Most of the previously developed watermarkingmethods usually determine their parameters experimentally.
Although, becausewatermarking algorithms have large parameter space, it is usually difficult toexperimentally determine optimal watermarking parameters. A good solution forthis problem is to regard it as an optimization problem. Hence, metaheuristicoptimization techniques (also called advanced optimization techniques) haveemerged as a considerable tool in recent years. Considering the nature of thephenomenon, Rao et al.
3 have divided thepopulation-based heuristic algorithms into two different groups: evolutionaryalgorithms (EA) and swarm intelligence algorithms. Some of the recognizedevolutionary algorithms are: Genetic Algorithms (GA), Differential Evolution(DE), Evolutionary Strategy (ES), Evolutionary Programming (EP), and ArtificialImmune Algorithm (AIA). Also some of the well-known swarm intelligencealgorithms are: Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO),Shuffled Frog Leaping (SFL) algorithm, and Artificial Bee Colony (ABC)algorithm.
In addition to these algorithms, there are some other algorithmswhich work on the principles of different natural phenomena. Some of them are:Harmony Search (HS) algorithm, Gravitational Search Algorithm (GSA),Biogeography-Based Optimization (BBO) and League Championship Algorithm (LCA).To date, several watermarking methods have been proposed by using themetaheuristic optimization techniques. Shih and Wu 4 presented a watermarking schemebased on DCT and genetic algorithm (GA) in which GA is applied to correct thewatermarking rounding errors. Wang et al. 5 presented a multi-objectivegenetic algorithm (GA) based image watermarking method. They used amulti-objective genetic algorithm with a variable-length mechanism toautomatically optimize the watermarking parameters and search the most suitablepositions for embedding watermark bits. Ebrahimi Moghaddam and Nemati 6 proposed a robust watermarkingtechnique using Imperialistic Competition Algorithm (ICA) in the spatial domainwhere the ICA is used to find a suitable location for watermark embedding indifferent color channels.
In Agarwal et al. 7, a hybrid GA-BPN intelligentnetwork based watermarking scheme was proposed, in which the HVScharacteristics of four host images in DCT domain are used to obtain a sequenceof weighting factor from a GA-BPN. Then this weighting factor is used to embeda binary watermark image in the host image in the DWT domain in LL3 sub band.
In Horng et al. 8, a blind image watermarkingmethod is introduced through a hybridization of DCT and SVD based on GA wherein the singular value of DCT-transformed host image is modified with thequantizing value that is found using GA. Maity et al.
9 proposed a collusion resilientoptimized spread spectrum image watermarking scheme by using genetic algorithms(GA) and multiband wavelets where the GA was employed to determine thresholdvalue of the host image coefficients (process gain e.g. the length of spreadingcode) and the respective embedding strengths compatible to the gain offrequency response.
Also they proposed in paper 10 an multicarrier spread spectrumimage watermarking algorithm using hybridization of genetic algorithms (GA) andneural networks (NN) where the GA selects appropriate gradient thresholds forpartitioning the host image and calculating the embedding strengths. The NN, aswell, calculates the weight factor in minimum mean square error combining(MMSEC) to improve the watermark decoding performance and interference cancelation.In Ali et al.
11, a watermarking scheme based ondifferential evolution (DE) in discrete wavelet transform-singular valuedecomposition (DWT–SVD) transform domain is proposed where the DE is used tosearch optimal scaling factors for improving imperceptibility and robustness.Peng et al. 12 introduces a ridgelet basedimage watermarking algorithm, and then develops a novel watermarking frameworkbased on tissue P systems in which a special membrane structure is designed andits cells are used as parallel computing units to find the optimal watermarkingparameters. In Abdelhakim et al.
13, a recent watermarking scheme isutilized as the embedding algorithm and also the Artificial Bee Colony (ABC) isselected as the optimization method in which the fitness function is used. Thefitness function is based on dividing the problem into two single objectiveoptimization sub-problems in which the robustness and imperceptibilityobjectives are optimized separately. So, there is no need for weightingfactors. Ansari and Pant 14 proposed a multipurpose imagewatermarking scheme in order to provide tampering detection and ownershipverification in which principal components of watermark is used to robustwatermark embedding and the last two LSB of host image is applied for thefragile watermark embedding. The robust insertion is optimized with the help ofArtificial Bee colony (ABC) by optimization of the scaling factors. Ansari et al.
15, introduced a secure optimizedimage watermarking ABC scheme in which the values of scaling factors are foundwith the help of artificial bee colony (ABC). In paper 16, a semi blind image watermarkingscheme in wavelet domain based on Artificial Bee Colony (ABC) is proposed wherethe encrypted watermark is embedded into wavelet coefficients by utilizingreference image generated by using SVD and scaling factor. The ABC method isemployed to optimize the scaling factor. The main limitation of all thementioned algorithms is having algorithm-specific parameters that tuning theseparameters is important for finding the optimum solution and it is anoptimization problem itself.
For example, the GA requires the crossoverprobability, mutation probability and selection operator. So inappropriatetuning of algorithm-specific parameters affects the effectiveness of thealgorithm and either increases the computational efforts or yields the localoptimum solution 3. Hence for solving this problem,Rao et al.
17-19 presented a newoptimization algorithm known as “Teaching-Leaning-Based Optimization (TLBO)”algorithm which requires only the common control parameters like populationsize and number of generations for its working. For it does not require anyalgorithm-specific parameter to be tuned, its implementation is simpler thanothers algorithms.