Multi-dimensional hypercomplex continuous orthogonal moments for light-field images

Image moments have always been topical in the domain of image processing, and the proposed hypercomplex moments and multi-channel moments have greatly broadened the application of image moments in recent years. However, the hypercomplex moments are limited by the specific number of imaginary parts of the hypercomplex number, and the redundancy of imaginary parts or the overflow of image channels will occur when the number of imaginary parts does not fit the image structure. The multi-channel moments allow flexible adjustment of the number of channels, but their loose structure will result in the loss of correlation between multiple channels of images. Moreover, the hypercomplex moments and multi-channel moments cannot handle images with multi-dimensional structures such as light-field (LF) images. For the purpose of addressing the above problems, this paper proposes generalized hypercomplex continuous orthogonal moments (HCOMs) and extends them to multi-dimensional hypercomplex continuous orthogonal moments (MHCOMs) in multi-dimensional space. MHCOMs can be used to process images with arbitrary multi-dimensional structures, and when they are used for LF image processing, there is no need to map the LF images to two-dimensional space to change the multi-dimensional structural properties of LF images. By calculating MHCOMs of LF images, a set of multi-dimensional hypercomplex tensors containing robust feature information of LF images can be obtained, and the original LF images can be reconstructed using this information. Furthermore, the MHCOMs-based zero-watermarking scheme is designed for LF images, which has excellent robustness and can achieve lossless copyright protection for LF images.