RETRACTED ARTICLE: Robust image watermarking using fractional Krawtchouk transform with optimization

Abstract

Fractional Krawtchouk Transform is a generalization of the Krawtchouk transforms which has two fractional orders. By adjusting these fractional orders in the weighted two dimensional Krawtchouk polynomials, local image features can be located. This paper proposes a robust image watermarking method using FrKT with firefly and cuckoo search optimization algorithms. The frequency domain image is obtained by applying FrKT for the input image blocks. The optimal fractional parameters of the transform improve the imperceptibility of the secret data in the host images. The fractional parameter selection for the image transformation is performed by Firefly optimization algorithm. Also, the optimal location in each block to hide the secret data is identified by the cuckoo search algorithm. The histogram shifting technique is used to embed the secret data in the optimal locations due to its less computational complexity. The parameters like Peak Signal to Noise Ratio, Normalized Correlation Coefficient, Structural SIMilarity index, Bit Error Rate are used for comparison of the proposed method using the optimization algorithms. The experimental results of the proposed method FrKT with combination of both Firefly and cuckoo search optimization shows better quality of the watermark, robustness and imperceptibility against various attacks. It can be concluded that the proposed FrKT + CS + FA provides an average of 0.92 for most of the attacks that prove the robustness of the proposed scheme.

1 Introduction

The digital environment is highly susceptible for illegal usage of the digital images. The most effective solution which is popular in the communication environment for the authentication and copyright protection of the digital images is image watermarking. The significant research field in information hiding technology is the digital watermarking. A digital watermark is an identification code that is embedded in the multimedia hosts such as images, audio, video, text, etc. Watermarking is the process of embedding a secret digital content into a host signal at the transmitting end and the same can be detected from the host signal at the receiving end, as cited in the works of Mohanarathinam et al. (2019), Singh and Bhatnagar (2020). Some of the major applications of digital watermarking are copyright protections, ownership identification, authentication, secret communication and medical applications (Verma and Jha 2015).

On domain based classification the watermarking technique is classified into spatial domain watermarking and spectral domain watermarking. The frequency domain watermarking approaches embed the watermarks in the host image by modifying its frequency coefficients. The Discrete Sine Transform (DST), Discrete Cosine Transform (DCT), Singular Value Decomposition (SVD), Discrete Fourier Transform (DFT), Discrete Wavelet Transform (DWT) are the most commonly used transformation methods for watermarking applications. Also, watermarking algorithms using geometric moments (Dong et al. 2005), Zernike moments (Xin et al. 2007), Fourier–Mellin Transform (Li and Zhu 2010a, b), Radon Transform and Angular Radial Transform (ART) (Singh and Ranade 2013), were discussed in literature to embed the watermark.

Discrete wavelet transform can be computed by separating the image pixels into non-overlapping blocks of a specific size. The result of the DWT has different sub band coefficients. The low frequency band contains the most of the visual parts and the higher band is removed during the compression process, so only the mid frequency bands coefficients of the image are used for the watermark embedding (Hsu and Wu 1999). The blocks of size 8 × 8 are used for the practical applications of DCT due to the better energy compaction (Liang and Tran 2001; Chau and Siu 2013).

A watermarking method based on DFT and two dimensional histogram of color image were proposed by Cedillo-Hernández et al. (2014). This method use the YCbCr combination for the watermarking scheme in which the luminance component is applied with DFT and Cb-Cr components are used for the geometric robust method.

In DWT based watermarking techniques the higher subbands are used for watermark embedding. By combining DWT and DCT a new imperceptible and robust 9 watermarking method was proposed by Al-Haj and Abu-Errub (2008). A DWT based watermarking technique is used for the evaluation of fidelity and robustness of the watermark, was proposed by Barni et al. (2001). These algorithms provide better quality in extraction of watermarks but have low robustness on various attacks on the host image. The DWT based watermarking methods provide better robustness and lead to enhanced level of imperceptibility (Mishra et al. 2014).

