The advancement of 5G technology, big data and cloud storage has promoted the rapid development of the Internet of Medical Things (IoMT). Based on the strict security requirements and high level of accuracy required for disease diagnosis and pathological analysis, 3D medical volume data have been created in large numbers. The IoMT facilitates the rapid transfer of medical information and also makes the protection of pathological information and privacy information of patients increasingly prominent. To solve the security problem, a robust zero-watermarking algorithm based on 3D hyperchaos and 3D dualtree complex wavelet transform is proposed according to the selected feature of medical volume data. The feature combines human visual features with improved perceptual hashing techniques. It is a robust and efficient binary sequence. When implementing the proposed algorithm, the watermark is first scrambled with 3D hyperchaos to enhance security. Then, 3D DTCWT-DCT transformation is applied to medical volume data, and the low-frequency coefficients that can represent the features are selected and binarized to generate the secret key to complete the watermark embedding and extraction. Zero embedding and blind extraction ensure that the original medical volume data is not altered in any form, which meets the special requirements for diagnosis. Simulation results show that the algorithm is robust and can effectively resist common attacks and geometric attacks. It used fewer robust features to effectively bound medical volume data and watermark information, saved bandwidth, and satisfied the security of transmission and storage of medical volume data in the Internet of medical things. In particular, compared with state-of-the-art technology, the proposed algorithm improves the average NC value by 46.67% under geometric attacks. INDEX TERMS Hyperchaos, Internet of medical things, medical volume data, robust watermark, 3D-DTCWT-DCT.