Image Analysis Based On Orthogonal Moments

Description of images invariant to affine transformations such as translation, scaling and rotation is useful in image analysis, object recognition and classification. Moments, as a popular class of the global invariant descriptors, have been widely used in image analysis, pattern recognition and computer vision applications. The existing moments can be roughly divided into two categories:nonorthogonal moments and orthogonal moments. Nonorthogonal moments such as geometric moments and complex moments are components of the projection of an image onto a set of monomial functions. The orthogonal moments including the circularly orthogonal moments and Cartesian orthogonal moments are the projections of the image onto a set of orthogonal basis functions. The Cartesian orthogonal moments such as Legendre moment, discrete Tchebichef moment, Krawtchouk moment, dual Hahn moment and Racah moment have been defined in the Cartesian coordinates, where moment invariants particularly rotation invariants are not readily available. The circularly orthogonal moments including Zernike moment (ZM) and orthogonal Fourier-Mellin moment (OFM) are defined in the polar coordinates, their magnitudes are natively rotation invariant, and so have been widely used in many image processing, pattern recognition and computer vision applications. The outline of this paper is organized as follows:(1) A fast and accurate calculation algorithm for Bessel-Fourier moments is proposed in this paper. In the proposed approach, in order to improve their the numerical stability, instead of the zeroth order approximation, the Bessel-Fourier moments are calculated via multi sampling point approximation, and then the computational cost is reduced by using the recursive relation of their circular basis functions and the spatial symmetrical characteristic of their radial basis functions. Experimental results demonstrate that this approach yields a better performance in terms of computational cost, reconstruction and classification accuracy in comparison with the original method.(2) A novel category of circular moments named circularly semi-orthogonal moments is proposed. In the proposed moment, a set of orthogonal basis functions modulated by a negative power exponential envelope is utilized as the radial basis function. For a given degree n, the radial basis function possesses more compact bandwidth, less cutoff frequency and more zeros compared with the frequently-used circularly orthogonal moments including Zernike and orthogonal Fourier-Mellin moments, and so the circularly semi-orthogonal moment calculated with the zeroth order approximation is more robust to numerical error than the frequently-used circularly orthogonal moments. Furthermore, the capability of the semi-orthogonal moment to describe high spatial frequency components of images is relatively higher than that of the frequently-used circularly orthogonal moments. Experimental results demonstrate that the semi-orthogonal moments calculated with the zeroth order approximation perform better than the frequently-used circularly orthogonal moments in terms of image reconstruction capability and invariant recognition accuracy in noise-free, noisy and smooth distortion conditions. It is also shown that the proposed high order moments are more numerically stable than the circularly orthogonal moments.(3) we proposed a new quaternion circularly semi-orthogonal moments, which are more suitable than the other quaternion orthogonal moments including quaternion Bessel-Fourier moments,quaternion orthogonal Fourier-Mellin moments and quaternion Zernike moments for color image analysis and invariant pattern recognition. Here, a distinctive image descriptor based on the magnitude and the phase information of quaternion circularly semi-orthogonal moments is used to an accurate estimation method for rotation angle and pattern recognition. Experimental results demonstrate that quaternion circularly semi-orthogonal moments perform better than the other common quaternion orthogonal moments(such as QBFMs, QOFMMs and QZMs) in terms of color image reconstruction, angle estimation and color image invariant recognition accuracy in noise-free and noisy conditions.