Interval type-2 fuzzy logic system based similarity evaluation for image steganography
Zubair Ashraf, Mukul Lata Roy, Pranab K.Muhuri, Q. M. Danish Lohani
RResearch article
Interval type-2 fuzzy logic system based similarity evaluation forimage steganography
Zubair Ashraf a , Mukul Lata Roy a , Pranab K. Muhuri a , * , Q.M.Danish Lohani b a Department of Computer Science, South Asian University, Akbar Bhavan, Chanakyapuri, New Delhi 110021, India b Department of Mathematics, South Asian University, Akbar Bhavan, Chanakyapuri, New Delhi 110021, India
A R T I C L E I N F O
Keywords:
Computer scienceData hidingInterval type-2 fuzzy logic systemSimilarity measureImage steganography
A B S T R A C T
Similarity measure, also called information measure, is a concept used to distinguish different objects. It has beenstudied from different contexts by employing mathematical, psychological, and fuzzy approaches. Image steg-anography is the art of hiding secret data into an image in such a way that it cannot be detected by an intruder. Inimage steganography, hiding secret data in the plain or non-edge regions of the image is signi fi cant due to thehigh similarity and redundancy of the pixels in their neighborhood. However, the similarity measure of theneighboring pixels, i.e., their proximity in color space, is perceptual rather than mathematical. Thus, this paperproposes an interval type-2 fuzzy logic system (IT2 FLS) to determine the similarity between the neighboringpixels by involving an instinctive human perception through a rule-based approach. The pixels of the imagehaving high similarity values, calculated using the proposed IT2 FLS similarity measure, are selected forembedding via the least signi fi cant bit (LSB) method. We term the proposed procedure of steganography as ‘ IT2FLS-LSB method ’ . Moreover, we have developed two more methods, namely, type-1 fuzzy logic system based leastsigni fi cant bits (T1FLS-LSB) and Euclidean distance based similarity measures for least signi fi cant bit (SM-LSB)steganographic methods. Experimental simulations were conducted for a collection of images and quality indexmetrics, such as PSNR (peak signal-to-noise ratio), UQI (universal quality index), and SSIM (structural similaritymeasure) are used. All the three steganographic methods are applied on dataset and the quality metrics arecalculated. The obtained stego images and results are shown and thoroughly compared to determine the ef fi cacyof the IT2 FLS-LSB method. We have also demonstrated the high payload capacity of our proposed method.Finally, we have done a comparative analysis of the proposed approach with the existing well-known stegano-graphic methods to show the effectiveness of our proposed steganographic method.
1. Introduction
Similarity describes the relationships between conceptual or percep-tual entities (Li and Liu, 2015). It has been evolved from different senses(Demirci, 2007), as given below:a)
Mathematical approach:
A number of mathematical distance functionshave been developed to calculate the similarity between pairs ofnumerical data, e.g., Hamming distance, Euclidean distance, and soon.b)
Psychological approach:
In terms of psychology, similarity has beenstudied by calculating the correlation between objects, humanperceptual resemblance, and rule-like or theory-like semanticrepresentations. c)
Fuzzy approach:
The similarity is measured through fuzzy logic bysimulating the human perception of similarity. It has the bene fi t ofbeing able to handle non-numerical quantities, degrees of similarity,and perceptual reasoning occurring due to human judgments.In the fi eld of image processing, similarity measures for image pixelsare typically evaluated using Euclidean distance in color space. However,Wuerger et al. (Wuerger et al., 1995) demonstrated that proximity incolor space – something that is perceptual rather than mathematical – cannot be evaluated using this distance measure. In other words, themeasure that we get using the Euclidean distance will not be adequate forjudging the similarity of image pixels (Demirci, 2007). Moreover, sincethe similarity of pixels involves an instinctive approach rather than anumerical one, it becomes necessary to consider human perception in its * Corresponding author. E-mail address: [email protected] (P.K. Muhuri).
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Heliyon https://doi.org/10.1016/j.heliyon.2020.e03771Received 7 December 2018; Received in revised form 26 March 2020; Accepted 7 April 20202405-8440/ © easurement. Based on the fuzzy sets (Zadeh, 1965), fuzzy logic (FL) hasconcerns with the degree of membership in a set. It differs from con-ventional logic and is an essential tool to handle the problems in whichimprecise information is associated with data. Prof. Zadeh himself wasthe fi rst to offer a way to judge similarity in terms of FL in (Zadeh, 1971),where he extended the theories of relations and equivalence to adapt forproblems where the parameters are not well-de fi ned.In the modeling of a real-life system, the incorporation of un-certainties plays an essential part. The uncertainties arise or exist becauseof lack of knowledge of system experts and incomplete informationregarding the system inputs. Such causes impreciseness and ambiguityand inconsistency in the modeling of the system. Another importantreason that causes the uncertainty in the system is the differences in theopinions of experts. In fuzzy sets or type-1 fuzzy sets (T1 FSs), the singleexpert opinion is incorporated with the membership function that sig-ni fi es the degree of uncertainty. However, due to the con fl icts in theopinions of various experts and various resources of uncertainty, T1 FSsare insuf fi cient for modeling those systems. To overcome this, Prof.Zadeh himself proposed the concept of type-2 fuzzy sets (T2 FSs) (Zadeh,1975). Further, Mendel et al. pioneered the interval type-2 fuzzy sets (IT2FSs) to reduce the burden of computation with general T2 FS (Mendeland Wu, 2010). Since then, a signi fi cant number of applications havebeen developed using IT2 FSs, such as machine learning (John et al.,2000), image processing (Castillo et al., 2007), pattern recognition(Melin and Castillo, 2013), reliability engineering (Ashraf et al., 2014,2015; Muhuri et al., 2017), real-time system (Muhuri et al., 2020a, b),similarity measures (Li et al., 2015), inventory system (Ashraf et al.,2017) etc.Steganography is a technique of protecting information in such a waythat it is not evident to unauthorized entities. Such a task has becomeincreasingly more critical as the popularity of the internet as a medium oftransmission increases. A steganographic method, therefore, aims to hideaway secret data as unobtrusively as possible; this is typically done by fi xing the data bits mentioned above deeply in another form of data.Both, the data to be embedded and the data needed for embedding, canbe of several kinds: text, image, audio or video (Cheddad et al., 2010;Johnson and Katzenbeisser, 2000; Petitcolas et al., 1999). Stegano-graphic methods consist of two parts: embedding and extraction.Embedding is the process of hiding the data in the pixels of the image,while extraction is the process of retrieving the hidden data from theimage. The image used for embedding is called the cover image, and theoutput image after embedding is called the stego image. The overallobjective of steganography – to hide the data so that it is indiscernible – can be achieved by ensuring a few things: the protected data inside thecover object must be transparently imperceptible; the method ofembedding itself must be able to withstand various attacks; the stegoobject should have a high embedding capacity for hiding data bits; andthe method used should be such that it can resist any damaging inter-ference (Jafari et al., 2013; Jero et al., 2016; Kanan and Nazeri, 2014; Liet al., 2010; Subhedar and Mankar, 2014; Wu and Tsai, 2003).In literature, there are several existing methods for steganography.These methods can be grouped based on their processing domain asfollows: (1) spatial domain and (2) transform domain. The differencebetween these two domain techniques is that, in the spatial domaintechniques, the embedding occurs directly in the pixels of the image,while in the transform domain techniques, the image is fi rst transformedinto the frequency domain and then the embedding is done. In imagesteganography, embedding in the plain or non-edge regions of the imagehas a signi fi cantly low effect on the human visual system. In other words,the pixel values in the plain (non-edge) regions of the image are similar,so they are good areas to embed. This is because the differences in theneighborhood pixel values of the plain region are very low (Melin et al.,2014). However, embedding in the textured region of the image is notadvisable, since a slight change in the pixel values of that region candistort the image. Additionally, the pixels, having integer values ranging between 0 and255, are redundant to its neighbors and the levels of differences betweenthem are almost negligible. Therefore, the corresponding differencesbased on numeric pixel values are not truly justi fi ed as similar