Color image blind watermarking method based on discrete Hankel transform

Abstract

The invention discloses a color image blind watermarking method based on discrete Hankel transformation in order to better and effectively protect the digital copyright of a color image in the Internet. The method comprises the following steps: firstly, carrying out dimensionality reduction on a watermark image, and encrypting a layered watermark image by utilizing a Lorenz chaotic mapping encryption algorithm; a color host image is also subjected to dimensionality reduction and layering preprocessing and is divided into non-overlapping image blocks. After discrete Hankel transformation is carried out on an image block, watermark information is embedded into the image according to the embedding sequence of a blue channel, a red channel and a green channel, and the algorithm has good performance in the aspects of robustness, safety, invisibility and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of information security and relates to copyright protection of large-capacity color digital images. Background Art

[0002] With the rapid development of mobile Internet, more and more devices are connected to the network. Technological innovation has greatly increased the speed of information transmission on the network, and has also generated massive amounts of information, making information sharing more convenient. However, the complex network environment has also brought about digital infringement problems such as piracy, tampering and data leakage, which has made copyright protection issues widely concerned by scholars at home and abroad. On the one hand, copyright protection logos are tending to be beautiful, practical and informative color images; on the other hand, early watermarking technology mainly relies on complex frequency domain processing, such as discrete cosine transform and discrete wavelet transform, to improve the robustness and concealment of watermarks. Therefore, in order to better protect the copyright of images, designing an effective color image digital watermarking method has become one of the key points and difficulties in the current research of digital watermarking technology. The color image blind watermarking method based on discrete Hankel transform was invented to meet these needs. Summary of the invention

[0003] The purpose of the present invention is to provide a color image blind watermarking algorithm based on discrete Hankel transform, which is characterized by being implemented through a specific watermark embedding process and an extraction process. The watermark embedding process is described as follows: Step 1: Take a picture of size 24-bit color image digital watermark Divide into 3 layered watermark images in the order of red, green and blue ; Then, each layered watermark image Key-based The Lorenz chaotic map encryption is used to obtain the encrypted layered watermark image. ; and the encrypted layered watermark image Each pixel represented by a decimal number in is represented by an 8-bit binary number and connected in sequence to form a length of The layered watermark bit sequence ,in, , representing the red, green and blue layers respectively; Step 2: Make a picture of size Color host image Divided into 3 layered host images in the order of red, green and blue layers ; Then, each layered host image Divide into size non-overlapping image blocks; according to the layered watermark bit sequence Total length , using key-based The MD5 hash pseudo-random scrambling algorithm generates a non-repeating block sequence, where: , representing the red, green and blue layers respectively; Step 3: Select one image block at a time from the generated non-overlapping image blocks According to formula (1), Perform discrete Hankel transform to obtain the transformed coefficient block matrix ; (1) in, is the discrete Hankel transform, is the input radius, is the number of sample points, is the transformation order, is the transformed coefficient block matrix, is the spatial frequency, is the radial distance, is the integral kernel, is the spectral factor, is the updated input radius; Step 4: Layer the watermark bit sequence In the above example, take out one bit of watermark information to be embedded in turn. , and embed it into the coefficient block matrix The first number of the first row According to the embedded watermark information and formula (2), the frequency domain coefficient after embedding the watermark is calculated. ,in, , representing the red, green and blue layers respectively; (2) in, , is the XOR function, is the remainder function, is the rounding function, is the quantization step size, , respectively represent the red, green and blue layers; Step 5: Update to the transformed coefficient block The corresponding position in the coefficient block matrix containing the watermark is obtained Then, the inverse transform of discrete Hankel transform is realized by formula (3) to obtain the image block containing watermark ; (3) in, is the inverse discrete Hankel transform, is the coefficient block matrix containing the watermark, is the integral kernel, is the spectral factor, is the updated input radius; Step 6: Block the watermarked image Update to its host image in layer The corresponding position in , where , representing the red, green and blue layers respectively; Step 7: Repeat and execute steps 3 to 6 of this process in sequence until all watermark information is embedded, thereby obtaining a layered carrier image containing watermark information. Finally, the layered carrier image containing the watermark information Reassemble and obtain the watermarked image ,in, , representing the red, green and blue layers respectively; The watermark extraction process is described as follows: Step 1: Set the size to Watermarked image Divided into 3 layers with watermark images , and each layer of watermarked image Further divided into Non-overlapping image blocks are selected according to the order of embedding to extract each image block, where , representing the red, green and blue layers respectively; Step 2: Select one image block at a time from each layer of non-overlapping image blocks According to formula (4), Perform discrete Hankel transform to obtain the transformed coefficient block matrix ; (4) in, is the discrete Hankel transform, is the selected image block, is the input radius, is the number of sample points, is the transformation order, is the transformed coefficient block matrix, is the spatial frequency, is the radial distance, is the integral kernel, is the spectral factor, is the updated input radius; Step 3: Extract the coefficient block matrix according to formula (5) The watermark contained in ; (5) in, Represents the number of the first row and first column of the coefficient block matrix, is the remainder function, is the rounding function towards zero, is the quantization step size, Indicates the final extracted watermark value; Step 4: Repeat steps 2 to 3 of this process to obtain the binary watermark bit sequence , and then convert each 8 bits of binary information into a decimal pixel value, where , representing the red, green and blue layers respectively; Step 5: Align the scrambled layered watermark image Using key-based The Lorenz chaotic map decryption algorithm is used to decrypt and combine the layered watermark image , get the completely extracted watermark image ,in, , representing the red, green and blue layers respectively.

