A fuzzy logic based contrast and edge sensitive digital image watermarking technique
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Abstract
In this paper, a fuzzy logic based digital image watermarking technique is proposed. The contrast and edge values of the host image are analyzed by the fuzzy inference system (FIS) against fuzzy rules and then the FIS evaluates the output which is proposed as the watermarking strength (α) of the image. By varying the contrast and edge values of the host image, the fuzzy logic adjusts the watermarking strength to keep the system performance unchanged which helps to improve imperceptibility of the watermarked image. DWT is performed to divide the cover image and watermark image into subbands and the maximum entropy region among the subbands is calculated for selecting the embedding location because it is less affected by the image processing attacks. Hence, it makes the scheme more robust than other fuzzy based methods. In the extraction phase, the watermark is recovered from the subband where it was embedded. The effectiveness of the algorithm is measured in terms of performance parameters like peak signal to noise ratio and normalized correlation. Experimental results indicate that the fuzzy logic adjusts the watermarking strength to keep the performance parameters unchanged irrespective of the contrast and edge values of the host image.
Keywords
Contrast and edge sensitivity Entropy Fuzzy logic Membership functions Normalized correlation (NC) Peak signal to noise ratio (PSNR)1 Introduction
In this modern age, digital contents are suffering from lack of security due to easier access to the internet and the availability of intelligent software. This kind of act threats the transmission of digital data over the communication channels [1]. Hence, some data hiding techniques are introduced to reduce this. They can be divided into two classes: steganography and digital watermarking. [2] Digital image watermarking is a process of hiding information without compromising the host image. Digital watermarking is more effective and secure than the steganography in terms of data ownership.
Two important properties of digital image watermarking are imperceptibility and robustness. Imperceptibility can be defined in terms of visual degradation of the host image [3]. If the host image is less visually degraded, the algorithm is more imperceptible. Again, robustness can be defined in terms of image processing attacks. If the host image can tolerate the image processing attacks and the watermark image is approximately reconstructed from the watermarked image, the algorithm is said to be robust. All efficient watermarking schemes need to increase these properties.
According to the necessity of host image for the watermark extraction process, digital image watermarking can be divided into blind, semiblind and nonblind schemes. Blind schemes do not require host image but semiblind and nonblind schemes require host image or secret keys to detect watermark image [4]. Digital image watermarking can also be classified on the basis of the embedding domain into two classes. They are spatial domain techniques and transform domain techniques. Spatial domain techniques directly modify the image pixel bits and these modifications are used in watermark reconstruction [5]. The scheme proposed by Abraham et al. [5] uses two different masks in embedding for improving the performance parameters of the scheme. It works efficiently as the watermark bits are scattered over a broad region.
Transform domainbased methods contain transformations like DWT, DCT or DFT. Watermark is then embedded by changing the domain coefficients [6]. Singh et al. [6] proposed a method based on 3 level DWT and student tdistribution. This method gives the benefits of student tdistributions compared to the normal and logistic distributions that are applied to the DWT coefficients. Lande et al. [7] proposed an adaptive method using human visual system (HVS) based fuzzy logic for masking and the model was implemented practically. The main turning point of the method is the use of fuzzy logic to determine the gain factor on the basis of HVS.
The method proposed by Jamali et al. [8] manipulates fuzzy logic for calculating embedding strength in DCT domain. This approach shows good PSNR and NC values due to the adaptive use of fuzzy mapping. Coumou et al. [9] proposed a scheme using fuzzy logic for determining the invisible embedding features. But this method has the limitation of optimization of the fuzzy system and robustness.
The scheme proposed by Arun Kumar et al. [10] utilizes a genetic algorithm for determining the locations of watermark embedding and fuzzy logic for optimization. It shows good performance in HH subband compared to the other subbands. Huang et al. [11] introduced a method using bacterial foraging instead of genetic algorithm along with fuzzy logic. It shows improved performance when compared with the schemes using the genetic algorithm as the method utilizes the continuous tuning of weighting elements.
Agarwal et al. [12] proposed a method utilizing hybridized fuzzy logic and backpropagation neural network for embedding the binary watermark. The performance is good for using block threshold values of HVS properties and fuzzy optimization techniques. Jagadeesh et al. [13] use fuzzy logic for HVS properties along with DCT for blind watermarking. It shows better results in terms of PSNR and NC compared to similar types of algorithms. The method proposed by Sridevi et al. [14] determines embedding strength based on fuzzy rules and also incorporates the features of DCT and SVD. Although the performance of the system is satisfactory, it has the limitation of multiple level DWT divisions and pointing out the perfect embedding location.
In the proposed method, HVS properties like the contrast and edge values are used by the fuzzy inference system to effectively calculate the embedding strength (α) and then the maximum entropy is calculated to determine the suitable embedding location. The scopes and objectives of the proposed work are information hiding, ownership authentication and copyright protection in the fields of image processing. The rest of the paper is organized as follows: Sect. 2 describes the importance of contrast and edge sensitivity. Then, watermark embedding algorithm of the proposed method is discussed in details in Sect. 3. The watermark extraction process of the proposed method is explained in Sect. 4. Performance parameters are included in Sect. 5. Then Sect. 6 includes the results and findings. Finally, Sect. 7 concludes the analysis of the results for the proposed method.
2 Importance of contrast and edge sensitivity
The sensitivity of human eye to an image depends on different properties. These are Brightness sensitivity, Frequency sensitivity, Edge Sensitivity and Contrast Sensitivity [1]. In our proposed scheme we use contrast and edge sensitivity as fuzzy inputs and their importance in watermarking are discussed below:
A. Contrast sensitivity
B. Edge sensitivity
Human eyes do not recognize the nonuniform changes in the image. Thus embedding in higher edges of the image is more advantageous than in the lower edges [8].
3 Proposed watermark embedding algorithm

