A robust digital watermarking method based on Hankel kernel analytic space domain

Abstract

In order to solve the problems of high computational complexity and insufficient robustness to geometric attacks of traditional transform domain watermarking methods, the present application provides a robust digital watermarking method based on Hankel kernel analytic spatial domain. The method firstly pre-computes fixed direct current component weight vector and pixel modification coefficient vector from the analytic Hankel transform kernel; during watermark embedding, the direct current component of the first column of pixels of the selected image block is directly calculated in the image spatial domain, and the direct current component is precisely adjusted by modifying a small number of pixel values according to the watermark bits to be embedded and the quantization step, so as to realize the quantization embedding of the watermark; during extraction, the direct current component of the watermark-containing block is directly calculated and dequantized, so as to realize blind extraction. The method has the advantages of high computational efficiency and good invisibility, and shows strong robustness to common attacks such as JPEG compression, noise, filtering, scaling, rotation and the like, and is suitable for copyright protection of digital images and videos.

Description

Technical Field

[0001] This invention belongs to the field of information security technology and relates to the copyright protection of robust color digital images. Background Technology

[0002] Digital watermarking technology is a key means of protecting the copyright of digital media and authenticating the integrity of content. Current mainstream robust watermarking methods are mostly based on frequency domain transforms, such as discrete cosine transform or discrete wavelet transform. These methods embed watermarks by modifying transform domain coefficients, but they have significant limitations: high computational complexity; weak resistance to geometric attacks such as image rotation and scaling; and during the transform, quantization, and inverse transform processes, floating-point operations and rounding errors can easily lead to pixel value overflow or visual artifacts, affecting the invisibility of the watermark. Discrete Hankel transform is considered a promising alternative due to its excellent energy concentration characteristics, but directly implementing the discrete Hankel transform and manipulating its high-dimensional coefficients also faces challenges of high computational cost and error accumulation. Therefore, there is an urgent need for a new watermarking technology that can inherit the robust theoretical foundation of transform domain methods while achieving efficient and low-error spatial domain operations. Summary of the Invention

[0003] The purpose of this invention is to provide a robust digital watermarking method based on Hankel kernel spatial domain analysis. Its key feature is that it is achieved through specific watermark embedding and extraction processes. The watermark embedding process is described below: Step 1: Convert an image with a pixel size of The color host image is divided into three layers in the order of red, green, and blue. ,in, They represent the red, green, and blue layers respectively; Step 2: Convert an image with a pixel size of... The color watermark image is divided into three layers in the order of red, green, and blue. Based on key , , The Lorenz chaotic mapping encryption algorithm will watermark each layer of the image. Encryption is performed; finally, the encrypted watermark image is... The decimal pixel values ​​are represented using 8 bits of binary, and the binary watermarks are concatenated to a length of 8. watermark sequence ,in, They represent the red, green, and blue layers respectively; Step 3: Layer the host image Divided into pixels with Non-overlapping blocks are selected in the three-layer host image according to a random block selection algorithm. Select the embedded image patch; Step 4: Select one image block from the selected image blocks in sequence. Then, according to formula (1), the pixel values ​​of its first column are directly calculated. DC component : , (1) in, It is the pre-calculated weight vector of the DC component. It is an image block The pixel values ​​in the first column; Step 5: Extract one watermark bit from the watermark sequence one by one. Based on the bit value of the watermark to be embedded and the quantization step size The target DC component is calculated using formula (2): , (2) in, The index variable representing the quantization interval. It is an XOR function. It is the modulo function. The watermark location to be embedded; Step 6: Calculate the DC component modification amount according to formula (3). : , (3) Step 7: Based on the pre-calculated pixel modification coefficient vector k and formula (4), obtain the pixel values ​​of the first column containing the watermark. and update the original image blocks. Obtain watermarked image blocks : , (4) in, ; Step 8: Repeat steps 4 through 7 of this process until all other watermark information has been embedded into the remaining image blocks, thereby obtaining a watermarked layered carrier image. Finally, the watermarked layered carrier image is... Reassemble and obtain pixel size Watermarked images ; The watermark extraction process is described as follows: Step 1: Set the pixel size to Watermarked images Divided into 3 layers of watermarked images Each watermarked image layer is further divided into pixels. Non-overlapping image patches, where These represent the red, green, and blue layers, respectively. Step 2: Layering the watermarked image In this process, the random block selection algorithm mentioned in the watermark embedding process is used to select image blocks, where... These represent the red, green, and blue layers, respectively. Step 3: Select one image block from the selected image blocks in the order they appear. The pixel values ​​of the first column are calculated directly according to formula (5). DC component : , (5) in, These are the pixel values ​​in the first column; Step 4: Extract the watermark position according to formula (6): , (6) in, For the extracted watermark position, The index variable representing the quantization interval; Step 5: Repeat step 4 of this process to obtain the binary watermark sequence for each layer. Then each layer of binary watermark sequence Each 8-bit binary number is converted into a 1-bit decimal image pixel value to obtain an encrypted layered watermark image. ,in They represent the red, green, and blue layers respectively; Step 6: Process the encrypted layered watermark image Execute key-based , , The Lorenz transform will transform each layer of the watermark image. Decryption is performed to obtain the decrypted layered watermark image. ,in They represent the red, green, and blue layers respectively; Step 7: Combine the decrypted layered watermark images To obtain the complete watermark extraction image ,in , representing the red, green and blue layers respectively. Attached Figure Description

