Abstract:  In order to solve these defects such as low detection accuracy and sensitivity of tampering contents, which are induced by converting three components R, G, B of the color image into grayscale image for achieving image content authentication without considering the chrominance information in current image Hash algorithm, this paper proposes the Hash authentication algorithm for color image based on super-complex Fourier transform coupled with polar coordinate mechanism. Firstly, the input image is preprocessed based on the mean filter and the rotation factor to enhance the algorithm robustness of image scaling, so as to minimize the effect of image information loss on algorithm. Then the log polar coordinate transformation is introduced to transform the pretreatment image into the log-polar field. And the super-complex discrete Fourier transform is constructed by super-complex theory and Fourier transform to extract image features with anti-rotation tampering. The image Hash model is constructed according to the amplitude coefficients of the super-complex discrete Fourier transform. Meanwhile, the position disturbance mechanism is designed based on Logistic chaotic map, which randomly scrambles the image Hash for enhancing the security of Hash model. Finally, by using a cryptographic Hash model and the Hamming distance, the similarity of the two Hash values between the original image and the user received image is calculated. The experimental results show that, for processing color image, this algorithm has stronger robustness and security, it can effectively resist the color, contrast, rotation, noise and scale tampering attacks compared with the current image hashing algorithm.

Key words: image Hash, hyper-complex Fourier transform, log-polar transform, position disturbing mechanism, true and false information authentication, Hamming distance

摘要： 当前图像哈希算法大都是通过将彩图三分量R、G、B转换成灰度图像来生成哈希，丢失了色度信息，降低了算法对篡改内容的检测精度与敏感性的不足，为了解决上述问题，提出了超复数离散傅里叶变换耦合位置随机扰乱的彩色图像哈希认证算法。首先，通过构建新的扩散系数，从而改进偏微分模型PED（partial differential equation），对输入图像进行预处理，增强算法对图像缩放的鲁棒性，从而最小化图像信息丢失对算法的影响；再引入对数极坐标变换机制，将预处理图像变成二次图像；基于超复数理论与Fourier变换，将彩图三分量R、G、B视为四元数的虚部，建立四元离散Fourier变换机制，提取抗旋转篡改的图像特征；并基于Logistic混沌映射，设计位置扰乱机制，对四元离散Fourier变换低频幅度系数进行随机置乱；根据置乱后的幅度系数，构建图像哈希模型；最后，引入汉明距离，优化认证阈值，建立图像哈希相似度计算模型，以评估初始图像与用户接收图像的哈希相似度，完成图像内容的真伪认证。实验结果显示：与当前图像哈希算法相比，在处理彩色图像时，该算法具有更强的鲁棒性与安全性，呈现出更好的ROC曲线特性，能够有效识别亮度、旋转、噪声以及缩放等篡改攻击。

关键词: 图像哈希, 超复数Fourier变换, 对数极坐标变换, 位置扰乱机制, 真伪认证, 汉明距离