Watermarking of digital images is required in diversified applications ranging from medical imaging to commercial images used over the web. Usually, the copyright information is embossed over the image in the form of a logo at the corner or diagonal text in the background. However, this form of visible watermarking is not suitable for a large class of applications. In all such cases, a hidden watermark is embedded inside the original image as proof of ownership. A large number of techniques and algorithms are proposed by researchers for invisible watermarking. In this paper, we focus on issues that are critical for security aspects in the most common domains like digital photography copyrighting, online image stores, etc. The requirements of this class of application include robustness (resistance to attack), blindness (direct extraction without original image), high embedding capacity, high Peak Signal to Noise Ratio (PSNR), and high Structural Similarity Matrix (SSIM). Most of these requirements are conflicting, which means that an attempt to maximize one requirement harms the other. In this paper, a

Watermarking of digital media is one of the most common requirements in the digital world [

Digital content type (Typically) | Image, video, audio, multimedia files | ||
---|---|---|---|

Embedding content type (Typically) | Text, logo. Small image | ||

Perceptible/Visible watermark | Example; Watermark on currency notes |
||

Imperceptible/Invisible watermark [ |
Example; Watermark on medical images, Magnetic Resonance Imaging (MRI), X-rays |
||

Non-blind watermarking | There is a requirement for non-watermarked image/media for watermark extraction | Straightforward additive embedding | Spatial domain: Change in pixel values |

Blind watermarking [ |
Algorithmic extraction. |
Requirement of a key. |
Transform domain: Change in transform domain coefficients. |

Hybrid: spatial and transform domain | |||

Enrichment processes | |||

Security enhancement [ |
Watermark is scrambled and then embedded | ||

Watermarking bits are embedded redundantly | |||

Imperceptibility and enhanced embedding capacity (Both these are conflicting requirements) [ |
Nature inspired algorithms example: Firefly technique and variants, whale optimization algorithm, etc. | ||

Metaheuristic approaches examples; Simulated annealing, stochastic gradient descent, etc. | |||

Performance metrics | |||

Mean Square Error (MSE) | Average of the square of differences in the pixel values: Original and changed | ||

Peak Signal to Noise Ratio (PSNR) [ |
Logarithm scale: Reciprocal of Mean Square Error (MSE) | ||

Structural Similarity Index Metric (SSIM) [ |
Quantifies visible differences in two images: Values are high at regions of low change and low at regions of high change. |

There are a large number of techniques proposed by researchers, for domain and type of watermarking requirements. Recent advancements in computational power have revolutionized the techniques for watermark embedding. This can be harnessed for optimal watermarking using metaheuristic and nature-inspired algorithms [

The primary motivation for using SGD-FA is that the effectiveness of FA depends upon the cost function (CF), formulated by following the desired type of watermarking. In the case of non-linear Cost Function, the algorithm occasionally gets trapped in a local-minima or a plateau or a ridge. A stochastic variant of FA will eliminate such possibilities and enables the algorithm to converge to a global minimum. We use the “local-minima” terminology as the process is gradient descent and not hill climbing. As a typical variation of the cost function, consider the formulation in which the numerator is Mean Square Error, and the denominator is the robustness parameter and embedding capacity. The said function, when plotted with the most common independent parameters like embedding positions, gives the type of plot as shown in

The above plot shows two local maxima, two local minima, a plateau and a possible ridge [

In the Section of the literature review, some of the important formulations of cost functions which are proposed by authors in metaheuristic techniques are investigated. We consider the one which is most widely accepted, consisting of a weighted sum of PSNR and SSIM indexes. The same formulation of the cost function is investigated with FA and SGD-FA. It turns out the proposed variant of FA outperforms and enables the algorithm to converge with fewer iterations to a global minimum state. Moreover, the flexibility of using different weights in the cost function gives the choice of a particular cost function that is suitable for a particular use case.

Several techniques have been proposed in the literature for Image Watermarking in the transform domain using Nature Inspired and Metaheuristic approaches [

Article#1 | |

Title [ |
LWT-Firefly algorithm-based approach for smooth images watermarking |

Authors | S. Y. Altay, G. Ulutas |

Publication year | 2019 |

Summarization | The authors propose watermarking technique based upon LWT and FA. The LWT operation results in 4 sub-bands. A selectively chosen sub-band is partitioned into 3 × 3 non-overlapping blocks. These blocks are sorted in the descending order of standard deviation. A 32 × 32-bit binary watermark (1024 bits) embedding is done in blocks that are chosen as per the FA. |

Review | The proposed technique is non-blind as it requires the transmission of a key, to be used as input for the extraction algorithm. The proposed technique cannot be extended to bigger and small watermark images |

Article#2 | |

Title [ |
Optimized blind image watermarking method based on firefly algorithm in discrete wavelet transform decomposition with Q-matrix and R-matrix (DWT-QR) transform domain |