[0004] Figure 1 (a) Figure 1 (b) are two original color carrier images.

[0005] Figure 2 (a) Figure 2 (b) are two original color watermark images.

[0006] Figure 3 (a) Figure 3 (b) is to respectively Figure 2 (a) Embedded into the host image Figure 1 (a) will Figure 2 (b) Embedded into the host image Figure 1 The peak signal-to-noise ratio (PSNR) values ​​of the watermarked images obtained after (b) are 40.422 dB and 40.451 dB, respectively, and their structural similarity indices (SSIM) are 0.965 and 0.969, respectively.

[0007] Figure 4 (a) Figure 4 (b) is sequentially from Figure 3 (a) Figure 3 The watermarks extracted in (b) have normalized cross-correlation coefficient (NC) values ​​of 1.000 and 1.000, respectively.

[0008] Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) Figure 5 (f) Figure 5 (g) is to Figure 3 The watermarks extracted from the watermarked image shown in (a) after being subjected to attacks such as JPEG (90), JPEG2000 (4:1), salt and pepper noise (0.1%), scaling (400%), cropping (6.25%), rotation (15 degrees clockwise), and translation (10, 10) in sequence have normalized cross-correlation coefficient (NC) values ​​of 1.000, 1.000, 0.9617, 1.000, 0.998, 0.957, and 0.996, respectively.

[0009] Figure 6 (a) Figure 6 (b) Figure 6 (c) Figure 6 (d) Figure 6 (e) Figure 6 (f) Figure 6 (g) is to Figure 3 The watermarks extracted from the watermarked image shown in (b) after being subjected to attacks such as JPEG (90), JPEG2000 (4:1), salt and pepper noise (0.1%), scaling (400%), cropping (6.25%), rotation (15 degrees clockwise), and translation (10, 10) in sequence have normalized cross-correlation coefficient (NC) values ​​of 1.000, 1.000, 0.999, 0.998, 0.997, 0.992, and 0.988, respectively. Detailed Implementation