[0004] This method uses the maximum coefficient obtained by discrete Hankel transform of the matrix to implement a method of color image watermark embedding and blind extraction. This method meets the requirements of invisibility, robustness, real-time and security. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Figure 1 (a) Figure 1 (b) are two original color host images.

[0006] Figure 2 (a) Figure 2 (b) are two original color watermarked images.

[0007] Figure 3 (a) Figure 3 (b) is to Figure 2 (a) Figure 2 The watermarks shown in (b) are embedded in Figure 1 (a) Figure 1 The structural similarity SSIM values ​​of the watermarked images obtained after (b) are 0.978 and 0.985, and the peak signal-to-noise ratio PSNR values ​​are 40.063dB and 40.050dB, respectively.

[0008] Figure 4 (a) Figure 4 (b) are respectively from Figure 3 (a) Figure 3The normalized cross-correlation coefficient NC values ​​of the watermarks extracted in (b) are 1.000 and 1.000 respectively.

[0009] Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) Figure 5 (f) is to Figure 3 The watermarks extracted from the watermarked image shown in (a) after being attacked with JPEG compression (70), JPEG2000 (4:1), salt and pepper noise (0.5%), median filtering (3×3), scaling (400%), and shearing (12.5%) have normalized cross-correlation coefficients NC values ​​of 0.967, 0.999, 0.994, 0.988, 0.995, and 0.996, respectively.

[0010] Figure 6 (a) Figure 6 (b) Figure 6 (c) Figure 6 (d) Figure 6 (e) Figure 6 (f) is to Figure 3 The watermarks extracted from the watermarked image shown in (b) after being attacked with JPEG compression (70), JPEG2000 (4:1), salt and pepper noise (0.5%), median filtering (3×3), scaling (400%), and shearing (12.5%), have normalized cross-correlation coefficients NC values ​​of 0.971, 1.000, 0.992, 0.999, 1.000, and 0.978, respectively. DETAILED DESCRIPTION