or notsimilar. Thus, to perform image steganography in those regions, rule-based categorization is required to calculate the similarity value forany pair of pixels (Demirci, 2006). In other words, the perceptualreasoning of the similarity of the redundant pixels in the neighborhoodshould be assessed by human judgment (Hampton, 1998; Seaborn et al.,2005). Therefore, linguistic variables are the most appropriate for themodeling of perceptual similarity, and FSs have long been thebest-recognized tool to represent these linguistic values.One of the most fundamental issues in the linguistic variable repre-sentation by employing T1 FSs is the selection of the membership func-tion (MF) that interprets the uncertainty in information. Additionally,there exists a need to justify the crispness of the membership value of thefuzzy set, as it seems to contradict the core idea of “ fuzziness ” . The type-1membership function (T1 MF) is mostly recommended by the systemexpert to signify the degree of belongingness to a T1 FS. However, whenthere is more than one expert involved to provide the opinions regardingthe MFs, T1 FSs risk being unable to capture the different kinds of un-certainties. The above situation can be resolved by considering the unionof all the T1 MFs representing the various expert opinions. This causesthe generation of interval type-2 membership functions (IT2 MFs),leading to IT2 FSs (Ashraf et al., 2018a; Muhuri et al., 2017). Therefore,we propose that the linguistic terms be portrayed as IT2 FSs. The IT2 MFsof IT2 FSs are able to capture higher uncertainty compared to T1 FSs. InIT2 MFs, the Footprint of Uncertainty (FOU) depicts a degree of uncer-tainty caused by the differences of human judgment (or expert opinion)regarding the T1 MFs. The FOU offers more fl exibility in the adjustmentof the decisive parameters, i.e., the IT2 MFs of linguistic variables. As aresult, the FOU of IT2 MFs are bounded by lower and upper membershipfunctions representing the uncertainty of the linguistic terms . Hence, asigni fi cant improvement has been made in shifting from a type-1 fuzzylogic system (T1 FLS) to interval type-2 fuzzy logic system (IT2 FLS) bythe researchers in recent years. IT2 FLSs have been effectively applied inthe various applications of image processing systems such as classi fi ca-tion (Majeed et al., 2018; Rubio et al., 2017), fi ltering (Singh et al.,2018), segmentation (Dhar and Kundu, 2019; Zhao et al., 2019), andedge detection (Castillo et al., 2017; Gonzalez and Melin, 2017; Gonzalezet al., 2016; Martínez et al., 2019; Melin et al., 2014).In this paper, we propose a novel steganographic procedure using anIT2 FLS based similarity measure to measure the similarity between thepixels in a digital image. For doing so, a (3 (cid:1)
3) window of pixels isselected to fi nd the similarity of the central pixel to its neighboring pixels.We calculate the difference of all the three color components, i.e., red (R),green (G), and blue (B), which are assigned linguistic terms. The resultfrom the IT2 FLS is a similarity matrix which contains values in the in-terval [0, 1] indicating the level of similarity of each pixel of the image toits neighbors. This similarity matrix is used to select pixels to perform theleast signi fi cant bit (LSB) method for hiding the secret message. We havenot found any previous work of similarity measure or steganographywhich has used an IT2 FLS. Cover images, namely, Lena, Baboon, Jet,Barbara, Boat, Peppers, Earth, House, Sailboat and Splash, have beenchosen as the dataset, upon which the proposed steganographic methodwas applied to generate the corresponding stego images. Quality indexmetrics are used to assure the visual quality of the stego images. We havealso demonstrated the high payload capacity of our proposed method.The signi fi cant contributions of this paper are summarized as:1) A new algorithm based on IT2 FLS was developed that calculatesthe perceptual similarity of an image.2) Linguistic variables represent the color differences between pixelsas {Low, Medium, High} and degree of similarity as {Not Similar,Slightly Similar, Moderately Similar, Quite Similar, ExactlySimilar}. These variables are formulated as IT2 MFs in the IT2 FLS. Z. Ashraf et al. Heliyon (2020) e03771 ) IT2 FLS takes the IT2 MFs of the linguistic variables as inputs andprovides the output describing the similarity between a pair ofpixels.4) Mamdani inference engine using fuzzy-rules operates on the IT2MFs to achieve the similarity. Consequently, the type-reductionand defuzzi fi cation generates the similarity value of a pixel inan image.5) Similarity matrix depicting the similarity of each pixel in an imageis evaluated based on a set of fuzzy-rules.6) The embedding and extraction procedures of steganography areperformed on the image using the least signi fi cant bit (LSB)method.7) A pixel of an image is selected for embedding if the correspondingsimilarity value (in the similarity matrix) is greater than aparticular threshold value, which indicates the degree of similar-ity to its neighbors.8) To show the ef fi cacy of our proposed method, type-1 fuzzy logicsystem (T1 FLS) based and Euclidean distance based similaritymeasures were also implemented to perform steganography.9) The experimental simulations were performed on a dataset con-sisting of ten different cover images, and the corresponding stegoimages are obtained. The whole procedure with the three methods:(a) proposed, (b) T1 FLS based, (c) Euclidean distance based, wasrepeated for different numbers of bits ( k ¼ f ; ; ; g ) hidden inthe LSBs of the pixels and for different thresholds.10) A thorough comparison has been done by investigating theperceptual transparency and visual quality of the stego images.These were measured by using three quality index metrics: peaksignal-to-noise ratio (PSNR), structural similarity measure (SSIM),and universal quality index (UQI).The rest of the paper is organized as follows: in Section 2, a literaturesurvey is presented, detailing past works relevant to this paper. Mathe-matical de fi nitions of T2 FSs, IT2 FSs, and IT2 FLSs are explained inSection 3. Steps of the proposed IT2 FLS based similarity measure tech-nique and consequent steganographic method is elaborated in Section 4.Details of the experimental simulations and results are reported in Sec-tion 5, which also includes a comparative discussion. Finally, weconclude in Section 6.
2. Literature survey
Similarity measures played important role in many image processingapplications such as edge detection (Demirci, 2007), fi ltering (Elmaset al., 2013), retrieval (Varish et al., 2017), steganography (Karakis¸ et al.,2015) and so on. Kokare et al. (Kokare et al., 2003) compared Euclidean,Manhattan, Chebychev, Mahalanobis, Canberra, Bray-Curtis, Weight-ed-Mean-Variance, Squared Chord, and Squared Chi-Squared dis-tances/similarity function for measuring the texture retrieval fromimage. Puzicha et al. (Puzicha et al., 1997) presented a similarity mea-sure based on non-parametric statistical tests to compare the empiricaldistributions of Gabor coef fi cients for textures in images. Holden et al.(2000) evaluated different similarity measure functions for rigid bodyregistration of serial magnetic resonance brain scans. Two probabilisticsimilarity measures were proposed by Aksoy et al. (Aksoy and Haralick,2001) and compared with geometric similarity measures for imageretrieval. Wang and Simoncelli (2005) proposed the similarity measurethat works in the wavelet frequency domain of image to measure thetranslation, scaling and rotation of images.A similarity assessment technique using fuzzy logic (FL) for judgmentof properties was proposed by Santini et al. (Santini and Jain, 1999) tofeature contrast in images. To distinguish meaningful objects in images,Chien et al. (Chien and Cheng, 2002) developed an image segmentationscheme that was based on fuzzy color similarity measure. A comparativestudy of crisp and fuzzy logic based similarity measures was done by Jainet al. (1995) to fi nd the similar or distinct textures of the images. To handle possible distortions in fi ngerprints of a non-linear nature, Chenet al. (Chen et al., 2006) developed a normalized fuzzy similaritymeasure.A fuzzy diffusion technique was proposed by Elmas et al. (2013) usingthe FL to obtain the similarity between pixels and generate a similarimage used as a heat diffusion coef fi cient. Demirci et al. (Demirci, 2007)used similarity in edge detection in images. The authors used the pixelwindow to get the similarity value of the central pixel to its neighboringpixels and created a similarity matrix to detect edges in the image byusing the threshold value. Wu et al. (Wu and Tsai, 2003) proposed asteganographic method in which secret data was embedded in thosepixels where the pixel-value differences of two consecutive pixels werelow. An adjacent pixel difference based steganographic technique waspresented by Li et al. (Y.-C. Li et al., 2010) in which the histogram ofadjacent pixels was employed to increase the capacity of embedding.Karakis et al. (Karakis¸ et al., 2015) proposed rule-based FL for imagesteganographic scheme to hide patient data in medical images.
