This paper proposes a new robust watermarking method for securing color medical images, where the proposed method relies on combining Slant, Singular Value Decomposition (SVD), and quaternion Fourier-Transform (QFT). The stimulus behind this combination is to improve the invisibility and durability of the proposed method. First, the input cover image is split into four equal parts for fast computation and then encrypted using one-time padding (OTP) encryption to increase robustness. Slant transform is applied to encrypted blocks to increase image compaction. The SVD is applied to the transformed image blocks to preserve quality during the embedding process. Finally, the QFT is applied to increase visual imperceptibility. The binary watermark is first compressed using SVD, scrambled using Arnold encryption to raise security, and then embedded in the modified QFT coefficients. The extraction procedures are the inverse operations of the embedding procedures. The proposed method achieves a good tradeoff between invisibility and robustness compared to existing schemes versus many geometrical, processing, and hybrid attacks. Also, the proposed method attains high visual imperceptibility. The extracted watermark seems to be the original watermark with minimum BER and high NC values. Empirical findings indicate that the proposed method is giving better invisibility and robustness results while maintaining a high capacity compared to other existing watermarking methods.