Search

This article introduces a new family of orthogonal moments, the fractional Racah moments (FrROMs), developed to meet the demands of copyright protection for medical images, a field requiring robust and secure methods that preserve the integrity of the original image. The FrROMs are derived from a matrix of fractional Racah orthogonal polynomials (FrROPs), which in turn are obtained from the matrix of classical Racah polynomials (ROPs) using the spectral decomposition theorem. To compute the ROPs, we enhanced a method for calculating the initial terms of these polynomials to avoid instability issues associated with higher-order ROPs. Subsequently, the FrROMs are used as descriptors for embedding and extracting a zero-watermark. Experimental results demonstrate that the proposed zero-watermarking scheme efficiently leverages the FrROMs, surpassing classical ROMs in terms of robustness and reconstruction capability. This scheme provides strong protection against various image processing attacks while maintaining the original content intact. Compared to existing methods, it stands out for its enhanced robustness and reliability, making a significant contribution to the secure protection of medical images.