3. Preliminaries
This section discusses the basics of interval type-2 fuzzy logic systems(IT2 FLS). In order to discuss an IT2 FLS, we must fi rst de fi ne type-2 fuzzysets (T2 FSs) and interval type-2 fuzzy sets (IT2 FSs). A T2 FS ~ A , is distinguished by a membership function μ ~ A ð x ; u Þ ,de fi ned over x and u , where x is an element taken from universe ofdiscourse X and u represents its primary membership function, respec-tively (R. John, 1998). Thus, the T2 FS ~ A can be expressed as Eq. (1): ~ A ¼ fð x ; u Þ ; μ ~ A ð x ; u Þj8 x X ; u J x ⊆ ½ ; (cid:3)g (1)If the secondary membership function μ ~ A ð x ; u Þ ¼
1, then a T2 FSbecomes an IT2 FS (Mendel and Wu, 2010) as de fi ned in Eq. (2). ~ A ¼ fð x ; u Þ ; μ ~ A ð x ; u Þ ¼ j8 x X ; u J x ⊆ ½ ; (cid:3)g (2)The graphical representation of an IT2 FS can be seen in Figure 1. InFigure 1, lower membership function (LMF) and upper membershipfunction (UMF) are denoted by μ ~ A ð x Þ and μ ~ A ð x Þ , repectively. The areathat lies between the LMF and UMF is known as the Footprint of Un-certainty (FOU), given be Eq. (3). FOU ¼ ½ μ ~ A ð x Þ ; μ ~ A ð x Þ(cid:3) (3)
An IT2 FLS consists of fuzzi fi cation, rule-based inference engine, type-reduction and defuzzi fi cation procedures. A typical IT2 FLS can be seenin diagram form in Figure 2 (Mendel and Wu, 2010). The fuzzi fi cationtakes input as a crisp value and consequently generates an IT2 FS using Figure 1.
Interval type-2 fuzzy set.
Z. Ashraf et al. Heliyon (2020) e03771 nterval type-2 membership functions (IT2 MF). By applying certain if-then rules, the inference engine combines all the input IT2 FSs and givesan output IT2 FS. The type-reduction process takes the output IT2 FS andreduces it to a T1 FS. After that, the type-reduced set is put throughdefuzzi fi cation to achieve a fi nal crisp output.
4. Proposed steganographic method
The proposed steganography method named ‘ IT2 FLS based similaritymeasure for image steganography ’ is depicted in the form of a fl ow di-agram in Figure 3. The detailed explanation of each step involved in theproposed method is discussed in the following sub-sections. An image is comprised of pixels that are used to hide the secret in-formation. A particular pixel is chosen for hiding if the value of similaritymeasure between the neighboring pixels is high. Figure 4 shows a typicalwindow of size ð (cid:1) Þ of the image that illustrates the neighboring pixels ð P ; P ; … ; P Þ of the central pixel P . Therefore, pixel P is selected forembedding if its similarity to its neighboring pixels is high.In the IT2 FLS based similarity measure procedure, a ð (cid:1) Þ windowcorresponding to the each pixel in the cover image of size ( H (cid:1) W (cid:1)
3) istaken to calculate the similarity value of the central pixel. Algorithm 1gives the step-by-step procedure of IT2 FLS based similarity measure. Itconsists of fi ve main steps: (i) calculating gray level differences of pixels,(ii) interval type-2 fuzzi fi cation, (iii) rule-based inference engine, (iv)type-reduction and defuzzi fi cation, and (v) calculation of the similaritymatrix. A detailed discussion on these steps is given in this sub-section.The output of Algorithm-1 is a similarity matrix ð S M Þ of size ( H (cid:1) W ),whose values lie within the interval ½ ; (cid:3) . Each element belonging to thesimilarity matrix gives the similarity of the central pixel to its neigh-boring pixels in the window. The pixels have three color components, Red ( R ), Blue ( B ), and Green( G ), with their corresponding gray-level intensities, L R , L B and L G ,respectively as given in Figure 5. The gray-level differences f δ R ; δ G ; δ B g between two pixels P i and P j corresponding to each of the color com-ponents, f R ; G ; B g , are calculated as follows: δ R ¼ (cid:1)(cid:1) L R ; i (cid:4) L R ; j (cid:1)(cid:1) (4) δ G ¼ (cid:1)(cid:1) L G ; i (cid:4) L G ; j (cid:1)(cid:1) (5) δ B ¼ (cid:1)(cid:1) L B ; i (cid:4) L B ; j (cid:1)(cid:1) (6) fi cation In this step, the gray-level differences of each pair of pixels in all threecolor components f δ R ; δ G ; δ B g are assigned interval type-2 member-ship functions (IT2 MFs). These IT2 MFs represent the correspondinglinguistic terms: Low, Medium and High. There are several IT2 MFs suchas triangular, trapezoidal, Gaussian, etc., available for handling theselinguistic terms. We have used the triangular MFs to model them, becauseeach of the linguistic values are provided in the form of intervals andtheir left and right ends are speci fi c to the experts (Muhuri et al., 2017).The interval type-2 triangular membership function (IT2 TMF) is given inEq. (7) which is de fi ned using the LMF and the UMF given as Eqs. (8) and(9) respectively. Crisp Input
Input IT2 FS
Fuzzification Rules Inference engine Defuzzification Type reduction Crisp Output
Type Reduced Set Output IT2 FS
Figure 2.
Interval type-2 fuzzy logic system.
Cover image Interval type-2 fuzzy logic system Similarity relation matrix Least significant bits embedding Secret Message Stego image Indicator matrix Number of bits to embed ( ) Similarity matrix (S M ) Figure 3.
Proposed LSB image steganographic method using IT2 FLS basedsimilarity measure.
Figure 4.
Neighboring pixels.
Algorithm 1.
