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. 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 and and diagonal matrix . The difference among the three sets of elements in the first column of the 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 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 . The watermark bit information is extracted according to the difference between the two elements in the first column of the orthogonal matrix and then transformed into a binary image

which is subjected to inverse Arnold transformation to obtain the watermark image. 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. 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 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.