Light-field image watermarking based on geranion polar harmonic Fourier moments

Light-field images provide a spatial and angular description of the light, and they can capture rich visual information in the natural world. In recent years, the research on light-field imaging has achieved many fruitful results. As more and more people are now focusing their attention to light-field imaging, the copyright protection of light-field images has become an urgent problem that needs to be addressed. Digital watermarking can effectively protect the copyright ownership of light-field images. Currently, there exists no light-field image watermarking scheme that can resist various geometric attacks. In this work, relying on geranion theory and polar harmonic Fourier moments (PHFMs), geranion polar harmonic Fourier moments (GPHFMs) are constructed and utilized for light-field image watermarking. The geranion represents a hypercomplex number containing one real part and thirty-one imaginary parts, and the imaginary parts of geranion can be used to encode multiple image color components while maintaining the correlation between each component. GPHFMs are stable image features, with good image reconstruction ability and stability. Essentially, the light-field image watermarking based on GPHFMs offers good imperceptibility and robustness, can resist various attacks, and effectively solves the problem of current watermarking schemes related to their inability of resisting geometric attacks. Furthermore, it is verified through experiments that the proposed scheme is more robust than the previously reported schemes.