IT2 FLS based similarity measure
Input : Gray level image of size ( H (cid:1) W (cid:1) Output : Similarity matrix ( S M )1: For each H For each W
3: Neighboring pixels of window (3 (cid:1)
For each window5: Color differences ( δ R ; δ G ; δ B ) // Eqs. (4)-(6)
6: Assign IT2 MFs // Fuzzi fi cation
7: Inference-engine // Using Rules
8: Type-Reduction // EKM Algorithm
9: Defuzzi fi cation10: End
11: Calculate S a and S M End
End
Z. Ashraf et al. Heliyon (2020) e03771 ~ A i ð x Þ ¼ (cid:3) μ ~ A i ð x Þ ; μ ~ A i ð x Þ (cid:4) ; x X (7)where μ ~ A i ð x ; α ; β ; γ Þ ¼ ; x (cid:5) α i x (cid:4) α i β i (cid:4) α i ; α i (cid:5) x (cid:5) β i γ i (cid:4) x γ i (cid:4) β i ; β i (cid:5) x (cid:5) γ i ; x (cid:6) γ i (8)and μ ~ A i (cid:5) x ; α ; β ; γ (cid:6) ¼ ; x (cid:5) α i x (cid:4) α i β i (cid:4) α i ; α i (cid:5) x (cid:5) β i γ i (cid:4) x γ i (cid:4) β i ; β i (cid:5) x (cid:5) γ i ; x (cid:6) γ i (9)In Eqs. (8) and (9), α ; α ; β ; γ ; γ are fi ve input parameters where β α ; γ (cid:3) and β α ; γ (cid:3) are used in the LMF μ ~ A i ð x ; α ; β ; γ Þ and the UMF μ ~ A i ð x ; α ; β ; γ Þ , respectively. When the gray-level differences β i ¼ f δ R ; δ G ; δ B g fall in the interval ½ α ; γ (cid:3) ¼ f½ ; (cid:3) ; ½ ; (cid:3) ; ½ ; (cid:3)g , then thelinguistic terms Low ( L ), Medium ( M ) and High ( H ) will be assigned tothem, respectively. Figure 6 gives a typical example of IT2 TMFs repre-senting the linguistic terms L ; M and H . In the inference engine, the generated IT2 MFs assigned to each gray-level difference of the three color components of a pair of pixels arecombined according to certain rules. As a result, a new IT2 MF describingthe similarity between each pair of pixels is generated by assigning thelinguistic terms such as NS - Not Similar, SS - Slightly Similar, MS -Moderately Similar, QS - Quite Similar, and ES - Exactly Similar. Figure 7shows the IT2 MFs with respect to each linguistic term to describe thesimilarity.The fuzzy-rules are given in Table 1 (Elmas et al., 2013). In Table 1,there are twenty seven fuzzy-rules listed to elaborate all the possible combinations of the input and output IT2 FSs. The inference engine mapsthe input difference IT2 FS to output similarity IT2 FS by combiningrules. Let us consider that x X ; … ; x n X n are n inputs and y Y isone output. Then, the i th rule given in the form of: R i : IF x is ~ A ; x is ~ A … x n is ~ A n Then y is ~ B can be written as Eq. (10) R l : ¼ ~ A l → ~ B l l ¼ ; … ; M (10)where, ~ A l ¼ ~ A l (cid:1) … (cid:1) ~ A lP and R l is the fuzzy relation described by IT2MF μ ~ A l → ~ B l ð x ; y Þ as Eq. (11) μ ~ A l → ~ B l ð x ; y Þ ¼ μ ~ A l ð x Þ ⨅ … ⨅ μ ~ A lp (cid:5) x p (cid:6) ⨅ μ ~ B l ð y Þ¼ h ⨅ pi ¼ μ ~ A li ð x i Þ i ⨅ μ ~ B l ð y Þ (11)In the IT2 FLS, we used product t -norm to perform the intersectionoperation ( ⨅ ), such that the result of combining the input and antecedentare contained in the fi ring set given as Eq. (12): F l (cid:5) x (cid:6) ¼ (cid:3) f l (cid:5) x (cid:6) ; f l (cid:5) x (cid:6)(cid:4) (12)where we use Eq. (13) to compute. f l (cid:5) x (cid:6) ¼ h ⨅ pi ¼ μ ~ A li ð x i Þ i ⨅ μ ~ B l ð y Þ (13)Eq. (14) gives the centroid of the IT2 FS. f l (cid:5) x (cid:6) ¼ h ⨅ pi ¼ μ ~ A li ð x i Þ i ⨅ μ ~ B l ð y Þ (14) fi cation The output IT2 FS from the inference engine is transformed into T1 FSand crisp value through the process of type-reduction and defuzzi fi ca-tion, respectively. The method used here is known as the EnhancedKarnik-Mendel (EKM) algorithm for type-reduction. The complete pro-cedure of EKM algorithm (Mendel and Wu, 2010) is explained in Algo-rithm 2. We have included the salient points of the Algorithms 2 (a-b) asbelow:The centroid C ~ A ð x Þ is the collection of all embedding T1 FSs in the IT2FS ~ A as given in Eq. (15). C ~ A ð x Þ ¼ f c l ð ~ A Þ ; … ; c r ð ~ A Þg ¼ ½ c l ð ~ A Þ ; c r ð ~ A Þ(cid:3) (15)
Figure 5.
Gray levels of pixels.
Figure 6.
IT2 TMFs of the color component differences δ R ; δ G ; δ B representingthe linguistic terms.
Figure 7.
Typical IT2 TMFs of the similarities for the representation of thelinguistic terms.
Z. Ashraf et al. Heliyon (2020) e03771 e apply the EKM algorithm to calculate the left and right endpointsof the interval, c l and c r respectively. The equations to calculate them aregiven below as Eq. (16) and Eq. (17): c l ¼ min θ i μ ; μ (cid:3) X Ni ¼ x i θ i , X Ni ¼ θ i ! (16) c r ¼ max θ i μ ; μ (cid:3) X Ni ¼ x i θ i , X Ni ¼ θ i ! (17) Table 1.
Fuzzy rules (Ashraf et al., 2018b).
Rule
Antecedent Consequent R : If μ δ R is L , μ δ G is L , μ δ B is L then μ S is ESR : If μ δ R is L , μ δ G is L , μ δ B is M then μ S is ESR : If μ δ R is L , μ δ G is L , μ δ B is H then μ S is QSR : If μ δ R is L , μ δ G is M , μ δ B is L then μ S is ESR : If μ δ R is L , μ δ G is M ; μ δ B is M then μ S is QSR : If μ δ R is L , μ δ G is M , μ δ B is H then μ S is MSR : If μ δ R is L , μ δ G is H , μ δ B is L then μ S is QSR : If μ δ R is L , μ δ G is H , μ δ B is M then μ S is MSR : If μ δ R is L , μ δ G is H , μ δ B is H then μ S is SSR : If μ δ R is M , μ δ G is L , μ δ B is L then μ S is ESR : If μ δ R is M , μ δ G is L , μ δ B is M then μ S is QSR : If μ δ R is M , μ δ G is L , μ δ B is H then μ S is MSR : If μ δ R is M , μ δ G is M , μ δ B is L then μ S is QSR : If μ δ R is M , μ δ G is M , μ δ B is M then μ S is MSR : If μ δ R is M , μ δ G is M , μ δ B is H then μ S is SSR : If μ δ R is M , μ δ G is H , μ δ B is L then μ S is MSR : If μ δ R is M , μ δ G is H , μ δ B is M then μ S is SSR : If μ δ R is M , μ δ G is H , μ δ B is H then μ S is NSR : If μ δ R is H , μ δ G is L , μ δ B is L then μ S is QSR : If μ δ R is H , μ δ G is L , μ δ B is M then μ S is MSR : If μ δ R is H , μ δ G is L , μ δ B is H then μ S is SSR : If μ δ R is H , μ δ G is M , μ δ B is L then μ S is MSR : If μ δ R is H , μ δ G is M , μ δ B is M then μ S is SSR : If μ δ R is H , μ δ G is M , μ δ B is H then μ S is NSR : If μ δ R is H , μ δ G is H , μ δ B is L then μ S is SSR : If μ δ R is H , μ δ G is H , μ δ B is M then μ S is NSR : If μ δ R is H , μ δ G is H , μ δ B is H then μ S is NS Algorithm 2(a).
