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The traditional embedded watermarking scheme achieves copyright protection of images by embedding watermarks into the original images. This process will deteriorate the original image, so it is not suitable for medical images. In order to overcome this limitation, this paper proposes a geometrically invariant color medical image null-watermarking scheme based on quaternion polar harmonic Fourier moments (QPHFM), which achieves the copyright protection without changing the original medical image. First, a high-precision QPHFM computation method based on wavelet numerical integration is designed, which can effectively improve the computation precision. Then based on the precise QPHFM (PQPHFM) and chaotic map, a robust null-watermarking scheme for color medical images is proposed to protect the copyright of color medical images. This scheme uses the PQPHFM to construct feature images and its good stability and geometric invariance make the proposed null-watermarking scheme has good robustness and resistance against geometric attacks. Extensive simulation experiments show that the proposed scheme is highly robust in resisting common attacks and geometric attacks such as scaling, rotation, change of length-width ratio, and flipping. The performance of the proposed scheme is superior to that of similar robust null-watermarking schemes and other color medical image watermarking schemes. INDEX TERMS Geometric attack, image flipping, length-width ratio change, null-watermarking, precise quaternion polar harmonic Fourier moments.

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