SVD is one of the effective tool to analysis the matrices. While using the SVD transformation a matrix is decomposed into three matrices U, D, V. U and V are the unitary matrices and D is a diagonal matrix. The Singular Value Decomposition (SVD) provides a clear view on image characteristics and the prediction on the image quality is performed by using the structural information. An algorithm based on the calculation of singular values and adding the watermark by modifying the parameters was proposed (Liu and Liu 2008). The SVD is applied for the modified singular value parameters to obtain the watermarked image. The combined DWT and SVD based watermarking method by using the properties of human visual system was developed by decomposing the host image into sub-bands using DWT and applying SVD to each sub bands for embedding the watermark (Li et al. 2007). A watermarking method for the estimation of geometric distortion with DWT and SVD using Zernike moments and invariant centroid has been discussed by Li and Zhu (2010a, b). The generalization of the Fourier transform is the Fractional Fourier Transform (FrFT). FrFT depends upon the rotation in time frequency plane and some additional parameters which are analysed in the signal processing applications and interpreted as the rotation in the time–frequency plane, also depends upon some additional parameters (Tao et al. 2009). A watermark embedding algorithm using the local regions of the image based on the Krawtchouk transform was proposed (Papakostas et al. 2010). A kernel function as the product of Krawtchouk function and the exponential function with a parameter was developed which is known as the fractional Fourier–Krawtchouk transform (Atakishiyev and Wolf 1997).

The imperceptibility, robustness, complexity and the embedding capacity of the watermarking algorithm are the quality parameters of the algorithm. The scaling factors used in the watermark embedding process determine the strength of the watermarks, so the selected scaling factors should protect the watermarks from the various attacks and the distortions in the watermarked image. In order to maintain the robustness and imperceptibility of the host image in the watermark embedding algorithms, the watermark locations and the multiple scaling parameter selections can be done by using the nature inspired optimization algorithms. The selection of the scaling parameter is an optimization problem which can be solved by optimization algorithms like Firefly Algorithm (FA), Modified Firefly Algorithm (MFA), Cuttlefish Algorithm (CA), Bat Algorithm (BA), Seed Based Plant Propagation Algorithm (SBPPA) (Sinsinwar and Chauhan 2016), Artificial Bee Colony Algorithm (ABCA) (Ansari et al. 2017), Genetic Algorithm (GA) (Surekha and Sumathi 2011), Particle Swarm Optimization (PSO) (Tamirat et al. 2017), Ant Colony Optimization (ACO).

An algorithm which uses the flashing behaviour of the fireflies, based on brightness proportional to the attractiveness is known as the firefly algorithm. The firefly with more brightness attracts the less brighter ones, which moves in a random direction, which is the nature of movement of the firefly. This random movement is modified to improve the performance of the algorithm, which is the Modified Firefly Algorithm (Ali and Ahn 2015). Another meta-heuristic optimization algorithm which is inspired by the changing of colour of the cuttlefish is the Cuttlefish Algorithm (CFA) which has the properties of reflection and visibility. The literature shows FA based method can achieve efficient, reliable and robust solutions when compared to GA, PSO, and ABC. The aim of this proposed method is to maintain the robustness and quality of the secret data. The main contribution of this work is the selection of fractional order with the help of Firefly algorithm and the watermark location identification by using the cuckoo search. The existing technique using FrKT has one of the main issues that is the fractional order selection and the location identification. This problem was solved by the optimization algorithms to maintain the robustness and quality of the secret data in watermarking. The proposed method can overcome these issues from existing techniques and modified to improve the performance of the algorithm.

2 Background

2.1 Fractional Krawtchouk transform

The 1-D Krawtchouk transform for signal f(x) of length N defined in (1) can be written in the following matrix form

$${\text{Q}} = {\text{K}}f$$

(1)

where the transform matrix K is defined by K_n,x= K_n(x; p,N −1), 0 ≤ n, x ≤ N −1.

A set of orthonormal eigenvectors of K can be constructed. Then, we can rearrange the columns of V to match the eigenvectors to the eigenvalues of K such that

$${\text{K}} = {\text{VDV}}^{\text{T}}$$

(2)

where D is a diagonal matrix with diagonal entries the eigenvalues of K, and V is a set of orthonormal eigenvectors,

$$V = \left\{ {\begin{array}{*{20}l} {\left[ {u_{1} ,v_{1} ,u_{2} ,v_{2} , \ldots u_{m} ,v_{m} } \right],} & { if\,\, N = 2m} \\ {\left[ {u_{1} ,v_{1} ,u_{2} ,v_{2} , \ldots u_{m} ,v_{m} ,u_{m + 1} } \right],} & {if\,\, N = 2m + 1} \\ \end{array} } \right.$$

