Stereo Image Analysis by Octonion Fractional-Order Orthogonal Color Moments

Polar harmonic Fourier moments (PHFMs) are popular for image analysis due to their properties of lower computation complexity and minimal redundant description capability of images. However, the traditional PHFMs are unavailable for color stereo image analysis on the one hand, and on the other hand the polar harmonic polynomials with integer-order are not able to extract fine features. In this paper, a new category of moments named octonion fractional-order PHFMs (OFrPHFMs) are proposed using the fractional-order basis functions of PHFMs and octonion theory. The proposed moments can be viewed as a generalization of quaternion orthogonal moments. Furthermore, since the image moments formed by the octonion descriptor can treat the color stereo image integrally, it has a strong representation capability. More importantly, some numerical instability and calculation issues are discussed and a fast computational framework using matrix operation and block Gaussian numerical integration is developed to improve the accuracy and efficiency of the proposed OFrPHFMs. Finally, to demonstrate the validation of the proposed moments, the image experiments are conducted and the results show that the proposed OFrPHFMs have favorable performance in the field of color stereo image analysis.