Novel Octonion Moments for color stereo image analysis

Abstract This paper proposes a new category of moments for color stereo image description, called Octonion Moments (OMs). These new descriptors are based on the octonion theory and the moment theory, they generalize the classical and quaternion moments. The octonion moments can be used for any six-layer image stack, allowing us to use them to characterize color stereo images in an efficient, compact and holistic way in both intra- and inter-channel color directions. As a result, redundancies between the six channels of a stereo color image can be well exploited. Tchebichef polynomials are used in this paper to construct the corresponding octonion moments called Octonion Radial Tchebichef Moments (ORTMs). Two applications, image reconstruction and image watermarking, are studied to validate the effectiveness of the proposed ORTMs. In the context of image watermarking, we propose a new zero-watermarking algorithm for copyright protection of color stereo images. The image watermarking requirements, namely imperceptibility, robustness, and security are ensured by the proposed algorithm. This algorithm uses the proposed ORTMs to build descriptors that are stable and robust against image processing attacks and invariant to geometric transformations. The experimental results demonstrate the effectiveness of the proposed ORTMs for reconstruction and image watermarking in a comparison to concurrent recent methods based on other types of moments.