(3)

The eigenvalues in D are arranged in the following form if the size of K is even,

$$D = \left| {\begin{array}{*{20}c} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & { - 1} & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & \ddots & 0 & 0 \\ 0 & 0 & 0 & 0 & \ddots & 0 \\ 0 & 0 & 0 & 0 & 0 & { - 1} \\ \end{array} } \right|$$

(4)

K is odd then

$$D = \left| {\begin{array}{*{20}c} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & { - 1} & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & { - 1} & 0 & 0 \\ 0 & 0 & 0 & 0 & \ddots & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} } \right|$$

(5)

Since the diagonal elements of D can be written as $e^{ - jk\pi }$ with k = 0, 1,…, N −1, as the generalization of DFrFT the fractional order as the power of eigenvalues in D. The FrKT transform matrix K_a of size N with order a corresponding to an angle α where α = πa can be defined as

$$K^{a} = VD^{a} V^{T} = \mathop \sum \limits_{k = 0}^{N - 1} e^{ - jk\alpha } v_{k} v_{k}^{T}$$

(6)

where vk is the kth column of V, and $D^{a}$ is defined as

$$D = \left| {\begin{array}{*{20}c} {e^{ - j0\alpha } } & 0 & 0 & 0 & 0 \\ 0 & {e^{ - j1\alpha } } & 0 & 0 & 0 \\ 0 & 0 & {e^{ - j2\alpha } } & 0 & 0 \\ 0 & 0 & 0 & \ddots & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & {e^{{ - j\left( {N - 1} \right)\alpha }} } \\ \end{array} } \right|$$

(7)

the 1D forward FrKT of signal f(x) of length N with order a can be expressed by

$$Q^{a} = K^{a} f$$

(8)

The corresponding inverse FrKT can be written as

$$f = Q^{a} K^{ - a}$$

(9)

The definition of 2-D FrKT with fractional order (a, b) corresponding to angle (α, β) where α = πa, β = πb of an image g(x, y) can be achieved by firstly performing the FrKT on each column of the image, and then on each row of the transformation. It can be expressed as

$$Q^{a,b} = K^{a} gK^{b}$$

(10)

The two matrices Ka and Kb generated from the Krawtchouk matrix defined in (Yap et al. 2003) may have different parameters for the weighted Krawtchouk polynomials. The weighted Krawtchouk polynomial parameters as p for K_a and as q for K_b with p, q ∈ (0, 1).

The corresponding inverse FrKT can be generated as

$$g = K^{ - a} Q^{a,b} K^{ - b}$$

(11)

It can be observed that there are two more extra parameters (a, b) in the transformation when compared with the traditional 2-D Krawtchouk transform. They come in addition to the two parameters (p, q) in the weighted Krawtchouk polynomials.

2.2 Firefly Algorithm (FA)

Firefly Algorithm is a swarm intelligence optimization technique which uses the flashing nature of firefly. The main purpose of the flashing is to attract prey and to attract mating partners. The swarm of fireflies will move to brighter and more attractive locations by the flashing light intensity that associated with the objective function of problem considered in order to obtain efficient optimal solutions (Sundararajana and Yamuna 2018). The development of firefly-inspired algorithm was based on three idealized rules:

• 1. Fireflies are unisex so that one firefly will be attracted to other fireflies regardless of their sex.

• 2. The fireflies having more brightness will have more attractiveness. So, the fireflies having higher brightness will attract the one which have less brightness, which moves towards the brighter ones.

• 3. The moving direction of the fireflies is random, if there are no fireflies brighter than a particular firefly.

The issues in formulating the FA are the variation in the light intensity and the attractiveness. The encoded objective function is proportional to brightness of the firefly which determines the attractiveness. The objective function and the brightness of a firefly at a particular location ‘x’ is proportional to each other. The attractiveness of the fireflies vary as the distance between the two fireflies varies. Consider the attractiveness parameter as β and the two fireflies as ‘a’ and ‘b’ respectively. So, the Cartesian distance $r_{i,j}$ between the two fireflies at location $x_{i} {\text{and}}x_{j}$ is given by

$$r_{i,j} = x_{i} - x_{j} = \sqrt {\mathop \sum \limits_{k - 1}^{c} \left( {x_{i,k} - x_{j,k} } \right)^{2} }$$

(12)

$x_{i,k}$ is the k^th component of the spatial coordinate $x_{i}$ of i^th firefly.

