In the current Internet of Medical Things, the emergence of new diagnosis and treatment modes such as telemedicine ensures that doctors can use CT, MRI, ultrasound or other medical equipment to diagnose diseases [1,2]. With the huge increase of 5G technology in communication speed, more and more medical images are being presented to doctors and patients in the form of 3D models. By performing operations such as scaling, rotating, and moving on these models [3,4], doctors can more intuitively find out whether there are lesions in tissues or organs, and further conduct comprehensive pathological inquiry, technical communication, demonstration and surgery simulation [5]. In order to ensure the safe transmission and storage of these medical images, watermark technology [6–9] is applied to medical data to solve the possible malicious tampering or attack in the process of medical data transmission.

As a new information hiding technology, medical watermarking embeds watermark information into digital media to protect the original carrier [10]. Through certain watermarking algorithms, watermark information such as patient's name, gender, age, and symptoms, etc., is embedded into medical data to prevent from being tampered in the process of transmission and storage. Also, this operation can protect the legitimate rights and interests of doctors and patients, and provide an effective way to solve the increasingly critical doctor-patient relationship [11]. The emerging remote consultation system can establish a communication bridge between patients, local medical personnel, and non-local experts, by which severe diseases are further accurately judged. In remote consultation, medical watermarking is an emerging technology that can help medical institutions to securely store or transmit medical information and ensure that the data is not attacked by illegal users [12].

3D watermarking technology is one of the rapid developing technologies in the field of multimedia information security. It as a new technology can protect copyright and authentication sources as well as integrity in an open internet environment. In recent years, it has attracted great attention and become a research hotspot. There are many ways to implement 3D medical models. Li et al. [13] proposed a new mechanism of digital watermarking. By replacing some vertex coordinates of 3D mesh models and embedding watermarked images, high-capacity watermark information can be embedded. Liu et al. [14] proposed a 3D point cloud model watermarking algorithm based on feature point location The watermark is embedded into the vertices with large average curvature by modifying the azimuth of the feature vertices. Hao et al. [15] proposed an adaptive embedding watermarking algorithm for 3D mesh models, which has a high embedding capacity by adaptive threshold to select the vertices to be embedded. Yang et al. [16] adopted the edge embedding technique in integer wavelet transform. It uses the amplitude information and sub-band category of wavelet coefficients to achieve the balance between the capacity and the visual invisibility. Ali et al. [17] used genetic algorithm to select the coefficients in integer wavelet transform and embedded the optimal watermark depth in the selected pixels. As can be seen from the literatures [18–20], some watermark authentication schemes may cause obvious deformation of the original carrier and cannot be effectively restored to the original version. However, in the medical field, any distortion of the original medical data is unacceptable. Therefore, these irreversible watermarking schemes which lead to the distortion of the original carrier are not suitable for the integrity protection of medical data.

To address the above challenge, a 3D medical watermarking algorithm based on wavelet transform is proposed in this paper, where the watermark is embedded by selecting the feature points whose normal vector changes greatly after dimension reduction. These points have a good invariance of rotation and translation, so that the embedded watermark can resist the attacks from translation, rotation, and scaling. At the same time, the multi-level wavelet transform is used to embed the watermark into the intermediate frequency region to maximize the visual invisibility of the original carrier. This study proposes a bacterial foraging algorithm based on particle swarm optimization, which combines the optimal solution with watermark pixels to achieve an optimal balance between embedding capacity and imperceptibility. The extraction process does not need the original 3D model and can realize a reversible embedding on the premise of protecting the integrity and security of medical data, which avoids the limitation of existing 3D watermarking technologies in low robustness and poor visual invisibility.

This paper studies the watermarking algorithm of a 3D medical model based on the wavelet transform. Firstly, the algorithm uses principal component analysis (PCA) to reduce the dimension of the 3D model, where, the data are projected to the low-dimensional subspace to reduce the complexity of data processing. At the same time, the vertices with large changes in the normal direction were selected as the feature points of the 3D model, and the bacterial foraging algorithm based on particle swarm optimization was used to adjust the embedding depth during the watermarking process. This part mainly introduces several corresponding key techniques used in the algorithm and their relationship each other, as shown in Fig. 1. These techniques and their improvements will be introduced in detail below.

3D medical model data such as CT and MRI, are different from 2D images. When they are used for disease analysis and diagnosis, the amount of data is large and the analysis is difficult [26]. During network transmission, in order ensure real-time diagnosis, fast transmission speed, as well as secure and robust watermarking, we propose a robust watermarking method in the wavelet domain. The dimension of the 3D model is reduced to lower the complexity of the data processing.

In the process of watermark embedding and extraction, the quality of the formed and extracted watermark image largely depends on the watermark embedding coefficient. The low value of the embedding coefficient will reduce the robustness of the watermark, while the higher value will minimize the invisibility of the watermark. Therefore, it is necessary to select an optimal value for embedding coefficient to balance the invisibility and robustness of the watermark.

The vertex coordinate vi′′=(xi′′,yi′′,zi′′) of the 3D model after dimension reduction is obtained by the PCA transformation, and translated into spherical coordinates Si=(ri,θi,∅i) , the calculation formula is as Eq. (10).

(10) {ri=xi′′2+yi′′2+zi′′2θi=arccos⁡(zi′′ri),φi=arctan⁡(yi′′xi′′)(i=1,2,…n)

The vertices with large changes in the extracted normal vector are taken as the feature points of the medical model. These points have a good rotation and translation invariance, so that the embedded watermark can resist geometric attacks such as translation, rotation, and scaling. Find out each vertex connected with v_i to form a set N(v_i), and v_p is the geometric center of the medical model.