Authors | Yong Guo1, Bing-Zhao Li1, Navdeep Goel |

Publication year | 2017 |

Summarization | The proposed approach uses QR decomposition in which Q is an orthogonal matrix and R is an upper diagonal matrix. It suggests the embedding of watermark data into the coefficients of the R matrix. The technique uses a P vector to store the locations of the coefficients where the watermark is embedded. |

Review | Providing an entire matrix at the receiver end for the detection and extraction of the watermark is a question of the applicability of the technique for a large class of problems. As such, the technique can be more appropriately categorized as semi-blind. Moreover, as the dimension of the cover image and the watermark image increases, it requires the transfer of a large P matrix which is certainly not feasible. |

Article#3 | |

Title [ |
Robust watermarking in DWT domain using Singular Value Decomposition (SVD) and opposition and dimensional-based modified firefly algorithm |

Authors | Elham Moeinaddini, Fatemeh Afsari |

Publication year | 2017 |

Summarization | The authors suggested an approach in which the watermark coefficients are embedded in the U and V matrices of the SVD transformation. Specifically, the watermark is embedded in the 2^{nd} and 3^{rd} elements of the first column of the V matrix. |

Review | The proposed technique classifies as a perfect blind watermarking technique. However, the strength of the embedding is controlled using a Threshold parameter Th, the values of which are computed using the proposed variant of the firefly technique. |

Article#4 | |

Title [ |
A robust digital image watermarking scheme based on bat algorithm optimization and Speed-Up Robust Feature (SURF) detector in Stationary Wavelet Transform (SWT) domain |

Authors | Ali Pourhadi, Homayoun Mahdavi-Nasab |

Publication year | 2020 |

Summarization | The paper utilizes SURF, which is a feature detection technique, extracting features that are invariant to various types of illumination and geometric variations. The authors used arnold transform technique for scrambling the image before embedding, thereby improvising the security of the embedding. |

Review | The proposed technique uses the SURF features which results in a blind watermarking technique. Moreover, with these features, the watermarking is robust against illumination and geometric attacks. |

Lifting Wavelet Transform [

Most of the lifting transforms are recursive. This means that the output is again fed into the input for smoother computing while generating an entire sequence in iterations, thereby getting a desirable compression. The following nomenclature is adopted here. The first subscript represents the even or odd component (e or o). The second subscript is the iteration count of the looping mechanism. The symbol in brackets is the index count.

The signal decomposition using LWT requires three steps as shown below.

Split Signal: The samples of the signal are split into even and odd as per their position in the array or matrix (corresponding to a one or two-dimensional transform). This is represented as follows:

The Predict step also replaces the odd elements of the set with the difference between the odd values and the predict-function values. These values are close to Zero as in most cases, the prediction function is fairly accurate.

Update Signal: The update operation can be described mathematically as shown in the below equation. Here, the second subscript represents the iteration cycle. The coefficient values at even positions are updated at each iteration.

This scheme is depicted as shown in

The most commonly used lifting scheme for Haar Wavelet Transformation includes the following operations in prediction and update.

Predict: It is presumed that the Odd position coefficient is equal in magnitude to the previous even coefficient. Thus

The odd elements are replaced by the difference in the even and odd elements in this step.

Update: The Update step updates the value of the even component as the average of the even-odd pair. This is depicted as shown below:

Substituting the value of

For a given image of dimensions NxN, the dimensions of the LWT coefficients are shown in

Dimension chart | Unit | |
---|---|---|

Original image | 512 × 512 × 3 | Pixels |

2D LWT-DWT using debuchies wavelet | ||

LL band | 64 × 64 × 3 | Coefficients |

LH band/HL band/HH band | 3 × 1 | Cells |

LH{1} = HL{1} = HH{1} | 256 × 256 × 3 | Coefficients |

LH{2} = HL{2} = HH{2} | 128 × 128 × 3 | Coefficients |

LH{3} = HL{3} = HH{3} | 64 × 64 × 3 | Coefficients |

The components LH, HL and HH corresponds to the frequency level components. The three dimensions of the matrix correspond to each of the three color bands in the three-color plane. The Blue color plane is chosen for optimal embedding for its least perceptiveness for the human eye. We consider watermark embedding in the LL band, thereby achieving ¼ embedding capacity of the dimensions of the original image.

Invariant moments [

The firefly algorithm [

Fireflies are unisexual. Each firefly can be attracted to any other firefly.

The strength of attraction is proportional to the brightness of the firefly. More accurately, the more the difference in the brightness of the firefly, the more the attraction strength.

The brightness (I) of a firefly, as seen from other fireflies depends upon the distance between the fireflies.

The brightness of a firefly is computed as an optimized Objective Function.

The following equations hold for intensity and attraction parameters respectively.