For 2D movement the cartesian distance is given by

$$r_{i,j} = \sqrt {\left( {x_{i} - x_{j} } \right)^{2} + \left( {y_{i} - y_{j} } \right)^{2} }$$

(13)

The attractiveness $\beta$ of the firefly is determined by

$$\beta \leftarrow \beta_{0} e^{{ - \gamma r_{i,j} }}$$

(14)

Where $\beta_{0}$ is the attractiveness at $r_{i,j} = 0$ and $\gamma$ is the light absorption coefficient.

The movement of the firefly i is attracted by another more attractive firefly j is given by

$$x_{i} \leftarrow x_{i} + \beta_{0} e^{{ - \gamma r_{i,j} }} \left( {x_{i} - x_{j} } \right) + \alpha u_{i}$$

(15)

where the random walk parameter $u_{i} = \left( {rand1 - \frac{1}{2}} \right)$

If there are no fireflies brighter than a particular firefly i with maximum objective value then i will move randomly according to the

$$x_{{i^{max} }} \leftarrow x_{{i^{max} }} + \alpha u_{{i^{max} }}$$

(16)

In this case the random walk parameter $u_{{i^{max} }}$ is evaluated as $u_{{i^{max} }} = \left( {rand2 - \frac{1}{2}} \right)$ where $rand 1 \approx {\text{U}}\left( {0,1} \right)$ and $rand 1 \approx {\text{U}}\left( {0,1} \right)$ are random numbers obtained from uniform distribution. The brightness of the firefly is affected or determined by the objective function f(x).

2.3 Cuckoo Search Algorithm

Cuckoo search algorithm is a nature-inspired algorithm developed based on reproduction of cuckoo birds (Friedberg et al. 1979). While working with CS algorithms, it is important to associate potential solutions with cuckoo eggs. Cuckoos normally lay their fertilised eggs in other cuckoos’ nests with the hope of their off-springs being raised by proxy parents. When the host bird discover that the eggs in their nests do not belong to them, in those cases the foreign eggs are either thrown out of the nests or the whole nests are abandoned. The CS optimization algorithm is basically based on the following three rules:

• 1. Each cuckoo selects a nest randomly and lays one egg in it.

• 2. The best nests with high quality of eggs will be carried over to the next generation. For a fixed number of nests, a host bird can discover a foreign egg with a probability pa є [0,1]. In this case, the host cuckoo can either throw the egg away or abandon the nest and build a new one somewhere else.

• 3. The last rule can be approximated by replacing a fraction pa of the n host nests with new nests (with new random solutions).

The quality or fitness of a solution can simply be proportional to the value of the objective function. To select the optimal location or best solution, primarily the cuckoo search algorithm chooses the number of nest k N. As a result, it assigns dimension to each nest (N_i) randomly named as X₁ and X₂. When generating new solutions x_i (t + 1) for the ith cuckoo, the following Levy flight is performed. The Levy flights calculate step size (α) value to generate a new value of nest by adding the existing value of the nest (Sejdic et al. 2011).

$$Y_{i}^{t + 1} = Y_{i}^{t} + \alpha \oplus Levy \left( \lambda \right)$$

(17)

Where, $\alpha$ > 0 it should be related to the scale of the problem of interest. The formation $\oplus$ is way entry wise multiplications.

3 Proposed watermarking method

Figure 1 shows the block diagram of proposed watermark embedding method. Here the input image is separated into 8 × 8 nonoverlapping blocks. For each block FrKT is applied. The FrKT uses two fractional orders α&β in the range of 0.1–0.9. These fractional orders define the angle of rotation in the transform. The quality of the reconstructed image varies based on the fractional order selection. The fractional order selection is done by Firefly algorithm. The objective function of the firefly algorithm is mainly based on the PSNR and the normalized correlation coefficients value under various images processing attacks. Then the optimized value selected by the FA is used for the transformation of the input image. Also, for each block the watermarking locations are identified using Cuckoo search algorithm. The objective function of the Cuckoo search is based on the quality of the watermark i.e. based on the BER of the watermark when subjected to various attacks. The optimized location is identified and the secret data is embedded in the transformed coefficients using histogram shifting technique. Then the watermarked image is transmitted after taking inverse FrKT. The Fig. 2 shows the block diagram of proposed watermark extraction method. Here, the received watermarked image is separated in 8 × 8 nonoverlapping blocks. The fractional orders selected in the embedding process are shared secretly for the extraction of the watermark. Using the fractional order of the image the FrKT is applied. Then the watermark embedded locations are identified for the extraction of the watermarked data. After extraction the original image is reconstructed by taking inverse FrKT using the same fractional orders used for the transformation process.