(11) N(vi)={vj||vivj|>0,j=1,…,N}

Determine the discrete normal vector of vertex v_i:

(12) θvi=∑vj∈N(vi)⁡(vj−vp)Ni

Estimate the area where the normal direction changes sharply:

(13) D(vi)=∑vi∈N(vi)⁡cos−1(θiθj)

The sequence D(v_i) is obtained according to the feature point extraction method, and the first 8S×8S results of the sequence are arranged in descending order. The corresponding vertices are taken as feature points, and then the r_i values corresponding to the feature points are composed into a matrix T of 8S×8S, where S×S is the size of the watermark image.

A series of multi-resolution sub-bands {HL_i, LH_i, HH_i}, i = 1, 2, 3 and approximate sub-bands LL₃ are obtained by three-level wavelet transform of matrix T. Then, HL₃ is divided into non-overlapping 2 × 2 sub blocks and recorded as B_k, k = 1, 2, …; The watermark bits are embedded into non-overlapping block B_k by wavelet transform. For each sub block, max[B3HL(i,j),B3HL(i+1,j),B3HL(i,j+1),B3HL(i+1,j+1)] and min[B3HL(i,j),B3HL(i+1,j),B3HL(i,j+1),B3HL(i+1,j+1)] are calculated, the sub-band coefficient is modified according to Eq. (14).(14) B3′HL(i,j)=(max⌊B3HL(i,j),B3HL(i+1,j),B3HL(i,j+1),B3HL(i+1,j+1)⌋+aw,ifw=1min⌊B3HL(i,j),B3HL(i+1,j),B3HL(i,j+1),B3HL(i+1,j+1)⌋−aw,ifw=0) This study proposes a bacterial foraging algorithm based on particle swarm optimization (BF-PSO) to obtain the best watermark embedding depth. Inspired by the historical optimal idea of particle position in PSO algorithm, the chemotaxis operator in BF algorithm is improved. When the chemotactic operator is executed, the bacteria whose fitness values are better than the average value are searched by tracking the optimal bacteria; on the contrary, searched by tracking the central position of the bacterial population. If the above two methods fail, the random search method of standard BFO algorithm is adopted. By evaluating the bacterial energy after reproduction and the fitness of new bacterial individuals after the migration cycle, the local optimal solution and global optimal solution are obtained. The embedding process of the watermark is shown in Fig. 3, and the extraction process is the inverse process of watermark embedding.

This section will evaluate the performance of the proposed algorithm. Simulation experiments use various attacks on the 3D model embedded with watermark information to verify the robustness and invisibility of the watermark algorithm in the paper. The experimental results show that the 3D model can still successfully extract the watermark information after being attacked, which shows the high robustness and visual invisibility of our algorithm. The watermark system is evaluated by Peak Signal-to-Noise Ratio (PSNR):(15) PSNR=10log1025521m∑i=1m⁡(wi−wi′)2 The original 3D model data [27] used for the test is the standard MRI brain data from MATLAB R2019a software. Fig. 4 shows the standard MRI brain slice image, and Fig. 5 shows the MRI brain model and watermark image.

Gaussian noise attacks with different intensity are applied to medical data. Fig. 6 shows the medical model and brain slice image under the interference of three kinds of different Gaussian noise. It can be seen that the greater the intensity of Gaussian noise, the worse the quality of the slice image after being attacked. Tab. 1 shows the calculated PSNR and Normalized Correlation (NC) values under three kinds of Gaussian noise attacks with different intensities. It can be seen from the data that although the model is attacked, the quality of the extracted watermark image is still good, indicating that our algorithm has strong robustness to Gaussian noise.

Fig. 7 shows the medical model and brain slice images when attacked by the JEPG compression under different intensities. It can be seen that the greater the compression intensity, the more obvious the blocking effect. Tab. 2 shows the calculated PSNR and NC values under three JEPG compression attacks with different intensities. Seen from the data, the calculated NC value is still close to 1.0, indicating that the invisibility of the watermark is good.

Fig. 8 shows the comparison of NC values between proposed algorithm and other algorithms. The comparison results in show that the NC value of the proposed algorithm is slightly higher than that proposed by Liu et al. [28] and loan et al. [29]. The algorithm proposed by loan et al. embedded the watermark by selecting and setting the difference and range of the intermediate frequency coefficient in advance, which effectively managed the intermediate frequency coefficient of the image. The algorithm proposed by Liu et al. generated a watermark for the region of interest and the region of non-interest separately, a recovery function of the region of interest is designed to ensure that the watermark can be extracted effectively. It is worth mentioning that although the proposed algorithm has no obvious change in scaling attack, compared with other algorithms, it remains the optimal value of 1.0. In addition, under a low scaling factor, the smaller the size of the image, the more obvious its robustness. Especially when the scale factor is as low as 0.1, the watermark can still be extracted completely, so it is obviously better than other algorithms in Fig. 8a. Seen from JEPG compression and clockwise rotation attacks, the overall performance of the proposed algorithm is better than other existing algorithms.

This paper proposes a 3D medical watermark based on wavelet domain, which embeds the watermark information into the vertices of the significant region in the 3D model, so as to ensure the invisibility of the 3D model. The bacterial foraging algorithm model based on particle swarm optimization (BF-PSO) uses the correlation between adjacent pixels in the image to achieve the optimal balance between embedding capacity and imperceptibility and further find the optimal wavelet coefficients for embedding. In telemedicine, the receiver needs undistorted medical data for diagnosis, and the watermark cannot destroy the readability of the original data. Our scheme realizes the invisibility of the watermark, guarantees the undistorted original data, and does not need any additional information in the extraction process. Simulation results show that our method has good imperceptibility and strong robustness, which can resist geometric attacks such as rotation, scaling and clipping. In future work, we will continue to study the watermark embedding capacity of the model, and find the best balance between capacity and robustness.