The attraction rate β between fireflies can be defined as:

With each iteration, the position of the fireflies is updated as per the following equation:

SGD-FA is a variant of FA which takes a randomization parameter, by following its name. In this variant of FA, there is a set of values, from largest to a given threshold, and the probability of the firefly being attracted to another firefly is proportional to its brightness. However, there exists a probability that the Fireflies can also be attracted to a firefly of comparatively lower brightness. In this case, the position of the fireflies can be updated with each iteration as per the following equation:

Here,

The Stochastic Gradient Descent FA is based upon the randomization process for implementing a local search. It considers the MSE values and the value of the strength parameter for embedding. As indicated previously, both these are conflicting parameters. As the process is of gradient descent, we propose an objective function whose value is to be a minimum. This function is termed the Cost Function (CF).

SGD-FA will iterate through the CF values to achieve a global minimum, eventually, corresponding to the optimum values of the watermark strength parameter and MSE.

It is clear from

Most Metaheuristics are designed to be used for non-blind watermarking techniques where the original, unmarked image is available for watermark detection. Such a privilege is not available in Blind Techniques where the challenge is bigger and requires more complex mathematical techniques. It is due to this limitation that the non-blind techniques found limited applications in real-world use cases. However, a large mass of literature is focused on nature-inspired meta-heuristics, based on watermarking in the transform domain.

In the case of the blind technique, we need a key which is preferably some key that is extracted, in the form of some invariant feature, from the image itself, to surpass the requirement of explicitly sending the key at the detector terminal. The watermark is required to be embedded in the host coefficients as per a policy known to both the embedder and the detector. The embedding policy proposed is illustrated below:

Transform domain coefficients:

String to be Embedded:

Lifting Wavelet Transform creates positive integer coefficients in the LL band of transform.

Let the Watermark Strength Factor be λ. For embedding a 1, we suggest an addition or subtraction operation which makes the coefficient exactly divisible by λ. The bigger the value of the λ, the more robustness of the watermark and the more will be the mean square error. The algorithm for watermark embedding is described as follows:

INPUT-1, Embedding Coefficients:

INPUT-2, Embedding Bits:

Consider the initial value of λ

#Iteration = k

Loop Until desired iteration count or when no update in Cost Function Value.

If Embedding Bit = 1

If

else

end

end

Compute

end

Update λ as per SGD-FA

Goto Step#1

This simple embedding scheme enriched using SGD-FA will give the optimum value of CF resulting in the best possible trade-off between robustness and imperceptibility. The extraction for the said technique is straightforward. It checks for those coefficient values which are exactly divisible by λ. However, this key is required to be provided to the receiver end for watermark extraction, failing which there is no way to extract the watermark.

Considering the legacy of benchmark images, we take the example of the (all-time) LENA image for the simulation of the proposed watermarking technique. The original colored image is shown in

We consider an input image of dimension 512 × 512, in RGB mode, with a watermark image of 64 × 64 which is binary. The two-level LWT produces LL, LH, HL and HH sub-bands corresponding to the high and low pass filtering scheme. The image sub-band images corresponding to LL, LH, HL and HH band of the transform are shown in

The simulation results in the form of extracted watermark and SSIM map are shown in

Watermark strength parameter | Original image | Watermarked image | Extracted watermark | SSIM map | PSNR/MSE | |
---|---|---|---|---|---|---|

% |
% |
% |
% |
39.5907 |
1.7802 | |

% |
% |
% |
% |
38.6854 |
4.7660 | |

% |
% |
% |
% |
36.5565 |
4.6713 | |

% |
% |
% |
% |
35.5993 |
7.3238 | |

% |
% |
% |
% |
30.2399 |
13.6075 |

It turns out that the optimum value of CF is achieved with the 4th iteration of the process, under strengthening-factor λ = 4 and CF = 4.6713. The value of the strength factor depends upon the image and the watermark under consideration. It also depends strongly upon the formulation of the cost function as shown in

The benchmark images for watermarking comparison are shown in

The comparison of the PSNR values of the proposed watermarking scheme with those of the benchmark LWT techniques is shown in the following

A robust, blind image watermarking scheme is presented using LWT-DWT, Hu’s invariant moments and SGD-Firefly metaheuristic-based optimization technique. The scheme presented is semi-blind as it requires sending the watermark strength parameter as a key to be sent to the receiver for extraction. This requirement is critical as the computation of the strength factor depends upon the image under investigation and the iterations of the SGD-FA. The embedding scheme uses a strength factor which acts as a key for the embedding of the watermark. Moreover, the Invariant Moments are used as a key to enhance the security as well as to give a robust watermarking technique resistant to rotation, scaling and translation attacks. For different resolution and image sizes, the SGD-FA would converge to a global minimum value of cost function which is the sum of PSNR and the strength factor, designed in a way to achieve its minimum for optimization. Other definitions of Cost Functions can be used as per the use-case of watermarking under consideration. Future work will focus on embedding the key value in the image itself to implement a pure blind watermarking scheme.

The authors acknowledge their Organizations for the support they provided for carrying out the research work in the stipulated time.

This research work is funded by

The authors declare that they have no conflicts of interest to report regarding the present study.