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Published： 16 February 2024 ，
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金丹， 徐达文. 2024. 结合Kd-树和熵编码的密文图像可逆数据隐藏. 中国图象图形学报， 29(02):0395-0407
Jin Dan， Xu Dawen. 2024. Reversible data hiding for encrypted images with Kd-tree and entropy coding. Journal of Image and Graphics， 29(02):0395-0407
目的
2
密文图像可逆数据隐藏技术既可以保证载体内容不被泄露，又可以传递秘密信息，在军事、医疗等方面发挥着重要的作用。然而，以往的大多数方法存在图像冗余未被充分利用、数据嵌入容量不足等问题。为解决这些问题，提出了一种结合Kd-树和熵编码的高容量密文图像可逆数据隐藏算法。
方法
2
该方法在图像加密之前需要对图像应用中值边缘检测（median-edge detector，MED）算法计算预测误差，并把得到的预测误差绝对值图像划分为两个区域：S0区域和S1区域。根据Kd-树标签算法和熵编码生成辅助信息，在对图像使用加密密钥
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加密之后嵌入辅助信息，生成加密图像；在秘密数据嵌入阶段，根据附加信息和数据隐藏密钥嵌入秘密数据，生成载密图像；在解密阶段可以根据附加信息、图像加密密钥和数据隐藏密钥提取秘密数据并无损恢复图像。
结果
2
实验测试了BOWS-2（break our watermarking system 2nd）数据集，平均嵌入容量为3.910 bit/像素。与现有的几种方法进行比较，该算法可以获得更高的秘密数据嵌入容量。
结论
2
该方法在图像加密前腾出空间，与相关算法相比，实现了更高的嵌入容量，并且可以实现原始图像的无损恢复。
Objective
2
Nowadays， many people upload their information to the Internet， but the transmission and storage processes have many security problems. In the early days， researchers used encryption technology to protect the information， easily attracting the attention of decipherers. Therefore， people began to study how to hide secret information in an image. The secret information is transmitted while avoiding the attention of potential attackers. Therefore， reversible data hiding technology has become one of the hotspots of security research. Reversible data hiding technology can embed secret data through subtle modifications to the original image. After the data are extracted， the image can be restored losslessly. The emergence of cloud storage and big data technology has encouraged many users to upload their images to the cloud server. Out of distrust of the service provider， the image is encrypted before being uploaded to the cloud server. Cloud storage service providers hope to embed additional data in images to facilitate image management， image retrieval， copyright protection， and other requirements. Therefore， for cloud applications， reversible data hiding in encrypted images （RDHEI） has attracted the attention of many researchers who hope to embed data in encrypted images for transmission to protect the carrier image effectively and ensure the security of embedded information. The existing RDHEI methods can be divided into two categories depending on whether vacating the space before encrypting the image is necessary： 1） vacating the room after encryption and 2） reserving the room before encryption （RRBE）. The reversible data hiding technology for encrypted images plays an important role in military， medical， and other aspects. This algorithm can ensure that the content of the carrier is not leaked. It can also transmit secret information. However， most previous methods have problems， such as low data-embedding capacity， errors in data extraction， and poor visual quality of reconstructed images. Therefore， a reversible data hiding algorithm for high-capacity ciphertext images based on Kd-tree and entropy coding is proposed to solve these problems.
Method
2
Our method needs preprocessing before image encryption. First， the median-edge detector（MED） predictor generates a prediction error absolute value image from the original image， and the prediction error absolute value image is divided into two regions， i.e.， S0 region and S1 region. The S0 region contains the 5th bit plane to the most significant bit plane， and the Kd-tree algorithm is used to construct the Kd-tree concept subtree， which marks the blocks of the four-bit planes to determine whether the blocks can accommodate secret bits. The S1 region is from the least significant bit plane to the 4th bit plane， and the bitstream of each bit plane is compressed using arithmetic coding. The remaining space can be used to embed the secret data. After the image is encrypted with the encryption key， additional information is embedded to generate the encrypted image. During the stage of secret data embedding， the secret data are embedded according to the additional information and data hiding key to generate the secret image. In the decoding stage， the secret data are extracted， and the image is restored losslessly according to the additional information， encryption key， and data hiding key.
Result
2
Experiments show that the proposed method can effectively reduce the number of reference pixels and additional information， thereby increasing the data embedding rate. The BOWS-2 data set is tested in the experiment. The average embedding capacity is 3.909 8 bit/pixel， which is higher than the existing five methods. Two indicators， peak signal-to-noise ratio（PSNR） and structural similarity index measure（SSIM）， are used to evaluate the similarity between the original and restored images. Experimental results prove that in the data extraction and image restoration stage， the original image does not show a difference after the extraction of the secret data and the use of the image encryption key to decrypt the image. The analysis of the Kd-tree label through encryption shows that texture complexity significantly impacts the embedding of the image’s secret data. The higher the label provided by the relatively smooth image is， the higher the embedding capacity is.
Conclusion
2
First， the image pixels are predicted by the predictor. Then， the image pixels are classified and divided into two regions. This method adopts the framework of RRBE. The image must be preprocessed before image encryption. It achieves a higher embedding capacity than the related algorithms. It can also perfectly reconstruct the original image and ensure the security of encrypted images and additional data. At present， many disciplines are combined with deep learning. However， studies combining deep learning with reversible data hiding algorithms in the encrypted domain are lacking. In the future， we hope to achieve breakthroughs in this area and will pay considerable attention to the application of RDHEI in reality， not just in academic research.
图像加密Kd-树标签MED预测器可逆数据隐藏（RDH）预测误差
image encryptionKd-tree labelMED predictorreversible data hiding（RDH）prediction error
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