Securing medical images are a very essential process in medical image authentication. Medical
image watermarking is a very popular tool to achieve this goal. In this paper, an extremely fast, highly
accurate, and robust algorithm is proposed for watermarking both gray-level and color medical images.
In the proposed method, a scrambled binary watermark is embedded in the host medical image. Simplified
exact kernels are used to compute the moments of the polar complex exponential transform (PCET) for
the host gray-level images and the moments of the quaternion PCET for the host color images without
approximation errors. The stability of the computed moments enables us to use higher order moments in
a perfect reconstruction of the watermarked medical images. The accurate moment invariant to rotation,
scaling, and translation ensures the robustness of the proposed watermarking algorithm against geometric
attacks. Performed experiments clearly show very high visual imperceptibility and robustness to different
levels of geometric distortions and common signal processing attacks. The implementation of parallel
multi-core CPU and GPU result in a tremendous reduction of the overall watermarking times. For a color
image of size 256 × 256, the watermarking time is accelerated by 20× and 11× using a GPU and a CPU
with 16 cores, respectively.