[0011] The purpose of the present invention is to provide a color image blind watermarking algorithm based on discrete Hankel transform, which is characterized by being implemented through a specific watermark embedding process and an extraction process. The watermark embedding process is described as follows: Step 1: Take a picture of size 24-bit color image digital watermark Divide into 3 layered watermark images in the order of red, green and blue ; Then, each layered watermark image Key-based The Lorenz chaotic map encryption is used to obtain the encrypted layered watermark image. ; and the encrypted layered watermark image Each pixel represented by a decimal number in is represented by an 8-bit binary number (for example, the decimal number 128 can be converted into the binary number 10000000), which is connected in sequence to form a length of The layered watermark bit sequence ,in, , representing the red, green and blue layers respectively; Step 2: Make a picture of size Color host image Divide into 3 layered host images according to the order of red, green and blue primary color channels ; Then, each layered host image Divide into size non-overlapping image blocks; according to the layered watermark bit sequence Total length , using key-based The MD5 hash pseudo-random scrambling algorithm generates a non-repeating block sequence, where: , representing the red, green and blue layers respectively; Step 3: Select one image block at a time from the generated non-overlapping image blocks According to formula (1), Perform discrete Hankel transform to obtain the transformed coefficient block matrix ; (1) in, is the discrete Hankel transform, is the input radius, is the number of sample points, is the transformation order, is the transformed coefficient block matrix, is the spatial frequency, is the radial distance, is the integral kernel, is the spectral factor, is the updated input radius; here, let the selected image block , =5, =3, =0, then we get , , , , , ; Step 4: Layer the watermark bit sequence In the above example, take out one bit of watermark information to be embedded in turn. , and embed it into the coefficient block matrix The first coefficient of the first row , the quantized frequency domain coefficients are calculated based on the embedded watermark information and formula (2) ; (2) in, , is the XOR function, is the remainder function, is the rounding function; here, = ,set up ='1', =375; then , can be obtained =4312.500; Step 5: Update to the transformed coefficient block The corresponding position in the coefficient block matrix containing the watermark is obtained Then, the inverse transform of discrete Hankel transform is realized by formula (3) to obtain the image block containing watermark ; (3) in, is the inverse discrete Hankel transform, is the coefficient block matrix containing the watermark, is the integral kernel, is the spectral factor, is the updated input radius; here, =3445.333, we can get , , , , , ; Step 6: Block the watermarked image Update to its host image in layer The corresponding position in , where , representing the red, green and blue layers respectively; Step 7: Repeat and execute steps 3 to 6 of this process in sequence until all watermark information is embedded, thereby obtaining a layered carrier image containing watermark information. Finally, the layered carrier image containing the watermark information Reassemble and obtain watermarked Image ,in, , representing the red, green and blue layers respectively; The watermark extraction process is described as follows: Step 1: Set the size to Watermarked image Divided into 3 layers with watermark images , and each layer of watermarked image Further divided into Non-overlapping image blocks are selected according to the order of embedding to extract each image block, where , representing the red, green and blue layers respectively; Step 2: Layer the watermarked image In the watermark embedding process, the key-based The MD5 hash pseudo-random scrambling algorithm selects image blocks According to formula (4), Perform discrete Hankel transform to obtain the transformed coefficient block matrix ,in, , representing the red, green and blue layers respectively; (4) in, is the discrete Hankel transform, is the selected image block, is the input radius, is the number of sample points, is the transformation order, is the transformed coefficient block matrix, is the spatial frequency, is the radial distance, is the integral kernel, is the spectral factor, is the updated input radius; here, let the selected image block , =5, =3, =0, then we get , , , , , ; Step 3: Extract the coefficient block matrix according to formula (5) The watermark contained in ; (5) in, is the remainder function, is the rounding function towards zero, Represents the final extracted watermark value; here, let , , we can get the watermark information w * ='0'; Step 4: Repeat steps 2 to 3 of this process to obtain the binary watermark bit sequence of each layer. To restore, , representing the red, green and blue layers respectively; Step 5: Perform key-based Lorenz chaotic map decryption algorithm to extract the complete layered watermark image , combined layered watermark image , get the complete extracted watermark ,in, , representing the red, green and blue layers respectively.

[0012] This method uses the maximum coefficient obtained by discrete Hankel transform of the matrix to implement a method of color image watermark embedding and blind extraction. This method meets the requirements of invisibility, robustness, real-time and security.

[0013] Verification of the effectiveness of the present invention In order to prove the effectiveness of the present invention, Figure 1 (a) Figure 1 (b) shows two 24-bit standard images with a pixel size of 512×512 as carrier images, and are respectively used as Figure 2 The two 24-bit color images with a pixel size of 32×32 are shown as digital watermarks for verification.

[0014] Figure 3 (a) Figure 3 (b) is to Figure 2 (a) Figure 2 (b) The watermarks shown are embedded into the carrier image Figure 1 (a) Figure 1 (b) The watermarked images obtained after that have a structural similarity SSIM value of 0.972 and 0.961, and a peak signal-to-noise ratio PSNR value of 40.023dB and 40.002dB, respectively; Figure 4 (a) Figure 4 (b) are respectively from Figure 3 (a) Figure 3 The normalized correlation coefficient NC values ​​of the watermarks extracted in (b) are 1.000 and 0.999 respectively; Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) Figure 5 (f) is to Figure 3The watermarks extracted from the watermarked image shown in (a) after being attacked by JPEG compression (70), JPEG2000 (4:1), salt and pepper noise (0.5%), median filtering (3×3), scaling (400%), and shearing (12.5%), the normalized cross-correlation coefficient NC values ​​are 0.967, 0.999, 0.994, 0.988, 0.995, and 0.996 respectively; Figure 6 (a) Figure 6 (b) Figure 6 (c) Figure 6 (d) Figure 6 (e) Figure 6 (f) is to Figure 3 The watermarks extracted from the watermarked image shown in (b) are subjected to JPEG compression (70), JPEG2000 (4:1), salt and pepper noise (0.5%), median filtering (3×3), scaling (400%), and shearing (12.5%) attacks, and their normalized cross-correlation coefficients NC values ​​are 0.971, 1.000, 0.991, 0.999, 1.000, and 0.978, respectively. In summary, the embedded color image digital watermark has good invisibility and meets the invisibility requirements of the watermark algorithm; at the same time, the color image digital watermarks extracted from various attacked images have good identifiability and high NC values, indicating that the method has strong robustness.