Fig. 1

Block diagram of proposed watermark embedding method

Fig. 2

Block diagram of proposed watermark extraction method

3.1 Watermark embedding

Let the cover image of size M × N be denoted by C and the grayscale watermark logo image of size M1 × N1. The input image is separated into 8 × 8 nonoverlapping blocks

• 1. The watermark image W, scrambled and encrypted using the FrKT transformation

• 2. Apply n-level FrKT transform on the cover image. The FrKT uses two fractional orders α&β in the range of 0.1–0.9.

• 3. Select the fractional order by using Firefly algorithm which define the angle of rotation in the transform.

• 4. The optimized value selected by the FA is used for the transformation of the input image using Cuckoo search algorithm.

• 5. The optimized location is identified and the secret data is embedded in the transformed coefficients using histogram shifting technique. Then the watermarked image is transmitted after taking inverse FrKT.

3.2 Watermark extracting

Let the received watermarked image is denoted in 8 × 8 nonoverlapping blocks.

• 1. Apply inverse FrKT so that the fractional orders selected in the embedding process are shared secretly for the extraction of the watermark.

• 2. Then the watermark embedded locations are identified for the extraction of the watermarked data.

• 3. After extraction the original image is reconstructed by taking inverse FrKT using the same fractional orders used for the transformation process.

4 Experimental results and discussions

The simulations of the proposed algorithms are performed using MATLAB. The Peak Signal to Noise Ratio (PSNR), Structural SIMilarity (SSIM) Index, Normalized Correlation Coefficient (NCC) and Bit Error Rate (BER) are used for evaluation of the proposed algorithm. The SSIM, NCC and PSNR are the indicators of perceptual quality of the images. The BER is the indicator of robustness of the image. The higher the PSNR and SSIM, higher the perceptual quality.

Normalized correlation coefficient for two images can be defined as

$${{\varphi }}_{\text{xy}}^{,} \left( t \right) = \frac{{{{\varphi }}_{xy} \left( t \right)}}{{{{\varphi }}_{xx} \left( 0 \right){{\varphi }}_{yy} \left( 0 \right)}}$$

(18)

Where

$${{\varphi }}_{xy} \left( t \right) = \mathop \sum \limits_{{{\text{j}} = \hbox{max} \left( {0,{\text{k}}} \right)}}^{{\hbox{min} \left( {{\text{M}} - 1 + {\text{k}},{\text{N}} - 1} \right)}} x_{j - k} + y_{j}$$

$${\text{x}}_{\text{i}} ,{\text{ i }} = \, 0,{ 1}, \, \ldots ,{\text{ M}} - 1;{\text{y}}_{\text{j}} ,{\text{ j }} = \, 0,{ 1}, \, \ldots ,{\text{ N}} - 1;$$

k = − (M + 1),…, 0,…, (N − 1)

The normalized quantity ${{\varphi }}_{\text{xy}}^{,} \left( t \right)$ will vary between − 1 and 1. A value of ${{\varphi }}_{\text{xy}}^{,} \left( t \right)$ = 1 indicates that at the alignment t, the two time series have the exact same shape (the amplitudes may be different) while a value ${{\varphi }}_{\text{xy}}^{,} \left( t \right) = - 1$ indicates that they have the same shape except that they have the opposite signs. A value of ${{\varphi }}_{\text{xy}}^{,} \left( t \right)$ = 0 shows that they are completely uncorrelated. In practice when one applies this normalization to real discrete signals, one will find that a correlation coefficient greater than about 0.7 or 0.8 indicates a good match.

