasi FourierMellin descriptor is robust to noise and requires less computation.