[0010] The purpose of this invention is to provide a robust digital watermarking method based on Hankel kernel spatial domain analysis. Its key feature is that it is achieved through specific watermark embedding and extraction processes. The watermark embedding process is described below: Step 1: Divide a 512×512×3 pixel color host image into three layers according to the order of red, green, and blue. ,in, They represent the red, green, and blue layers respectively; Step 2: Divide a 32×32×3 pixel color watermark image into three layers of watermark image in the order of red, green, and blue. Based on key , , The Lorenz chaotic mapping encryption algorithm will watermark each layer of the image. Encryption is performed; finally, the encrypted watermark image is... The decimal pixel values ​​are represented using 8 bits of binary, and the binary watermarks are concatenated to form a length of 8×32. 2 =8192 watermark sequence ,in, They represent the red, green, and blue layers respectively; Step 3: Layer the host image Divide the image into non-overlapping blocks of 4×4 pixels, and apply a random block selection algorithm to the three-layer host image. Select the embedded image patch; Step 4: Select one image block from the selected image blocks in sequence. Then, according to formula (1), the pixel values ​​of its first column are directly calculated. DC component : , (1) in, It is the pre-calculated weight vector of the DC component. It is an image block The pixel values ​​in the first column; here, Let the selected image patch be ,but , ; Step 5: Extract one watermark bit from the watermark sequence one by one. Based on the bit value of the watermark to be embedded and the quantization step size The target DC component is calculated using formula (2): , (2) in, The index variable representing the quantization interval. It is an XOR function. It is the modulo function. The location to be embedded for the watermark; here, ,but If the selected watermark value is '1', that is... ,but , ; Step 6: Calculate the DC component modification amount according to formula (3). : , (3) Here, ; Step 7: Modify the coefficient vector based on the pre-calculated pixel values. Using formula (4), we obtain the pixel values ​​of the first column containing the watermark. and update the original image blocks. Obtain watermarked image blocks : , (4) in, Here, , ; Step 8: Repeat steps 4 through 7 of this process until all other watermark information has been embedded into the remaining image blocks, thereby obtaining a watermarked layered carrier image. Finally, the watermarked layered carrier image is... Reassemble and obtain a watermarked image with a pixel size of 32×32×3. ; The watermark extraction process is described as follows: Step 1: Extract the watermarked image with a pixel size of 32×32×3 pixels. Divided into 3 layers of watermarked images Each watermarked image layer is further divided into non-overlapping image blocks of 4×4 pixels, where These represent the red, green, and blue layers, respectively. Step 2: Layering the watermarked image In this process, the random block selection algorithm mentioned in the watermark embedding process is used to select image blocks, where... These represent the red, green, and blue layers, respectively. Step 3: Select one image block from the selected image blocks in the order they appear. The pixel values ​​of the first column are calculated directly according to formula (5). DC component : , (5) in, These are the pixel values ​​in the first column; here, if ,but ; Step 4: Extract the watermark position according to formula (6): , (6) in, For the extracted watermark position, This represents the index variable of the quantization interval; here, , , ; Step 5: Repeat step 4 of this process to obtain the binary watermark sequence for each layer. Then each layer of binary watermark sequence Each 8-bit binary number is converted into a 1-bit decimal image pixel value to obtain an encrypted layered watermark image. ,in They represent the red, green, and blue layers respectively; Step 6: Process the encrypted layered watermark image Execute key-based , , The Lorenz transform will transform each layer of the watermark image. Decryption is performed to obtain the decrypted layered watermark image. ,in They represent the red, green, and blue layers respectively; Step 7: Combine the decrypted layered watermark images To obtain the complete watermark extraction image ,in , representing the red, green and blue layers respectively.

[0011] To demonstrate the effectiveness of this invention, the following were selected: Figure 1 (a) Figure 1 (b) shows two standard images with a pixel size of 512×512×3 as the host images, and respectively use the following... Figure 2 The two 24-bit color images with a pixel size of 32×32×3 shown are used as digital watermarks for verification.

[0012] Figure 3 (a) Figure 3 (b) is to respectively Figure 2 (a) Embedded into the host image Figure 1 (a) will Figure 2 (b) Embedded into the host image Figure 1The peak signal-to-noise ratio (PSNR) values ​​of the watermarked images obtained after (b) are 40.422 dB and 40.451 dB, respectively, and their structural similarity indices (SSIM) are 0.965 and 0.969, respectively. Figure 4 (a) Figure 4 (b) is sequentially from Figure 3 (a) Figure 3 The watermarks extracted in (b) have normalized cross-correlation coefficient (NC) values ​​of 1.000 and 1.000, respectively. Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) Figure 5 (f) Figure 5 (g) is to Figure 3 The watermarks extracted from the watermarked image shown in (a) after being subjected to attacks such as JPEG (90), JPEG2000 (4:1), salt and pepper noise (0.1%), scaling (400%), cropping (6.25%), rotation (15 degrees clockwise), and translation (10, 10) in sequence have normalized cross-correlation coefficient (NC) values ​​of 1.000, 1.000, 0.962, 1.000, 0.998, 0.957, and 0.996, respectively. Figure 6 (a) Figure 6 (b) Figure 6 (c) Figure 6 (d) Figure 6 (e) Figure 6 (f) Figure 6 (g) is to Figure 3 The watermarks extracted from the watermarked image shown in (b) after being subjected to attacks such as JPEG (90), JPEG2000 (4:1), salt and pepper noise (0.1%), scaling (400%), cropping (6.25%), rotation (15 degrees clockwise), and translation (10, 10) in sequence have normalized cross-correlation coefficient (NC) values ​​of 1.000, 1.000, 0.999, 0.998, 0.997, 0.992, and 0.988, respectively.

