目的 为协调水印算法不可见性与鲁棒性之间的矛盾，提高水印算法抵抗几何攻击的能力，提出一种图像块的不可见性与鲁棒性均衡水印算法。方法 将宿主图像分成互不重叠的图像块，利用人类视觉系统的掩蔽特性对每个图像块的纹理特征和边缘特征进行分析，选择掩蔽性好的图像块作为嵌入子块。对嵌入子块作2级离散小波变换，将其低频子带进行奇异值分解，通过修改U矩阵第1列元素间的大小关系嵌入Arnold置乱后的水印信息。在水印提取前，对几何失真含水印图像利用图像尺度不变特征变换（SIFT）特征点的坐标关系和尺度特征进行几何校正，恢复水印的同步性。结果 对标准灰度图像进行实验，含水印图像的峰值信噪比都可以达到44 dB以上。对含水印图像进行常规攻击和几何攻击，提取出的水印图像与原始水印图像的归一化互相关系数大部分都能达到0.99以上，说明该算法不仅具有良好的不可见性，对常见攻击和几何攻击都具有较强的鲁棒性。结论 选择掩蔽性好的图像块作为水印嵌入位置能够充分保证水印算法的不可见性，特别是水印提取前利用SIFT特征点具有旋转、缩放和平移不变性对几何失真含水印图像实现有效校正，提高了含水印图像抵抗几何攻击的能力，较好地协调水印算法不可见性与鲁棒性之间的矛盾。

Objective Embedding watermark information into the host image leads to a contradiction between invisibility and robustness. High watermark embedding strength means strong watermark robustness but poor invisibility. Low watermark embedding strength means good watermark invisibility but weak robustness. As an effective means of copyright protection, a watermarking algorithm must ensure good invisibility and effectively resist various attacks. Geometric attacks destroy the synchronization between the watermark and host image and thus leads to the failure of the watermarking algorithm. To address the contradiction between invisibility and algorithm robustness and improve the capability to resist geometric attacks, this study proposes an invisible and robust watermarking algorithm based on an image block.Method The host image is divided into non-overlapping image blocks, and the texture and edge features of each image block are analyzed by using the masking property of the human visual system to calculate the masking value of each image block. The masking values are arranged in a descending order, and an appropriate number of good masking image blocks are selected as embedded sub-blocks according to the size of the watermark information. Two-level discrete wavelet transform is performed on the sub-block, and its low-frequency sub-band is decomposed by singular value decomposition to obtain orthogonal matrices U and V and diagonal matrix S. The difference among the three sets of elements in the first column of the U orthogonal matrix is calculated according to the watermark bit information. If the difference is less than the threshold value, the Arnold scrambled watermark information is embedded into the U orthogonal matrix. Then, inverse singular value decomposition is applied on the selected image block, and the low-frequency sub-band and other middle-and high-frequency sub-bands of the image block are subjected to inverse wavelet transform. Afterward, all the image blocks are combined to obtain watermarked images. The scale-invariant feature transform (SIFT) feature points of the watermarked images are extracted, and the coordinate, scale, direction, and descriptor information are stored. In watermark extraction, the SIFT feature points of the watermarked image that may be attacked are extracted and matched with the feature points saved in the watermark embedding to determine if the watermarked image is subjected a geometric attack. If the image is subjected to geometric attacks, geometric correction of the watermarked image is realized by the coordinate relations and scales features of the SIFT feature points. Geometric correction restores the synchronization of the watermark. If no geometric attack occurs, two-level discrete wavelet transform is performed on the selected image block, and its low-frequency sub-band is decomposed by singular value decomposition to obtain orthogonal matrix U. The watermark bit information is extracted according to the difference between the two elements in the first column of the U orthogonal matrix and then transformed into a binary image, which is subjected to inverse Arnold transformation to obtain the watermark image.Result Through experiments on standard gray-scale images, the watermark information is embedded into three images:Lena, Elaine, and Baboon. With the increase in the threshold value, image quality is reduced correspondingly, but the normalized correlation coefficient of the extracted watermark is improved. Hence, the threshold value of the experimental image is 0.04 considering invisibility and robustness. The peak signal-to-noise ratios (PSNRs) of the three watermarked images, Lena, Elaine, and Baboon, are 49.864 5, 46.304 6, and 44.683 2 dB, respectively. These values show that the algorithm possesses good invisibility. When no attack occurs, the normalized correlation coefficients between the original and extracted watermark images can reach 1, which shows the effectiveness of the algorithm. Various types of attacks, including JPEG compression, noise, and filter, are applied to the watermarked images. With the increase in the attack intensity, the normalized correlation coefficients of the extracted watermark are influenced but mostly exceed 0.99. In particular, the normalized correlation coefficients of the watermark extracted from the compression attack can reach 1. Rotating, scaling, cyclic shifting, and shearing attacks are then performed on the watermarked images. Afterward, geometric correction of the watermarked images is realized with the coordinate relations and scales features of the SIFT feature points. Given that the watermarked images are subjected to rotating attacks without changing the size of the images, some of the pixel information is lost during the rotation, such that the normalized correlation coefficients of the extracted watermark could not reach 1. The normalized correlation coefficient of the extracted watermark when a watermarked image is enlarged is larger than the normalized correlation coefficient of the extracted watermark when the watermarked image is reduced. All normalized correlation coefficients of the extracted watermarks under the cyclic shifting attack can reach 1. Shearing of the good masking region affects the anti-shearing attack capability, but the normalized correlation coefficients of the extracted watermarks under the shearing attack exceed 0.95. Experimental results on conventional and geometric attacks show that this algorithm exhibits strong robustness against both attacks.Conclusion The texture and edge information of the image can be calculated to obtain the masking value of each image block. The invisibility of the watermarking algorithm can be ensured by selecting the image block with good masking as the embedded sub-block. Selecting the pair of elements with the largest difference in the first column of the U orthogonal matrix as the embedded position minimizes the influence on the overall visual quality of the original image and improves the robustness of the watermarking algorithm. Given that SIFT feature points are a type of space-based image local feature description operators that are invariant to image rotation, scaling, translation, and so on, geometric correction of the watermarked image is realized by with the coordinate relations and scales features of the SIFT feature points to improve the ability of resisting geometric attacks. The above mentioned methods enable the watermarking algorithm to effectively address the contradiction between invisibility and robustness.