Calculation for c l ð L Þ Set k ¼ ½ N = : (cid:3) (the nearest integer to N = :
4) and compute:1. a ¼ P ki ¼ x i μ ~ A ð x i Þ þ P ki ¼ k þ x i μ ~ A ð x i Þ b ¼ P ki ¼ μ ~ A ð x i Þ þ P ki ¼ k þ μ ~ A ð x i Þ
2. Compute c ¼ a = b
3. Find k ; N (cid:4) (cid:3) such that x k (cid:5) c x k þ
4. Check if k ¼ k : If yes, stop and set c ¼ c l ð L Þ ; and k ¼ L : If no, go to step 5.Compute s ¼ sign ð k (cid:4) k Þ and5. a ¼ a þ s P max ð k ; k Þ i ¼ min ð k ; k Þþ x i ½ μ ~ A ð x i Þ (cid:4) μ ~ A ð x i Þ(cid:3) . b ¼ b þ s P max ð k ; k Þ i ¼ min ð k ; k Þþ ½ μ ~ A ð x i Þ (cid:4) μ ~ A ð x i Þ(cid:3)
6. Compute c ð k Þ ¼ a = b
7. Set c ¼ c ð k Þ ; a ¼ a ; b ¼ b and go to Step 2. Algorithm 2(b).
Calculation for c r ð R Þ Set k ¼ ½ N = : (cid:3) (the nearest integer to N = :
7) and compute:1. a ¼ P ki ¼ x i μ ~ A ð x i Þ þ P ki ¼ k þ x i μ ~ A ð x i Þ b ¼ P ki ¼ μ ~ A ð x i Þ þ P ki ¼ k þ μ ~ A ð x i Þ
2. Compute c ¼ a = b
3. Find k ; N (cid:4) (cid:3) such that x k (cid:5) c x k þ
4. Check if k ¼ k : If yes, stop and set c ¼ c r ð R Þ ; and k ¼ R : If no, go to step 5.Compute s ¼ sign ð k (cid:4) k Þ and5. a ¼ a (cid:4) s P max ð k ; k Þ i ¼ min ð k ; k Þþ x i ½ μ ~ A ð x i Þ (cid:4) μ ~ A ð x i Þ(cid:3) . b ¼ b (cid:4) s P max ð k ; k Þ i ¼ min ð k ; k Þþ ½ μ ~ A ð x i Þ (cid:4) μ ~ A ð x i Þ(cid:3)
6. Compute c ð k Þ ¼ a = b
7. Set c ¼ c ð k Þ ; a ¼ a ; b ¼ b and go to Step 2. Figure 8.
Similarity network (Demirci, 2007). Z. Ashraf et al. Heliyon (2020) e03771 urther, defuzzi fi cation produces a crisp output using the centroidmethod. This procedure of defuzzi fi cation uses the left centroid ð c l Þ andthe right centroid ð c r Þ (Mendel and Wu, 2010). The fi nal crisp output ( y d )is then obtained by taking a simple mean of c l and c r , as given below inEq. (18): y d ¼ c l þ c r (18) The IT2 FLS thus calculates the similarity value of every pair of pixels inthe ð (cid:1) Þ window, as may be seen in Figure 8 of the similarity network.The fi nal result will be a similarity relation matrix that can be shown as S m ; n ¼ S ; S ; S ; S ; ⋯ S ; ⋯ S ; ⋮ ⋮ S ; S ; ⋱ ⋮ … S ; (19)In Eq. (19), S m ; n represents a similarity relation matrix, with all theelements belonging to the interval ½ ; (cid:3) . Therefore, we can calculate thesimilarity of every i th pixel in the ð (cid:1) Þ window to its neighboring pixelsas follows: S i ¼ X n ¼ S i ; n for i n (20)To calculate the similarity of the central pixel in the window, we useEq. (20) as follows: S a ¼ X n ¼ S i : (21)In Eq. (21), S a is the similarity of a single pixel in the image to itsimmediate surrounding neighbor pixels. Hence, the whole process of IT2FLS and calculation of S a is iterated for every pixel in the image. The fi nalresult of this will be a similarity matrix ( S M ) that holds the similarityvalue S a corresponding to each pixel of the cover image. In order to choose which pixel is used for embedding, we employ asimilarity threshold ( Th ) to generate an indicator matrix ( I ), given as follows: I i ; j ¼ (cid:7) ; S M i ; j (cid:6) Th ; S M i ; j < Th (22)where Th is the similarity threshold. The indicator matrix is a matrix ofsize ð H (cid:1) W Þ whose values are either 1, if the corresponding value of thesimilarity matrix S M is higher than the threshold Th , or 0, if it less than Th . In the embedding procedure of the proposed algorithm, we used theleast signi fi cant bit (LSB) embedding procedure to hide the message. Inthe LSB method, the decimal pixel value is converted into the binary bitstream, and the last k bits are then replaced with the bits of the secretmessage (Ker, 2005; Yang et al., 2008). The output of the LSB embeddingprocedure is a new bit stream which is then converted back into decimal.The pixel of the cover image is selected for embedding if its value ishigher than the threshold. The whole procedure is repeated for everypixel of the cover image. The fi nal output of the IT2 FLS-LSB stegano-graphic method is the stego image. Algorithm 3 gives the completeembedding procedure. In the extracting procedure, the indicator matrix ( I ) is used to fi nd thelocation of the embedding pixels of the stego image. For every embed-ding pixel, the last k bits from its LSB are extracted and combined. Theoutput of this procedure is the hidden secret message. Algorithm 4 givesthe complete extracting procedure.
5. Experimental simulations and comparative analysis
The experimental simulations are performed to show the integrity ofthe proposed IT2 FLS based similarity measure in image steganography.The experimental simulations are conducted in MATLAB and run onIntel(R) Xeon(R) processor with 16 GB of RAM (3.40 GHz, Windows 7, 64bits). We have used a set of well-known images as dataset (Cheddad et al.,2010; Johnson and Katzenbeisser, 2000; Petitcolas et al., 1999). Theperceptual transparency of the proposed algorithm is measured usingdifferent quality metrics. Since, the least signi fi cant bits (LSB) procedureis used to perform embedding (as discuss in Section 4.4), we have termedthe proposed IT2 FLS based similarity measure for LSB embedding as IT2FLS-LSB steganography scheme.Moreover, we have considered two more methods for evaluating thesimilarity of a pixel in an image as: (i) type-1 fuzzy logic system (T1 FLS)based similarity measure (Karakis¸ et al., 2015) and (ii) Euclidean dis-tance based similarity measure (Demirci, 2007). Utilizing these twoprocedures for LSB embedding, we have develop and implemented two Algorithm 3.
Embedding procedure
Input : Cover image ( C Þ , indicator matrix ( I ), Number of bits ( k ), Secret message ( m ). Output : Stego image1:
For each color level2:
For each H // height of cover image3: For each W // width of cover image4: If I ¼¼
15: Convert pixel value into binary bit stream6: Replace k LSB bits with the m bits8: Convert changed binary into new pixel value9: Assign new pixel value to stego10: End
End
End
End
Algorithm 4.
Extracting procedure
Input : Stego image, Number of bits ( k ) Output : Secret message ( m ).1: For each color level2:
For each H // height of cover image3: For each W // width of cover image4: If I ¼¼
15: Convert pixel value into binary bit stream6: Extract k LSB bits from binary pixel value7: Combine all the extracted bits into m End End
End
End © Elsevier science. Used with permission from the publisher.
