Reversible data hiding in encrypted 3D meshes is a critical technique for safeguarding 3D content while ensuring perfect reversibility and structural integrity. However, existing prediction-based approaches often face challenges such as limited embedding capacity, ineffective vertex classification, and the absence of authentication support. To address these limitations, this article proposes a novel and robust framework that integrates effective vertex traversal, vertical embedding, and multi-hider secret sharing. The traversal strategy improves prediction accuracy by identifying high-quality embeddable-reference vertex pairs, while the vertical embedding design allows each vertex to carry both hidden data and an authentication code, enabling pre-embedding model authentication. Moreover, multi-MSB prediction is combined with Huffman coding to compress auxiliary information and improve embedding efficiency. To further enhance robustness and capacity, a threshold secret-sharing scheme is introduced, allowing multiple data hiders, and securely reusing previously non-embeddable bits for message embedding. Unlike conventional sharing methods, this design significantly increases usable space while maintaining reversibility. Experimental results on various 3D models show that the proposed method achieves near-100% embedding rates and outperforms existing techniques in embedding capacity, authentication, and robustness, offering a new benchmark for secure and authenticable data hiding in encrypted 3D mesh environments.

Reversible data hiding techniques serve as a cornerstone in the protection of embedded information across diverse media. Traditionally, methods applied to 3D models have primarily focused on modifying vertex coordinates. However, this approach neglects the untapped potential of polygonal faces, which, being more abundant than vertices, offer a scalable and efficient avenue for data embedding. By leveraging polygon indices for reversible data hiding—particularly when integrated with encryption—it becomes possible to randomize the model's structure, facilitating secure modifications while preserving geometric integrity. This study introduces an innovative reversible data hiding algorithm that embeds messages within the polygon indices of encrypted 3D models. The algorithm harnesses the inherent similarities among vertex indices to conceal additional information. To maintain the consistency of polygon normal vectors, we implement a right circular shifting mechanism that systematically reorganizes the indices, ensuring that the smallest value consistently occupies the initial position. Additionally, we incorporate techniques such as leading zero count and multi-MSB prediction to enhance embedding capacity while keeping index values within permissible ranges. Experimental results demonstrate that our approach significantly outperforms conventional vertex-based methods, yielding substantial improvements in embedding efficiency. Crucially, the reversible nature of the proposed technique ensures the exact restoration of the original 3D model upon data extraction, guaranteeing zero information loss and no compromise in quality. Moreover, the algorithm is designed to integrate with vertex-based reversible data hiding techniques for encrypted 3D models, potentially enhancing data embedding capacity under compatible conditions.

Reversible data hiding in encrypted media involves using algorithms to perform data encryption to improve the privacy of the original media and hide data for covert communication or access control. This study explores the feasibility of applying coordinate transformation and random sampling to enhance the embedding rate and total embedding capacity of separable reversible data hiding in encrypted polygonal models based on multiple most significant bit (multi-MSB) prediction and Huffman coding. We first transform each vertex coordinate value of the input model into a decimal value between 0 and 1 and then convert the value into numerous binary digits with a user-defined compression threshold. Thereafter, the random sampling concept is used to generate embeddable vertices with only partial neighboring vertices as a reference. Thus, the embedding rate and total embedding capacity can both be increased considerably. The multi-MSB prediction technique is adopted to obtain the embedding capacity of each embeddable vertex, each vertex coordinate value in the proposed study can have a respective embedding length. Finally, the auxiliary information compressed through Huffman coding and an encrypted secret message are embedded in the multi-MSB of each embeddable vertex coordinate value through bit substitution. The experimental results of this study indicate the feasibility of the proposed algorithm.

Reversible data hiding for encrypted media not only preserves the privacy of the media content but also can convey additional information during message transmission. Some studies advocate separability, that is, the message can be correctly extracted irrespective of whether the encrypted media has been decrypted. However, current research has focused on encrypted images. Urgent research is required on encrypted three-dimensional (3D) models. This paper proposes a separable reversible data hiding method based on spatial subdivision and space encoding for encrypted 3D models. A bounding volume is first constructed using the vertices with boundary values in the processing model. Each vertex coordinate value is then converted into a ratio (between 0 and 1) of the distance between the vertex and minimum boundary point to the side length of the bounding volume. The owner of the 3D model then uses a secret key to encrypt all ratios except those of the boundary vertices to obtain an encrypted 3D model of the same size as the original model. The spatial subdivision technique and a subdivision threshold are subsequently used to divide the bounding volume into a series of blocks and simultaneously control the vertex distortion. The secret message is embedded in the encrypted vertex by using the space encoding method with an embedding threshold. Experimental results indicate that the proposed algorithm enables high privacy, performs separable reversible data hiding, and has low computational complexity, high embedding capacity, and controllable distortion.

This paper proposes a method that utilizes two stages of deep learning networks for segmentation and recognition of spinal vertebrae. The first stage involves a y-shaped model that learns the basic shape of vertebrae to segment the spine. The second stage determines the order of each vertebra in the spine. This two-stage method provides more reliable spine segmentation results.

This study proposes a low-complexity region-based authentication algorithm for three-dimensional (3D) polygonal models, based on local geometrical property evaluation. A vertex traversal scheme with a secret key is adopted to classify each vertex into one of two categories: embeddable vertices and reference vertices. An embeddable vertex is one with an authentication code embedded. The algorithm then uses reference vertices to calculate local geometrical properties for the corresponding embeddable vertices. For each embeddable vertex, we feed the number of reference vertices and local properties into a hash function to generate the authentication code. The embeddable vertex is then embedded with the authentication code, which is based on a simple message-digit substitution scheme. The proposed algorithm is of low complexity and distortion-controllable and possesses a higher and more adaptive embedding capacity and a higher embedding rate than most existing region-based authentication algorithms for 3D polygonal models. The experimental results demonstrate the feasibility of the proposed algorithm.