A watermarking algorithm is proposed in this paper to address the copyright protection issue of implicit 3D models. The algorithm involves embedding watermarks into the images in the training set through an embedding network, and subsequently utilizing the NeRF model for 3D modeling. A copyright verifier is employed to generate a backdoor image by providing a secret perspective as input to the neural radiation field. Subsequently, a watermark extractor is devised using the hyperparameterization method of the neural network to extract the embedded watermark image from that perspective. In a black box scenario, if there is a suspicion that the 3D model has been used without authorization, the verifier can extract watermarks from a secret perspective to verify network copyright. Experimental results demonstrate that the proposed algorithm effectively safeguards the copyright of 3D models. Furthermore, the extracted watermarks exhibit favorable visual effects and demonstrate robust resistance against various types of noise attacks.

To protect the copyright of the 3D scene represented by the neural radiation field, the embedding and extraction of the neural radiation field watermark are considered as a pair of inverse problems of image transformations. A scheme for protecting the copyright of the neural radiation field is proposed using invertible neural network watermarking, which utilizes watermarking techniques for 2D images to achieve the protection of the 3D scene. The scheme embeds the watermark in the training image of the neural radiation field through the forward process in the invertible network and extracts the watermark from the image rendered by the neural radiation field using the inverse process to realize the copyright protection of both the neural radiation field and the 3D scene. Since the rendering process of the neural radiation field can cause the loss of watermark information, the scheme incorporates an image quality enhancement module, which utilizes a neural network to recover the rendered image and then extracts the watermark. The scheme embeds a watermark in each training image to train the neural radiation field and enables the extraction of watermark information from multiple viewpoints. Simulation experimental results demonstrate the effectiveness of the method.

The utilization of implicit representation for visual data (such as images, videos, and 3D models) has recently gained significant attention in computer vision research. In this letter, we propose a novel model steganography scheme with implicit neural representation. The message sender leverages Neural Radiance Fields (NeRF) and its viewpoint synthesis capabilities by introducing a viewpoint as a key. The NeRF model generates a secret viewpoint image, which serves as a backdoor. Subsequently, we train a message extractor using overfitting to establish a one-to-one mapping between the secret message and the secret viewpoint image. The sender delivers the trained NeRF model and the message extractor to the receiver over the open channel, and the receiver utilizes the key shared by both parties to obtain the rendered image in the secret view from the NeRF model, and then obtains the secret message through the message extractor. The inherent complexity of the viewpoint information prevents attackers from stealing the secret message accurately. Experimental results demonstrate that the message extractor trained in this letter achieves high-capacity steganography with fast performance, achieving a 100\% accuracy in message extraction. Furthermore, the extensive viewpoint key space of NeRF ensures the security of the steganography scheme.