Linear weighted watermarking using normalized principal components

DWT–SVD watermarking techniques, available in the literature, use LL subbands for WM embedding. ‘S’ matrices are derived for the LL subbands of the host and the WM and further used for watermark embedding. The steps involved in DWT–SVD watermarking are elaborated below and shown in Fig. 1.where ‘\(\alpha \)’ is a scaling factor

Apply inverse SVD (ISVD) to get WM embedded Singular value matrix

Principal component analysis fusion is one of the fusion techniques performed in spatial domain. PCA is a dimension reduction technique [23] which represents a whole data set with very few principal components [24] and hence the principal components derived from the covariance properties of the source data sets deliver meaningful weights for a linear weighted spatial domain fusion [25]. This spatial domain fusion is often degraded by spectral distortions [26, 27] and thus frequency domain fusion is often preferred. Evaluation of normalized principal components is shown in Fig. 2 and the steps are given below

Consider two source images \(I_{1}(x,y)\) and \(I_{2}(x,y)\) with the spatial resolution of \(M \times M\). Principal component evaluation is given bywhere E—Eigen vectors D—Diagonal matrix with Eigen values

Normalized principal components \(P_{1}\) and \(P_{2}\) are evaluated by

If \(D_{11}>\) \(D_{22}\) Else

PCA fusion is given by

A host image H(x, y) and a WM image WM(x,y) with the size of \(M \times M\) are considered for WM embedding. DWT is applied to the images with ‘Haar’ wavelet.

Performance analysis is accomplished by the three matrices PSNR in dB, SSIM and CC. PSNR is inversely proportional to mean square error which finds out the quantitative difference between the two images. Hence, higher value of PSNR [28] denotes better performance. Mean SSIM is the quality assessment metric that exhibits much better consistency with the qualitative visual presentation based on luminance subtraction, contrast and structural characteristics [29]. CC is the metric which finds out the correlation between two images by evaluating the difference between the mean and gray value of the individual pixels. This is another quantitative metric that demonstrates the closeness of one image with the reference image. SSIM and CC values close to one demonstrate superior watermarking process.

Six host images are experimented with a WM with the same spatial resolution. DWT with ‘Haar’ wavelet is applied to the host and the WM images. PSNR values of embedding and extraction are used to select the appropriate wavelet for DWT decomposition and given in Table 3. Mexican hat and bior2.2 wavelets deliver better embedding but result in poor extraction process. Both embedding and extraction are better with Haar wavelet and hence Haar wavelet is selected for decomposition. Bior1.1 wavelet also delivers similar results to that of Haar wavelet and can be alternatively used in embedding and extraction. Principal components are derived from the S matrices of ‘HH’ subbands of the host and the WM images. The amount of WM embedding into the host decides PSNR, SSIM and CC. For comparative analysis, DWT–SVD and RDWT–SVD watermarking methods are evaluated and given in Table 4. Upon analyzing the metrics, it is revealed that the proposed method is able to deliver better PSNR, SSIM and CC values compared to other two methods for all the host images. Higher PSNR value demonstrates better imperceptibility for the observer. Watermarks are also not visible, since the embedding is carried in transformed domain. This is illustrated by the watermarked host images in Fig. 6. SSIM and CC values of close to one demonstrate high similarity between the host and the watermarked images. SSIM reveals the qualitative performance of the proposed method by analyzing the structural characteristics and contrast of the watermarked image with respect to the original image.

For ensuring authentication, copyright and ownership, extraction of both the images needs to be experimented. By carrying out reverse process, as stated in “Watermark and host extraction” section, host and WM images can be extracted and analyzed for performance evaluation. After extraction, both the host and WM images should be similar to the original host and the WM images. This is can be objectively analyzed by evaluating PSNR, SSIM and CC between the extracted and the original images. Upon analyzing Tables 5 and 6, it is observed that the proposed method is able to extract the host and the WM images with higher PSNR compared to other methods. SSIM and CC values of one denote that the extracted images are similar to that of the original images.

The proposed algorithm is also experimented on Caltech background dataset [30] with 451 images and the metrics for embedding and extraction are given in Table 7. Mean value of the metrics are evaluated to all the images of background dataset. This dataset comprises of low and high contrast images of varying illumination. Upon analyzing the metrics, it is evident that the proposed method delivers better embedding and extraction for the images of different contrast and background.

DWT–SVD and RDWT–SVD use LL subbands for WM embedding, but the proposed method is tested with HH subbands. In our experiments, selection of subband for WM embedding is not only decided by embedding process and also by the host and WM extraction. From the metrics given in Table 8, one can observe that the selection of HH subbands not only results in better embedding but also delivers better extraction.

Image authentication, copyright and ownership can be established by watermarking algorithms with better robustness against geometrical and non-geometrical attacks on WM embedded images. The robustness of the proposed method is tested with different attacks and the extracted WM images are given in Fig. 7. Extracted WM images are also given for other methods also. Crop and rotation attacks don’t change the gray values of the pixels, but results in loss of pixel values in certain spatial locations. Watermarking in DWT–SVD domain distributes watermark coefficients all over the host image and hence the crop and rotation hampers the recovery of watermark with cropped and out of bound details of the host image. For these two attacks, DWT–SVD and RDWT–SVD methods are able to extract the WM with less imperceptibility but the proposed methods delivers better results. Mean, median attacks change the gray values of the pixels and hence lead to poor extraction. In mean and median attacks, edges of the extracted watermark are blurred and this effect is similar to the dead band effect. When the watermarked image is corrupted by additive noises such as impulse and white Gaussian noise, noise values are distributed over the entire spatial location of the host image. The recovery of the watermark entirely depends on the noise density. If the noise density is less, then the extracted watermark will be good and vice versa. Upon analyzing the extracted images, it is observed that the proposed method delivers better results compared to other two methods.

The three methods are compared based on the cost of computation for embedding and extraction process and given in Table 9. DWT–SVD method takes less time for embedding and extraction because of down sampling of subbands and absence of evaluation of \(\alpha \). RDWT–SVD method takes more time because of the absence of down sampling in DWT decomposition. Because of the evaluation of normalized principal components, the proposed method consumes more time than DWT–SVD.