The performance of the proposed method was evaluated using four grayscale medical images in the DICOM format, “Chest”, “T-spine”,” Hands”, and “Skull” of the size of 512 × 512 pixels as host images. A binary watermark of size 16 × 16 is generated from the host images to be embedded. The experiment is performed on a computer with an Intel Core i5, 2.6 GHz CPU, 4 GB memory, windows 10 and MATLAB 2016b (the MathWorks, Natick, MA, USA).

#### 5.2.2. Robustness Analysis

Robustness analysis is evaluated by calculating BER and NC. The BER is the number of bit errors divided by the total number of bits of the watermark. It is calculated to measure the similarity between the extracted attacked watermark and the original one. Lower BER expresses high robustness of watermarking against different attacks. The NC is used to indicate the similarity between original and extracted watermark, its value is between [1,−1]. When the NC= 1 the original and extracted watermarks are absolutely identical. When NC= 0 the original and extracted watermarks are divergent. When NC = −1 the original and extracted watermarks are completely anti-similar.

The watermark should be robust against attacks (the distortions due to attacks should remain minimal). In our experiments, we consider some geometric and non-geometric attacks. These attacks consist of median filtering, salt-and-pepper, average filter, Wiener filtering, cropping, contrast enhancement, scaling, Gaussian filtering, low pass filtering, histogram equalization, noise, rotation, sharpening, and translate attacks. Detailed results of BER and NC in an average for all images are summarized in

Table 3.

We can see from

Table 3 that the average values of NC between original and extracted watermarks are close to 1 except in one case, and the average values of BER between the original watermark and the extracted one are close to 0, which shows that the proposed scheme is robust against different processing attacks.

To demonstrate the effectiveness of the proposed method, comparisons with other works are presented in

Table 4 and

Table 5.

From

Table 4, we can see that our method has a better BER value for salt and pepper noise and noise attack (0.01) than the method of J. Dagadu et al. [

18], while the method of J. Dagadu et al. [

18] performs well than our method in the case of the cropping left top corner (25%) attack with a BER value equal to 0.

Comparing our method with that of Chauhan et al. [

40], one can see that our method is more robust in the case of sharpening, Gaussian filter, and contrast enhancement attacks. The results show that our method performs well for these three attacks as BER is close to 0. However, when we consider the histogram equalization attack, the method of Chauhan et al. [

40] has a better BER value than ours.

The method of S.A. Parah et al. [

21] is more robust than ours in the case of the cropping left top corner (25%), salt and pepper noise (0.01), sharpening, histogram equalization, Wiener filtering, and Gaussian noise (0.0001), but it is less robust than our method for the other attacks.

The method of Singh et al. [

22] has been tested for only sharpening, median filtering 2 × 2, Wiener filtering, Gaussian noise (0.01), and rotation (10°). The average BER values of sharpening, Wiener filtering, and Gaussian noise are equal to 0. Therefore, this method is very robust and performs well with these three attacks while in the case of median filtering 2 × 2 our method is more robust.

A comparison of the proposed technique with [

18,

21,

40,

41] for average NC values is shown in

Table 5. The comparison of the results with [

18] proves that the technique proposed by Joshua Dagadu et al. [

18] is more robust than ours in the case of cropping, salt and pepper noise, and noise attacks but in [

18] the other attacks were not tested. Comparing our results with [

40], our NC values between the original watermark and the extracted watermark in the case of sharpening and Gaussian filtering are better than the results of [

40].

By comparing our NC values with the NC values of [

21], one can see that in the case of average filtering and rotation (1°) our method is more robust than the method of [

21]. While in the case of the other attacks such as cropping left top corner, sharpening, histogram equalization, median filtering, rotation (5°) and rotation (10°), the method of S.A. Parah et al. [

21] is more robust than our method but there is no big difference. Comparing the results of our method with the method of S.Thakur et al. [

41] in terms of NC, we can see that the results obtained after applying sharpening, median filtering 2 × 2, rotation (1°), Gaussian low-pass filter, and image scaling ×1.1 attacks to the watermarked image are better with our method while in the case of attacks such as cropping, salt and pepper, histogram equalization, the method in [

41] is more robust than ours.

The experimental results of our method show that after all attacks the extracted watermarks are visually recognizable and all extracted watermarks are similar to the original watermark. The average NC value is equal to 0.9055 which is a good ratio, the BER value on average is equal to 0.0374, the SSIM on average is equal to 0.9823, and the PSNR on average is equal to 53.45 dB. Therefore, our method is robust against different attacks.