## 1 Introduction
proposed a robust medical image watermarking algorithm based on contourlet transform and DCT, using contourlet transform to extract multi-scale texture information and DCT to extract feature vectors in low-frequency directional subbands. In the area of industrial image copyright protection [16], [PERSON] et al. [17] proposed 'DWFCAT', a dual watermarking framework for industrial image content authentication using discrete cosine transform coefficients and exploiting their energy compression properties to achieve robust watermark embedding. At present, the research results of copyright protection for 3D images are relatively few. With the rapid development of 3D display technology based on integrated imaging [18], 3D images are increasingly being transmitted and used, and if these 3D images are not effectively protected, they can easily be illegally stolen without permission and cause losses. Therefore, the research on the copyright protection technology of 3D images is very necessary. Watermarking technology has become a hot research topic in the field of optical information security as a method to effectively protect the copyright of images and video works [19; 20]. Since some watermarking techniques do not take encryption measures or have simple encryption methods, unauthorized persons can easily detect or extract the embedded digital watermark and tamper with it through some computational operations, thus affecting the security of the watermark. Therefore, encryption pre-processing of watermarked images before watermark embedding has an important role. Existing encryption methods can be divided into two categories: symmetric and asymmetric encryption. It involves a secret key, or a symmetric key, used at the encryption and decryption sides, as in [21]. In symmetric encryption, the secret key used for encryption and decryption is the same. The process of encrypting and decrypting a message in asymmetric encryption requires the use of a set of key pairs, called a public key and a private key. If the public key is used to encrypt a message, only the private key can be used to decrypt it, and if the private key is used to encrypt it, only the public key can be used to decrypt it. The public key is required to be made public to others, and the private key must be kept by the user and kept secret. Symmetric encryption and decryption is faster, while asymmetric encryption and decryption takes longer and is relatively slower. The encryption method based on optical 4f system double random phase coding [22] is a classical optical encryption method, but it encrypts the real plaintext image as a complex-valued image, and it brings inconvenience to the transmission of the ciphertext. Computational ghost imaging encryption, which has emerged in recent years, has attracted the research interest of many scientists because of its small ciphertext data size, simple experimental setup and good encryption effect. [PERSON] et al. proposed optical encryption based on computational ghost imaging [23], which encodes the information of an object as a light intensity value. [PERSON] et al. combined computational ghost imaging (CGI) with compressed sampling (CS) [24]. [PERSON], [PERSON] et al. proposed an optical encryption method based on double random phase encoding compressed ghost imaging [25], which further improved the effect of ghost imaging encryption. In this paper, we propose a copyright protection method for 3D light-field images based on binarized computational ghost imaging encryption and cellular automata transform watermarking algorithms. First, we generate an elemental image array (EIA) of hexagonal lens arrays from three-dimensional (3D) objects, which has a higher fill factor compared with the rectangular lens array case, and thus the hexagonal lens arrays are more effective. Secondly, we extract the carrier image from EIA and encrypt the watermarked image by ghost imaging system and binarize the encrypted data.