Z. Ashraf et al. Heliyon (2020) e03771 ore methods, referred as, T1 FLS based similarity measures for leastsigni fi cant bits (T1FLS-LSB) steganographic method and Euclidean dis-tance based similarity measures for least signi fi cant bit (SM-LSB) steg-anographic method.In T1 FLS-LSB method, the similarity relation matrix (as in Eq. (19)) iscalculated by the T1 FLS where the MFs are the TI MFs. Mamdani-rulesare used in the inference engine and centroid approach is applied tocalculate the defuzzify similarity value of a ð (cid:1) Þ window. The obtainedsimilarity relation matrix is used to evaluate the similarity of a pixel (as inEq. (21)) and, hence the indicator matrix (Eq. (22)) is generated via thethreshold value. Finally, the embedding procedure, using Algorithm 3, isapplied to obtain the stego image. For the SM-LSB method the distancebetween any two pixels is calculated by Euclidean nom as D i ; j ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð δ R þ δ G þ δ B Þ q , where δ R , δ G and δ B are three color componentscalculated by Eqs. (4), (5), and (6). Using the distance matrix, the simi-larity relation matrix (as in Eq. (19)) is calculated and the similarity of apixel is obtained. Thus, the LSB embedding procedure is applied usingindicator matrix to to obtain the stego image. Both of these approachesare used to perform steganography and the obtained results arecompared with our proposed IT2 FLS-LSB scheme.In the following subsections, we have discussed about the imagedataset which was taken to perform the experimental simulations and thequality matrices. All the three steganographic methods are applied onthese images and the metrics are calculated. The obtained stego imagesand the results are shown and thoroughly compared. Finally, we havedone a comparative analysis of the proposed approach with some existingand well-known steganographic methods. The performances of all three steganographic procedures evaluated byusing ten standard gray-level cover images, namely Lena, Baboon, Jet, Bar-bara, Boat, Peppers, Earth from space, House, Sailboat, and Splash, each of size ð (cid:1) (cid:1) Þ pixels, shown in Figure 9 (a)-(j). We chose the Lena image ofsize ð (cid:1) (cid:1) Þ pixels shown in Figure 10, as the secret message.To measure the perceptual transparency of the proposed stegano-graphic procedure, we have used three quality matrices, namely, PSNR,SSIM, and UQI (Subhedar and Mankar, 2014). The mathematicalformulae for calculating the aforementioned measures are given below:The PSNR compares the cover and stego images to test the effect ofembedding, de fi ned as follows: PSNR ¼
10 log (cid:9) (cid:1)
MSE (cid:10) (23)In Eq. (23), MSE is the mean square error and it is calculated as fol-lows using Eq. (24):
MSE ¼ MN X M (cid:4) i ¼ X N (cid:4) j ¼ (cid:5) f (cid:5) x i ; y j (cid:6) (cid:4) g (cid:5) x i ; y j (cid:6)(cid:6) (24)where M and N are the dimensions of the images; f ð x ; y Þ and g ð x ; y Þ arethe cover and the stego images respectively. The higher the values ofPSNR, better the quality of the stego image. The lowermost PSNR valuefor an acceptable image steganographic method is 32 dB (Cheddad et al.,2010).SSIM measures the similarity between the cover and the stego images.However, UQI measures the distortion between the cover and the stegoimages. They are de fi ned as:If x ¼ f x i j i ¼ ; :::; N g is considered to be the original image and y ¼ f y i j i ¼ ; :::; N g to be the stego image, then SSIM and the UQI arede fi ned as Eq. (25) and Eq. (26), respectively: Figure 9.
Cover images: (a) Lena, (b) Baboon, (c) Jet, (d) Barbara, (e) Boat, (f) Peppers, (g) Earth from space, (h) House, (i) Sailboat, (j) Splash.
Figure 10.
Secret Message: (Gray-scale Lena image of size ð (cid:1) (cid:1) Þ pixels). Z. Ashraf et al. Heliyon (2020) e03771 SIM ð x ; y Þ ¼ (cid:5) μ x μ y þ C (cid:6)(cid:5) σ xy þ C (cid:6)(cid:5) μ x þ μ y þ C (cid:6)(cid:5) σ x þ σ y þ C (cid:6) (25) UQI ð x ; y Þ ¼ σ xy : μ x : μ y (cid:5) σ x þ σ y (cid:6)(cid:3) μ x þ μ y (cid:4) (26)where, C ; C ; C are the constants; μ x and μ y are the mean, σ x and σ y are the variance of x and y , and σ xy is the covariance between x and y .The values of the SSIM and UQI measures lie within the range ½ ; (cid:3) , with0 indicating poor quality, while 1 indicating excellent quality. For better study of the proposed steganographic method, we tookdifferent number of bits ( k ) to embed into the LSBs of the selected pixels.Across all cover images, the number of bits are k ¼ f ; ; ; g . Thismeans, after calculating the similarity matrix using the IT2 FLS basedsimilarity measure and converting the secret message into a bit stream,we embed k bits of the secret message into the k LSBs of the selectedpixels. The same process is replicated for T1 FLS-LSB and SM-LSB pro-cedures for the number of bits.In order to test the ef fi cacy of the proposed steganographic methodover T1 FLS-LSB and SM-LSB, we have chosen different thresholds ( Th ).As discussed previously, these thresholds are applied to the similaritymatrices ( S M ) to obtain the indicator matrices ( I ). The matrix I indicatesthe location of the pixels selected for embedding. For each Th , the matrix I is also embedded in the cover image along with the secret message tohelp in the extraction process. Since, S M contains values in the range ½ ; (cid:3) , we have arbitrarily chosen four different threshold values, Th ¼f : ; : ; : ; : g . The interpretation of S M > Th is that thesimilarity of that pixel is high, depicting a smooth or plain region of theimage. Hence, that pixel is used for embedding. We perform theembedding procedure for each value of k , i.e., k ¼ f ; ; ; g corre-sponding to all Th ¼ f : ; : ; : ; : g values using IT2 FLS-LSB,T1 FLS-LSB and SM-LSB steganographic methods and the stego imagesare generated.The stego images for Lena, Baboon, Jet, Barbara, Boat, Peppers, Earthfrom space, House, Sailboat, and Splash cover images generated through the IT2 FLS-LSB for k ¼ Th ¼ :
80 are depicted in Figure 11 (a)-(j).For k ¼ f ; ; ; g and Th ¼ :
80, the quality metrics, i.e. PSNR, SSIMand UQI, comparing the visual transparency of the IT2 FLS-LSB, T1 FLS-LSB and SM-LSB steganographic methods for all the cover and stegoimages are shown in Table 2. For k ¼ Th ¼ :
80, stego images forall cover images produced by the T1 FLS-LSB and SM-LSB steganographicmethods are shown in Figures 12 (a)-(j) and 13 (a)-(j), respectively. Fromthe Figures 11, 12, and 13, it can be observed that there are no muchdifferences among the cover and stego images with respect to all threemethods. A comparative plots, for k ¼ f ; ; ; g and Th ¼ :
80, of thequality metrics, i.e. PSNR, SSIM and UQI, comparing the visual trans-parency between the IT2 FLS-LSB, T1 FLS-LSB and SM-LSB methods forall the cover and stego images are depicted in Figures 14, 15 and 16,respectively. From Figs. 14 (a) – (d), we can observe that the PSNR valuesfor the proposed IT2 FLS-LSB method are signi fi cantly high in compare toT1 FLS-LSB and SM-LSB methods for all images. Moreover, the number ofbits for hiding the secret data within the pixels of images increases thevalue of PSNR deceases for all images. Though, the minimum values ofPSNR are moderate high (approximately (cid:6) – (d) and 16 (a)-(d),we can see that SSIM and UQI values for the proposed IT2 FLS-LSBmethod are better in compare to T1 FLS-LSB and SM-LSB methods foralmost all images. From the Table 2 and the Figures 14, 15, and 16, weobserve that the achieved values of PSNR, SSIM and UQI are relativelyhigher for our proposed method compared to the other two. Thus we cansee that the proposed IT2 FLS-LSB for steganography outperforms bothT1 FLS-LSB and SM-LSB methods.Results of PSNR, SSIM and UQI values corresponding to k ¼f ; ; ; g and Th ¼ : Th ¼ :
77 and Th ¼ :
81 for Lena, Baboon,Jet, Barbara, Boat, Peppers, Earth from space, House, Sailboat, andSplash cover images with IT2 FLS-LSB, T1 FLS-LSB and SM-LSB methodsare given in Appendix A. The comparative plots for k ¼ f ; ; ; g and Th ¼ : Th ¼ :
77 and Th ¼ :
81 corresponding to each qualitymetrics, i.e. PSNR, SSIM and UQI, comparing the visual transparencybetween the IT2 FLS-LSB, T1 FLS-LSB and SM-LSB methods for Lena,Baboon, Jet, Barbara, Boat, Peppers, Earth from space, House, Sailboat,and Splash images are depicted in Appendix B.