Claims

1. A color image blind watermarking algorithm based on discrete Hankel transform, characterized in that This is achieved through a specific watermark embedding process and extraction process. The watermark embedding process is described as follows: Step 1: Take a picture of size 24-bit color image digital watermark Divide into 3 layered watermark images in the order of red, green and blue ; Then, each layered watermark image Key-based The Lorenz chaotic map encryption is used to obtain the encrypted layered watermark image. ; and the encrypted layered watermark image Each pixel represented by a decimal number in is represented by an 8-bit binary number and connected in sequence to form a length of The layered watermark bit sequence ,in, , representing the red, green and blue layers respectively; Step 2: Make a picture of size Color host image Divided into 3 layered host images in the order of red, green and blue layers ; Then, each layered host image Divide into size non-overlapping image blocks; according to the layered watermark bit sequence Total length , using key-based The MD5 hash pseudo-random scrambling algorithm generates a non-repeating block sequence, where: , representing the red, green and blue layers respectively; Step 3: Select one image block at a time from the generated non-overlapping image blocks According to formula (1), Perform discrete Hankel transform to obtain the transformed coefficient block matrix ; （1） in, is the discrete Hankel transform, is the input radius, is the number of sample points, is the transformation order, is the transformed coefficient block matrix, is the spatial frequency, is the radial distance, is the integral kernel, is the spectral factor, is the updated input radius; Step 4: Layer the watermark bit sequence In the above example, take out one bit of watermark information to be embedded in turn. , and embed it into the coefficient block matrix The first number of the first row According to the embedded watermark information and formula (2), the frequency domain coefficient after embedding the watermark is calculated. ,in, , representing the red, green and blue layers respectively; （2） in, , is the XOR function, is the remainder function, is the rounding function, is the quantization step size, , respectively represent the red, green and blue layers; Step 5: Update to the transformed coefficient block The corresponding position in the coefficient block matrix containing the watermark is obtained Then, the inverse transform of discrete Hankel transform is realized by formula (3) to obtain the image block containing watermark ; （3） in, is the inverse discrete Hankel transform, is the coefficient block matrix containing the watermark, is the integral kernel, is the spectral factor, is the updated input radius; Step 6: Block the watermarked image Update to its host image in layer The corresponding position in , where , representing the red, green and blue layers respectively; Step 7: Repeat and execute steps 3 to 6 of this process in sequence until all watermark information is embedded, thereby obtaining a layered carrier image containing watermark information. Finally, the layered carrier image containing the watermark information Reassemble and obtain the watermarked image ,in, , representing the red, green and blue layers respectively; The watermark extraction process is described as follows: Step 1: Set the size to Watermarked image Divided into 3 layers with watermark images , and each layer of watermarked image Further divided into Non-overlapping image blocks are selected according to the order of embedding to extract each image block, where , representing the red, green and blue layers respectively; Step 2: Select one image block at a time from each layer of non-overlapping image blocks According to formula (4), Perform discrete Hankel transform to obtain the transformed coefficient block matrix ; （4） in, is the discrete Hankel transform, is the selected image block, is the input radius, is the number of sample points, is the transformation order, is the transformed coefficient block matrix, is the spatial frequency, is the radial distance, is the integral kernel, is the spectral factor, is the updated input radius; Step 3: Extract the coefficient block matrix according to formula (5) The watermark contained in ; （5） in, Represents the number of the first row and first column of the coefficient block matrix, is the remainder function, is the rounding function towards zero, is the quantization step size, Indicates the final extracted watermark value; Step 4: Repeat steps 2 to 3 of this process to obtain the binary watermark bit sequence , and then convert each 8 bits of binary information into a decimal pixel value, where , representing the red, green and blue layers respectively; Step 5: Align the scrambled layered watermark image Using key-based The Lorenz chaotic map decryption algorithm is used to decrypt and combine the layered watermark image , get the completely extracted watermark image ,in, , representing the red, green and blue layers respectively.

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