# A Watermarking Technique for Biomedical Images Using SMQT, Otsu, and Fuzzy C-Means
## 4 Experimental Results  
For evaluating the robustness and imperceptibility of the proposed model, we set up an experiment using a personal computer (PC) with the following configurations: AMD FX(tm)-8300 Eight-Core Processor, \(\sim\)3.3 GHz, 16384 MB RAM. As a simulation tool, we utilize MATLAB software version R2016a. To evaluate the proposed model, we used the Computer Vision Group, University of Granada (CVG UGR) Image dataset, where all of the images are \(256\times 256\) in size. As a watermark image, we used an image of size \(512\times 512\), which is presented in Figure 7b. To keep the uniform size of the input image and watermark image, we converted both images to \(2048\times 2048\). The watermark image  
Figure 5: (**a**) Image after Otsu threshold, (**b**) Image after fuzzy c-means cluster. Figure 6: (**a**) Structure of second level DWT, (**b**) Second level DWT of the image. was embedded into the MR host image. Figure 7 shows a sample of the host image, watermark, and watermarked image. After the embedding process, the watermarked image was passed through different attacks. Then, the watermark image was extracted from the watermarked image. The extraction process was performed by IDWT [23], which is the reverse process of DWT. After completion of the extraction process, the performance was evaluated by comparing the extracted watermark image and the original watermark image. The performance (in terms of robustness and imperceptibility) of our model was evaluated with the following parameters: PSNR, BER, CC, and SSIM, where PSNR was used for imperceptibility, and BER and CC were used for robustness. SSIM was used to measure the similarity between the image before and after extraction. PSNR measured the amount of distortion of the watermarked image. In general, the greater value of PSNR represents less distortion. \[PSNR=10\ \log_{10}\left(\frac{peakval^{2}}{\sqrt{\frac{\sum_{x=1}^{M}\sum_{y=1}^{N }\{W(x,y)-W^{\prime}(x,y)\}^{2}}{M\times N}}}\right). \tag{1}\]  
For Equations (1) and (2), \(M\) and \(N\) are the number of rows and columns, respectively, \(\mathrm{w}\) and \(\mathrm{w^{\prime}}\) represent the original image and extracted image, respectively, and \(\mathrm{x}\) and \(\mathrm{y}\) denote the pixel location. Length of the watermark image is expressed by L [24]. Pixel values can be positive or negative. Due to this fact, the summation is squared to avoid the issue where positive and negative values can cancel out each other. Then, the mean value is the square rooted for equality. On the other hand, peakval represents the maximum possible pixel value of the original image. When each pixel is denoted by 8 bits, the peakval will be 255. For instance, if two images are identical to each other, then the divisor value is zero, which is eventually converted to a PSNR value of infinity. BER evaluates the transmission accuracy where the value closer to zero illustrates a higher quality of image. \[BER\ =\ \frac{\sum_{x=1}^{M}\sum_{y=1}^{N}\left|w^{\prime}(x,y)-w(x,y)\right|}{ L}. \tag{2}\]  
The CC is calculated using Equation (3). A CC value near to one illustrates better robustness. \[\rho(A,B)=\frac{1}{N-1}\sum_{i=1}^{N}\left(\frac{\overline{A_{i}-\mu_{A}}}{ \sigma_{A}}\right)\left(\frac{B_{i}-\mu_{B}}{\sigma_{B}}\right). \tag{3}\]  
Figure 7: (a) Image after segmentation, (b) Watermark image and (c) Watermarked image. The SSIM measures the similarity between the original image and the extracted image. \[SSIM=\frac{\sum_{x=1}^{M}\sum_{y=1}^{N}\left[W(x,y)*W^{\prime}(x,y)\right]}{\sum_{ x=1}^{M}\sum_{y=1}^{N}W(x,y)^{2}*\sum_{x=1}^{M}\sum_{y=1}^{N}W^{\prime}(x,y)^{2}}. \tag{4}\]  
To evaluate the effectiveness, imperceptibility, and robustness, the result of the proposed model was compared with the other state-of-the-art watermarking models. Tables 1-4 present the evaluation results and comparison.