Figure 11.
Stego images obtained via IT2 FLS-LSB scheme: (a) Lena, (b) Baboon, (c) Jet, (d) Barbara, (e) Boat, (f) Peppers, (g) Earth from space, (h) House, (i)Sailboat, (j) Splash.
Z. Ashraf et al. Heliyon (2020) e03771 able 2. Quality matrices of SM-LSB, T1 FLS-LSB and proposed method for k ¼ f ; ; ; g and Th ¼ : SM-LSB T1 FLS-LSB Proposed SM-LSB T1 FLS -LSB Proposed SM-LSB T1 FLS-LSB Proposed SM-LSB T1 FLS-LSB ProposedLena PSNR 51.2541 51.4005 51.6526 45.3338 45.4070 45.6694 39.1425 39.1561 39.4178 33.3102 33.5585 34.8785SSIM 0.9982 0.9964 0.9964 0.9937 0.9862 0.9863 0.9769 0.9486 0.9492 0.9276 0.8435 0.8451UQI 0.9999 0.9999 0.9999 0.9997 0.9995 0.9995 0.9987 0.9980 0.9981 0.9962 0.9926 0.9929Baboon PSNR 51.3801 52.1170 54.6426 45.3972 46.1367 48.6754 39.1431 39.8766 42.4214 33.3663 34.1130 36.6535SSIM 0.9987 0.9988 0.9989 0.9951 0.9953 0.9959 0.9814 0.9819 0.9844 0.9382 0.9400 0.9488UQI 0.9999 0.9999 0.9999 0.9995 0.9996 0.9998 0.9980 0.9982 0.9990 0.9924 0.9935 0.9962Jet PSNR 51.2764 51.4121 51.8790 45.2662 45.4127 45.8726 39.1003 39.2380 39.7138 33.2529 33.3899 33.8472SSIM 0.9955 0.9955 0.9956 0.9831 0.9831 0.9833 0.9404 0.9405 0.9413 0.8292 0.8292 0.8317UQI 0.9999 0.9999 0.9999 0.9995 0.9995 0.9996 0.9982 0.9982 0.9984 0.9933 0.9934 0.9940Barbara PSNR 51.3543 51.8192 52.9861 45.3624 45.8211 47.0036 39.1199 39.5811 40.7677 33.2855 33.7452 34.8956SSIM 0.9973 0.9973 0.9974 0.9896 0.9896 0.9901 0.9614 0.9617 0.9635 0.8830 0.8843 0.8902UQI 0.9999 0.9999 0.9999 0.9997 0.9997 0.9998 0.9988 0.9989 0.9991 0.9953 0.9958 0.9967Boat PSNR 51.2474 51.4245 52.1463 45.2171 45.3846 46.1282 39.0089 39.1952 39.9227 33.1830 33.3701 34.0806SSIM 0.9963 0.9963 0.9964 0.9858 0.9858 0.9862 0.9489 0.9492 0.9504 0.8529 0.8538 0.8578UQI 0.9999 0.9999 0.9999 0.9996 0.9997 0.9997 0.9986 0.9987 0.9989 0.9948 0.9950 0.9957Peppers PSNR 51.2661 51.3590 51.5642 45.1845 45.2665 45.4745 38.9167 38.9900 39.1970 33.0803 33.1559 33.3626SSIM 0.9961 0.9962 0.9962 0.9832 0.9833 0.9834 0.9408 0.9409 0.9415 0.8310 0.8312 0.8330UQI 0.9999 0.9999 0.9999 0.9996 0.9996 0.9996 0.9984 0.9985 0.9985 0.9941 0.9942 0.9944Earth PSNR 51.1830 51.3538 51.6727 45.1997 45.3733 45.7018 38.9573 39.1242 39.4430 33.2247 33.4066 33.7280SSIM 0.9973 0.9973 0.9973 0.9895 0.9896 0.9898 0.9606 0.9608 0.9614 0.8746 0.8757 0.8780UQI 0.9998 0.9998 0.9998 0.9993 0.9993 0.9993 0.9971 0.9972 0.9974 0.9893 0.9897 0.9904House PSNR 51.2704 51.6899 52.2922 45.3007 45.7154 46.3142 39.0425 39.4617 40.0706 33.2468 33.6588 34.2613SSIM 0.9968 0.9968 0.9969 0.9883 0.9885 0.9887 0.9580 0.9585 0.9594 0.8725 0.8744 0.8777UQI 0.9999 0.9999 0.9999 0.9997 0.9997 0.9997 0.9987 0.9988 0.9989 0.9950 0.9954 0.9959Sailboat PSNR 51.3154 51.6514 52.2377 45.3185 45.6644 46.2410 39.0950 39.4323 40.0174 33.3280 33.6613 34.2622SSIM 0.9973 0.9974 0.9974 0.9898 0.9901 0.9902 0.9624 0.9629 0.9638 0.8835 0.8852 0.8884UQI 0.9999 0.9999 0.9999 0.9997 0.9997 0.9998 0.9989 0.9990 0.9991 0.9959 0.9962 0.9966Splash PSNR 51.2545 51.2761 51.3652 45.1960 45.2269 45.3184 38.9479 38.9736 39.0675 33.1143 33.1340 33.2288SSIM 0.9941 0.9941 0.9942 0.9756 0.9756 0.9758 0.9176 0.9176 0.9186 0.7794 0.7790 0.7803UQI 0.9999 0.9999 0.9999 0.9997 0.9997 0.9997 0.9987 0.9987 0.9987 0.9949 0.9950 0.9951
Figure 12.
Stego images obtained via T1 FLS-LSB scheme: (a) Lena, (b) Baboon, (c) Jet, (d) Barbara, (e) Boat, (f) Peppers, (g) Earth from space, (h) House, (i) Sailboat,(j) Splash.
Z. Ashraf et al. Heliyon (2020) e03771 he embedding capacity can be de fi ned as the amount of secret datathat is hidden into an image. It is the ratio of number of bits hidden to thetotal number of bits. The embedding capacities (in percentage (%)) of theproposed IT2 FLS-LSB, T1 FLS-LSB and SM-LSB steganographic methodsare presented in Table 3. In Table 3, the percentage embedding capacitiesfor k ¼ f ; ; ; g corresponding to each threshold Th ¼ f : ; : ; : ; : g of the ten images used as the dataset are given. We havetaken the average percentage embedding capacities across the ten images for each value of k since, for each threshold, there are different amount ofbits that are selected for embedding. In this section, we have compiled the similarity, differences, and someessential points of our proposed steganography scheme with other statesof the art schemes. We have gone through many research works done in
Figure 13.
Stego images obtained via SM-LSB method: (a) Lena, (b) Baboon, (c) Jet, (d) Barbara, (e) Boat, (f) Peppers, (g) Earth from space, (h) House, (i) Sailboat,(j) Splash. (a) (b) (c) (d) P S NR Figure 14.
Comparison of PSNR of SM-LSB, T1 FLS-LSB and proposed methods for Th ¼ :
80: (a) k ¼
1, (b) k ¼
2, (c) k ¼
3, (d) k ¼ (a) (b) (c) (d) Figure 15.
