Table 4. Algorithms for embedding digital watermarks into images..
Table 4. Algorithms for embedding digital watermarks into images
| № | Characteristics of digital watermarks | Principle of operation | Advantages | Disadvantages |
|
Additive algorithms |
||||
| A17 | A sequence of pseudo-random numbers distributed according to the Gaussian law, 1000 numbers long | Modification of the 1000 largest coefficients of the discrete cosine transform (DCT) | Strong robustness of the digital watermark for compression and other types of signal processing | The complexity of calculating a two-dimensional DCT |
| A18 | A sequence of binary pseudorandom numbers wi I {-1, 1}, the length of which is determined by the dimensions of the original image |
Modification of all coefficients of the detailed subranges of the first decomposition sublevel when performing a four-level wavelet transform | Possibility of detecting a watermark without the original image. Strong visual invisibility of a watermark | To extract the watermark, you must have the original image |
| A19 | An array of pseudo-random numbers distributed according to the Gaussian law, the size of 1024 numbers | Modification of all LL coefficients of the wavelet transform subrange of the image | Possibility of modifying the algorithm to use a secret key | To extract the watermark, you must have the original image |
| A20 | A sequence of pseudo-random real numbers distributed according to the Gaussian law | Modification of the largest coefficients of the detailed subranges of the three-level image decomposition | Good visual masking of embedded data. The presence of the original image is not required to detect the watermark | |
| A21 | A sequence of pseudo-random real numbers distributed according to the Gaussian law, 1000 numbers long | Modification of perceptually significant coefficients of three-level image decomposition using biorthogonal wavelet filters | Robustness of the digital watermark to many types of attacks. The presence of the original image is not required to detect the digital watermark | |
| A22 | A sequence of pseudo-random real numbers distributed according to the Gaussian law | Modification of the largest coefficients of each sub-range of the three-level decomposition of the image (except for the sub-ranges of the highest resolution level) | The presence of the original image is not required for detecting the watermark | |
| A23 | Bipolar pseudorandom number array | Modification of the 1000 largest coefficients of the complex wavelet transform (the watermark is also transformed) | No source image is required to detect the watermark | |
| A24 | A sequence of pseudo-random real numbers distributed according to the Gaussian law wi I {1, -1} | Modification of the largest coefficients of the three-level wavelet transform (the coefficients are selected in accordance with a given threshold) | High robustness of the digital watermark to some types of attacks | To extract the digital watermark, you need to have the original image |
| A25 | A sequence of pseudo-random real numbers, the length of which depends on the image bandwidth, calculated based on the human vision model | Modification of the coefficients of the four-level wavelet transform, selected taking into account a given threshold | High robustness of the implemented watermark | To extract the watermark, you need to have the original image |
| A26 | Sequence of pseudo-random real numbers distributed according to the Gaussian law | Modification of the largest coefficients from the high-frequency and mid-frequency ranges of the Haar transform | Highly robust to attacks with a change in scale. Possibility of reducing the number of computational operations when detecting a watermark | To extract a watermark, you need to have the original image |
| A27 | Sequence of pseudo-random real numbers distributed according to the Gaussian law (length corresponds to the number of modifiable coefficients) | Modification of significant coefficients of all sub-ranges of the five-level wavelet transform | Possibility of modifying the algorithm to use a stego key | To extract the digital watermark, you must have the original image |
| A28 | Ditto | Algorithm A28 is a modified version of algorithm A27, with blind extraction of watermarks | Not required to have the original image to detect watermarks | Significantly reduced noise immunity compared to algorithm A27 |
|
Algorithms based on merging watermarks and containers |
||||
| A29 | Black and white logo, up to 25% of the original image in size | Modification of all coefficients of single-level decomposition of the original image | Large size of the hidden watermark (up to a quarter of the original image in size) | To extract the watermark, you must have the original image |
| A30 | Black and white logo | Modification of all coefficients of detailed sub-ranges of wavelet transform of the original image | No need for the original image to detect watermarks | |
|
Algorithms using scalar quantization |
||||
| A31 | ±1 sequence | Modification of high-frequency coefficients of the blue component of the image after five-level integer wavelet transform | The original image is not required for watermark detection | |
| A32 | Binary image, 1/2 the size of the original | Modification of the HF-LF and LF-HF regions of the two-level wavelet transform of the original image | Large size of hidden watermark | To extract watermark, it is necessary to have the original image; Low stability of the algorithm with respect to signal processing operations |
| А33 | A sequence of characters obtained from a logo 25% the size of the original image | Modification of the n-dimensional vector of discrete wavelet transform coefficients of the original image | Large size of the hidden watermark It is possible to control the robustness, distortion level and quality of the embedded image | To extract the watermark, you must have the original image |
|
Algorithms using fractal transformations |
||||
| A34 | Formed from the original image (up to 15 different watermarks) | The original image is not required to detect the watermark | ||
| A35 | Bit string | Presence of a secret key; JPEG compression resistance | ||
| A36 | Bit string | Presence of secret key | Noticeable degradation of image quality when embedding watermark | |
Note. Table 4 uses the notations adopted in [2] for watermark algorithms