[0013] In summary, the embedded color image digital watermark has good invisibility, meeting the invisibility requirement of the watermarking algorithm; the color image digital watermark extracted from various attacked images has good identifiability and a high NC value, indicating that the method has strong robustness; at the same time, the watermark embedding time is 0.068 seconds and the extraction time is 0.046 seconds, achieving high real-time performance and meeting the needs of multimedia big data copyright protection.

Claims

1. The purpose of this invention is to provide a robust digital watermarking method based on Hankel kernel spatial domain analysis, characterized in that: This is achieved through specific watermark embedding and watermark extraction processes. The watermark embedding process is described below: Step 1: Convert an image with a pixel size of The color host image is divided into three layers in the order of red, green, and blue. ,in, They represent the red, green, and blue layers respectively; Step 2: Convert an image with a pixel size of... The color watermark image is divided into three layers in the order of red, green, and blue. Based on key , , The Lorenz chaotic mapping encryption algorithm will watermark each layer of the image. Encryption is performed; finally, the encrypted watermark image is... The decimal pixel values ​​are represented using 8 bits of binary, and the binary watermarks are concatenated to a length of 8. watermark sequence ,in, They represent the red, green, and blue layers respectively; Step 3: Layer the host image Divided into pixels with Non-overlapping blocks are selected in the three-layer host image according to a random block selection algorithm. Select the embedded image patch; Step 4: Select one image block from the selected image blocks in sequence. Then, according to formula (1), the pixel values ​​of its first column are directly calculated. DC component : ， （1） in, It is the pre-calculated weight vector of the DC component. It is an image block The pixel values ​​in the first column; Step 5: Extract one watermark bit from the watermark sequence one by one. Based on the bit value of the watermark to be embedded and the quantization step size The target DC component is calculated using formula (2): ， （2） in, The index variable representing the quantization interval. It is an XOR function. It is the modulo function. The watermark location to be embedded; Step 6: Calculate the DC component modification amount according to formula (3). : ， （3） Step 7: Based on the pre-calculated pixel modification coefficient vector k and formula (4), obtain the pixel values ​​of the first column containing the watermark. and update the original image blocks. Obtain watermarked image blocks : ， （4） in, ; Step 8: Repeat steps 4 through 7 of this process until all other watermark information has been embedded into the remaining image blocks, thereby obtaining a watermarked layered carrier image. Finally, the watermarked layered carrier image is... Reassemble and obtain pixel size Watermarked images ; The watermark extraction process is described as follows: Step 1: Set the pixel size to Watermarked images Divided into 3 layers of watermarked images Each watermarked image layer is further divided into pixels. Non-overlapping image patches, where These represent the red, green, and blue layers, respectively. Step 2: Layering the watermarked image In this process, the random block selection algorithm mentioned in the watermark embedding process is used to select image blocks, where... These represent the red, green, and blue layers, respectively. Step 3: Select one image block from the selected image blocks in the order they appear. The pixel values ​​of the first column are calculated directly according to formula (5). DC component : ， （5） in, These are the pixel values ​​in the first column; Step 4: Extract the watermark position according to formula (6): ， （6） in, For the extracted watermark position, The index variable representing the quantization interval; Step 5: Repeat step 4 of this process to obtain the binary watermark sequence for each layer. Then each layer of binary watermark sequence Each 8-bit binary number is converted into a 1-bit decimal image pixel value to obtain an encrypted layered watermark image. ,in They represent the red, green, and blue layers respectively; Step 6: Process the encrypted layered watermark image Execute key-based , , The Lorenz transform will transform each layer of the watermark image. Decryption is performed to obtain the decrypted layered watermark image. ,in They represent the red, green, and blue layers respectively; Step 7: Combine the decrypted layered watermark images To obtain the complete watermark extraction image ,in , representing the red, green and blue layers respectively.

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