Comparison of SSIM of SM-LSB, T1 FLS-LSB and proposed methods for Th ¼ :
80: (a) k ¼
1, (b) k ¼
2, (c) k ¼
3, (d) k ¼ Z. Ashraf et al. Heliyon (2020) e03771 he past few decades on the image steganography. To the best of ourknowledge, the IT2 FLS based steganographic method using the IT2 fuzzyrules and least signi fi cant bits (LSBs) has never appeared in the literature.For comparison, we have considered several research works that performthe embedding in the LSB domain of the cover image. Table 4 summariesthe signi fi cant features of these prominent steganographic schemes(Amirtharajan and Balaguru Rayappan, 2012; Chan and Cheng, 2004;Sajasi and Eftekhari Moghadam, 2015; Wang et al., 2001), including theSM-LSB (Demirci, 2007), T1 FLS-LSB (Karakis¸ et al., 2015) and proposedIT 2FLS-LSB.In Table 4, we have compared the hiding data size (bits), payloadcapacity (%) and PSNR (dB) for Lena, Baboon and Jet images that havebeen used in the different steganography schemes. A Genetic Algorithm(GA) based LSB steganographic scheme was developed by Wang et al. (2001). A secret data of 65,536 bits were embedded in cover images ofsize (512 (cid:1) þ LSB methods were inferior for all the Lena, Baboon andJet images. Chan et al. (Chan and Cheng, 2004) proposed a stegano-graphic scheme that performs the embedding by using the LSB methodand utilized an optimal pixels adjustment procedure (OPAP) to reducethe distortion between the cover image and the stego image. The pro-posed approach was an extension of the simple LSB method (Wang et al.,2001) that could embed about 1,31, 608 bits and attain comparativelyhigher PSNR values ( ffi :
72) for the three images.Amirtharajan et al. (Amirtharajan and Balaguru Rayappan, 2012)proposed adaptive LSB embedding approach. They considered coverimages of size ð (cid:1) Þ , which was divided into blocks of (4 (cid:1) (a) (b) (c) (d) Figure 16.
Comparison of UQI of SM-LSB, T1 FLS-LSB and proposed methods for Th ¼ :
80: (a) k ¼
1, (b) k ¼
2, (c) k ¼
3, (d) k ¼ Table 3.
Embedding capacity in percentage (%). Th SM-LSB T1 FLS-LSB IT2 FLS-LSB k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ k ¼ Table 4.
Comparative overview of the state of the art steganographic schemes.
Cover Studies Method Hiding data size (bits) Payload Capacity (%) PSNR (DB)Lena Wang et al. (Wang et al., 2001) GA þ LSB. 65,536 25.00 38.72Chan et al. (Chan and Cheng, 2004) OPAP þ LSB. 1,31,072 50.00 40.72Amritharajan et al. (Amirtharajan and Balaguru Rayappan, 2012) Chaotic approach þ LSB. 65,536 25.00 38.66Sajasi et al. (Sajasi and Eftekhari Moghadam, 2015) NVF and Chaotic þ LSB. 81,920 31.25 44.48Demirci (Demirci, 2007) SM þ LSB 1,96,608 49.54 45.33Karakis (Karakis¸ et al., 2015) T1FLS þ LSB. 1,96,608 49.05 45.41
Proposed scheme IT2 FLS þ LSB. þ LSB. 65,536 0.25 38.73Chan et al. (Chan and Cheng, 2004) OPAP þ LSB. 1,31,072 50.00 40.72Amritharajan et al. (Amirtharajan and Balaguru Rayappan, 2012) Chaotic approach þ LSB. 65,536 25.00 38.67Sajasi et al. (Sajasi and Eftekhari Moghadam, 2015) NVF and Chaotic þ LSB. 81,920 31.25 47.66Demirci (Demirci, 2007) SM þ LSB 1,96,608 49.54 45.40Karakis (Karakis¸ et al., 2015) T1FLS þ LSB. 1,96,608 49.05 46.14
Proposed scheme IT2 FLS þ LSB. þ LSB. 65,536 0.25 38.72Chan et al. (Chan and Cheng, 2004) OPAP þ LSB. 1,31,072 50.00 40.72Amritharajan et al. (Amirtharajan and Balaguru Rayappan, 2012) Chaotic approach þ LSB. 65,536 25.00 38.68Demirci (Demirci, 2007) SM þ LSB 1,96,608 49.54 45.27Karakis (Karakis¸ et al., 2015) T1FLS þ LSB. 1,96,608 49.05 45.41
Proposed scheme IT2 FLS þ LSB.
Z. Ashraf et al. Heliyon (2020) e03771 ¼ fi cant bit (SM þ LSB) method(Demirci, 2007), type-1 fuzzy logic based least signi fi cant bit (T1 FLS þ LSB) method (Karakis¸ et al., 2015) and the proposed interval type-1 fuzzylogic based least signi fi cant bit (IT2 FLS þ LSB) method, the secret datasize that are embedded in the cover images are much higher in com-parison to others. The PSNR values for all three images are highest for theproposed IT2 FLS þ LSB method in contrast to other approaches.
6. Conclusion
This work proposed an interval type-2 fuzzy logic system (IT2 FLS)based least signi fi cant bit (LSB) steganographic method, termed as IT2FLS-LSB method, to perform steganography in high similarity valuedpixels of an image. The IT2 FLS assigns interval type-2 membershipfunctions (IT2 MFs) to color differences between pixels, expressed aslinguistic variables such as low, medium and high. The idea of going intohigher order fuzzy logic is to achieve better models of uncertainty and inthis case they can be applied in image steganographic systems. Based on aset of interval type-2 fuzzy rules, the Mamdani inference engine operateson the IT2 MFs to produce the interval type-2 fuzzy similarity betweenthe pixels in the images. To show the ef fi cacy of our proposed method, wehave also developed type-1 fuzzy logic system (T1 FLS)-LSB and simi-larity measure (SM)-LSB steganographic methods which evaluate pixelsimilarity through TI FLS and Euclidean distance, respectively. Based ona set of threshold values, which discriminate the similarity values of apixel as high for these three steganographic methods, depicting a smoothor plain region of the image, we have embedded for different numbers ofbits ð k ¼ f ; ; ; gÞ in the LSBs of the pixels. The experiments are per-formed on a dataset consisting of ten cover images, namely Lena, Baboon,Jet, Barbara, Boat, Peppers, Earth from space, House, Sailboat, andSplash, and the corresponding stego images are obtained. The perceptualtransparency and visual quality of the stego images were measured byusing three quality index metrics: peak signal-to-noise ratio (PSNR),structural similarity measure (SSIM), and universal quality index (UQI).We observed that the proposed IT2 FLS-LSB steganographic methodoutperforms both T1 FLS-LSB and SM-LSB methods, as the achievedvalues of PSNR, SSIM and UQI are relatively higher while maintainingcomparable payload capacities.Our future direction will be the extension of fuzzy bounded variationapproach for the other higher order fuzzy sets like general type-2 fuzzysets, interval type-2 fuzzy sets, and interval-valued-intuitionistic fuzzysets, etc. Further, we will perform steganalysis on the proposed steg-anographic approach through the imperceptibility and robustnessagainst different attacks. Moreover, instead of performing embedding inthe spatial domain of the image, we may use transform domain tech-niques such as discrete wavelet transform, integer wavelet transform, andso on. Declarations
Author contribution statement
Zubair Ashraf: Conceived and designed the experiments; Performedthe experiments; Analyzed and interpreted the data; Contributed mate-rials, analysis tools or data.Mukul Lata Roy: Conceived and designed the experiments; Performedthe experiments; Analyzed and interpreted the data; Wrote the paper.Pranab K. Muhuri: Conceived and designed the experiments;Analyzed and interpreted the data; Contributed materials, analysis toolsor data. Q. M. Danish Lohani: Conceived and designed the experiments;Analyzed and interpreted the data.
Funding statement
This research did not receive any speci fi c grant from funding agenciesin the public, commercial, or not-for-pro fi t sectors. Competing interest statement
The authors declare no con fl ict of interest. Additional information
Supplementary content related to this article has been publishedonline at https://doi.org/10.1016/j.heliyon.2020.e03771.
Acknowledgements
The authors would like to express their sincere thanks to the re-viewers and the editors of the journal for their helpful comments andsuggestions that helped in the improvement of the manuscript. Authorsgratefully acknowledge the infrastructural and research facilities pro-vided by the South Asian University, New Delhi through the Computa-tional Intelligence lab of the Department of Computer Science whiledesigning the experiments and conducting investigation.
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