Step 1 Host image and the watermark image are decomposed into four subbands using DWT.
 Step 2 The entropy of each subband is calculated to determine the maximum entropy location. This location is selected for watermark embedding. Maximum entropy area is the location with a maximum degree of information variation and embedding in this region do not change the original information very much. The entropy of an image subband is calculated by the following formula [15]:where L is the entropy of the subband and R_{i} is the intensity of pixel i.$${\text{L}} = \sum {{\text{R}}_{\text{i}} \,\log \left( {{\text{R}}_{\text{i}} } \right)}$$(2)
 Step 3 For calculating the embedding strength, first the contrast and edge values of the host image are calculated using the following functions:$${\text{Ic}} = {\text{f}}\left( {\text{Im} } \right)$$(3)where Im is the host image. Ic and Ie are the contrast and edge values which are the functions of Im. The contrast and edge values are varied for evaluating system performance later.$${\text{Ie}} = {\text{g}}\left( {\text{Im} } \right)$$(4)
 Step 4 Contrast and edge values determined in the previous step, work as input to the fuzzy system. A Mamdani type FIS with centroid defuzzification is used in the process as shown in Fig. 2. It gives proposed watermarking strength (α) as output based on the inputs. So, the embedding strength can be expressed by the following function:$$\upalpha = {\text{f}}\,({\text{Ic}}\,\&\, {\text{Ie}})$$(5)
 1.
If contrast is high or low, embedding strength is high.
 2.
If contrast is medium, embedding strength is low.
 3.
If edge is high, embedding strength is high.
 4.
If edge is low, embedding strength is low.
 5.
If edge is medium, embedding strength is medium.

Step 5 Watermark is embedded in the maximum entropy subband of the host image with the maximum entropy subband of the watermark image according to the embedding strength output of FIS.

Step 6 Perform IDWT to get the watermarked image.
4 Proposed watermark extraction algorithm

Step 1 Apply DWT to the watermarked image. The image will be decomposed into four subbands.
 Step 2 Locate the subband in which the watermark was embedded. Subtract the original subband from it and divide it with the embedding strength to determine the watermark pixels. It can be expressed by the following formula:where We is the located subband in which the watermark was embedded, Wo is the original subband prior to watermarking and Rw is the recovered watermark pixel.$$Rw = \frac{We  Wo}{\alpha }$$(6)

Step 3 Apply IDWT to the recovered subband which contains the recovered pixels to reconstruct the watermark image.
5 Performance parameters
Performance of the watermarking scheme is determined on the basis of following parameters:
A. PSNR
B. NC
6 Results
 1.
Without contrast and edge sensitivity:
Performance of the proposed scheme without contrast and edge sensitivity
Host image  PSNR (dB)  NC 

Lena  48.2257  0.9949 
Peppers  47.3105  0.9949 
Cameraman  37.2036  0.9949 
 2.
With contrast and edge sensitivity:
Simulated α, PSNR and NC for Lena image
Contrast  Edge  α  PSNR (dB)  NC 

39,790  0.4451  0.691  50.5210  0.9949 
40,991  0.4588  0.718  50.1881  0.9949 
46,247  0.5373  0.747  49.8441  0.9949 
Simulated α, PSNR and NC for peppers image
Contrast  Edge  α  PSNR (dB)  NC 

39,903  0.5294  0.739  49.9377  0.9949 
47,937  0.4667  0.730  50.0441  0.9949 
48,323  0.5353  0.747  49.8441  0.9949 
Simulated α, PSNR and NC for cameraman image
Contrast  Edge  α  PSNR (dB)  NC 

10,425  0.6510  0.799  38.2376  0.9832 
11,493  0.3451  0.693  39.4738  0.9832 
11,550  0.4039  0.691  39.4989  0.9832 
 3.
Comparison of the proposed method with other methods
Comparison of different fuzzy based watermarking methods for no attack on image
Performance of various watermarking schemes against median filtering attack
Performance of various watermarking schemes against noise attack
Performance of various watermarking schemes against cropping attack
Performance of various watermarking schemes against rotation attack
Performance analysis of the proposed method for the cameraman image
Type of attack  PSNR (dB)  NC 

No attack  39.0701  0.9832 
Median Filter  27.7508  0.9815 
Salt and pepper noise  33.8520  0.9796 
Cropping  7.4520  0.9796 
Rotation  19.9866  0.9784 
7 Conclusion
In this paper, a fuzzy rulebased watermarking algorithm is discussed which eliminates the varying performance of the algorithm with varying contrasts and edges. The fuzzy logic effectively determines the watermarking strength based on contrast and edge sensitivity. Performance of the system is better than the conventional fuzzy based watermarking algorithms as it shows a higher degree of robustness and imperceptibility. Use of maximum entropy region also gives the advantage to hide the information based on entropy which is unpredictable in the extraction phase of an unknown receiver. Based on these advantages, this method can be a potential solution for the drawbacks of existing fuzzy based watermarking algorithms and can be applied in the related fields. In Future, more fuzzy rules on other properties of HVS can be added for smooth and precise operation of the algorithm. Besides, other fuzzy logic based systems apart from Mamdani type can also be investigated. The sophisticated physical implementation equipments which will handle the embedding and extraction process can also be experimented in future.
Notes
Funding
This work was financially supported by Chittagong University of Engineering & Technology.
Compliance with ethical standards
Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper. The images are used with no conflict of copyright statements.
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