The similarity between the two images is measured by a the parameter known as the Structural SIMilarity (SSIM) index, expressed as

$$SSIM\left( {x,y} \right) = y\frac{{\left( {2\mu_{x} \mu_{y} + c_{1} } \right)\left( {2\sigma_{xy} + c_{2} } \right)}}{{\left( {\mu_{x}^{2} + \mu_{y}^{2} + c_{1} } \right)\left( {\sigma_{x}^{2} + \sigma_{y}^{2} + c_{2} } \right)}}$$

(19)

where$\mu_{x} - mean of x; \mu_{y } - mean of y \sigma_{xy} - covariance of xy$; $\sigma_{x}^{2} - variance of x$$\sigma_{y}^{2}$-variance of y;$c_{1} \& c_{2} - variables$

Bit error rate (BER) is the ratio of number of error bits received to the total number of bits transmitted.

$$BER = \frac{Numbere\, of\, errror\, bits\, recived}{Total\, number\, of\, bits\, transmitted}$$

(20)

The Peak Signal to Noise Ratio (PSNR) is define as the ratio of maximum possible pixel value of the image and the Mean Square Error (MSE).

$$PSNR = 20\log \left( {\frac{255}{{\sqrt {MSE} }}} \right)dB$$

(21)

where

$$MSE = \frac{1}{mn}\mathop \sum \limits_{i = 1}^{m} \mathop \sum \limits_{j = 1}^{n} \left( {I\left( {i,j} \right) - W\left( {i,j} \right)} \right)^{2}$$

(22)

$$W\left( {i,j} \right) - Watermarked\, image$$

$$I\left( {i,j} \right) - Original\, image$$

The higher PSNR and SSIM and lower BER indicates the better performance of the watermarking methods. Fig. 3 shows the sample host images used for watermark embedding.

Fig. 3

Sample images

The parameters are compared for FrKT, FrKT with firefly optimization, FrKT with cuckoo search optimization and FrKT with firefly and cuckoo search optimization algorithms with different attacks. The simulation results shows better performance in all the parameters for the watermarking using FRKT with firefly and cuckoo search optimization when compared to FrKT without any optimization, FrKT Firefly optimization and FrKT with cuckoo Search optimization. The FrKT + Firefly + Cuckoo search shows better performance because the firefly algorithm is used for sectional of fractional orders for FRKT which improves the imperceptibility and robustness of the host image against various attacks., the Firefly algorithm is used for the selection of watermark embedding locations which improves the robustness of the watermark i.e. the BER of the watermark image is minimized against various attacks. The time complexity is very less for the watermarking using FRKT with firefly and cuckoo search optimization.

Table 1 shows the comparison of normalized correlation coefficient between host image and the reconstructed image against various attacks. In this impulse noise, poisson noise and Gaussian noise models are compared to analyze the performance. These are the fundamental noise so the proposed system compared these noise models. Table 2 shows the comparison of Structural similarity index between host image and the reconstructed image against various attacks. Table 3 shows the comparison of PSNR between host image and the reconstructed image against various attacks. Table 4 shows the comparison of BER between embedded watermark and the extracted watermark. Table 5 shows the performance of different techniques applied in robust watermark image.

Table 1 Comparison of Normalized correlation coefficient between host image and the reconstructed image against various attacks

Table 2 Comparison of structural similarity index between host image and the reconstructed image against various attacks

Table 3 Comparison of PSNR between host image and the reconstructed image against various attacks

Table 4 Comparison of BER between embedded watermark and the extracted watermark against various attacks

Table 5 Performance of various techniques used in robust image watermarking

5 Conclusion

The problem in image watermarking using FrKT is the fractional order selection and the location identification. This problem was solved by the optimization algorithms to maintain the robustness and quality of the secret data. This paper proposes an optimization based image watermarking based on the fractional Krawtchouk transform. The selection of fractional order using Firefly algorithm and the watermark location identification using the cuckoo search major contribution of the proposed method. The experimental results show that the proposed has better PSNR, SSIM and NCC, also shows lower bit error rate. The proposed work has been compared with the same FrKT without any optimization, FrKT with Firefly and FrKT with Cuckoo search. The watermarked image is subjected to various attacks to check the robustness of the watermark. With different attacks the proposed method shows better, BER values of the extracted watermarked data and PSNR the reconstructed image which proves the robustness of the proposed algorithm. As a future work, to improve the imperceptibility and robustness, hybrid or new optimization algorithms applied for the fractional krawtchouk transform for image watermarking application.