【正文】 n, the TAF in percentage is defined asTAF =1mnbracketleftBiggm?1summationdisplayn?1summationdisplayw(i, j) ⊕ w(i, j)bracketrightBigg100, (10)i=0 j=0. Patra et al. / Digital Signal Processing 20 (2020) 442–453 447Fig. 2. Flowchart to embed a watermark bit.where, w(i, j) and w(i, j) represent the original and extracted watermarks at position, (i, j) respectively, and ⊕ is anexclusiveOR operator. The acceptance level of TAF is 5% because, above this value, the extracted watermark will not berecognizable.Peak SignaltoNoise Ratio (PSNR) measures the quality between two images. Usually we would pare the modifiedsignal against the original signal, ., in this case, the watermarked image against the original host image. The value of PSNRusually ranges from 20 dB (low quality) to 40 dB (high quality). Since the host images used for the experiments are in 8bitgrayscale format, the peak value of the image is taken to be 255. The PSNR in dB is given byPSNR = 10log10bracketleftBigg25521M1NsummationtextM?1i=0summationtextN?1j=0[A(i, j) ? A(i, j)]2bracketrightBigg, (11)where, A represents the host image, A represents the watermarked image and M and N represent the dimensions of thetwo images.In this study we carry out performance parison among the three schemes considering the following performancecriteria:1. Computational plexity of the embedding and extracting procedures.2. Quality of the watermarked images.3. Robustness of the schemes to different attacks.4. Further increase in embedding capacity.448 . Patra et al. / Digital Signal Processing 20 (2020) 442–453Fig. 3. The three host images (256 256): (a) Lenna, (b) Baboon, (c) Airplane, and (d) the watermark image, Panda (64 64).Fig. 4. Comparison of embedding and extracting times for the three schemes: (a) embedding time, (b) extraction time.. Computational plexityThe putational time for embedding and extraction is an important performance measure, especially when the watermarking is to be carried out for online applications, ., video or audio broadcasting. Several experiments were conductedto evaluate performance of the proposed scheme against the two SVDbased schemes. The experiments were carried outin a laptop PC with Intel Pentium M processor, GHz clock and 512 MB RAM. Three benchmark graylevel images of256 256 pixels of Lenna, Baboon and Airplane were used as host images, as shown in Fig. 3. A black and white (binary)image of Panda was used as the watermark. Several watermark dimensions were used in the simulations, ., 32 32,32 64, 64 64 and 128 64. The results are based on Lenna (host image, 256 256) watermarked with Panda (watermark, 32 32), unless otherwise stated. We have observed that the results of simulations using the other two host images(Baboon and Airplane) were similar to that of Lenna.We pare the embedding and extraction time of the proposed scheme against Schemes 1 and 2. Ten simulation runswere conducted for each scheme to determine the average timing for each scheme and are plotted in Fig. 4. The host imageswere watermarked with Panda image (32 32).From Fig. 4 one can see that the proposed scheme is able to embed and extract the watermark in much less time thanSchemes 1 and 2. On averaging over the three host images, the embedding time for Scheme 1, Scheme 2 and proposedCRTbased scheme were found to be 250, 130 and 40 ms, respectively. The proposed scheme is faster because only simpleCRT calculations are required for embedding, which makes up the bulk of the embedding time. The difference in timingsbetween Schemes 1 and 2 is due to the calculation of ranks of the individual blocks and selection of blocks to embed thewatermark bits. Furthermore, it can also be seen that the time taken to select blocks based on rank is imagedependentthat gives rise to significant differences in timing. However, in our proposed scheme, the embedding time is found to beindependent of the host image. The extraction time in the proposed scheme (as shown in Fig. 4(b)) is also reduced to alarge extent, because only CRT calculations are needed during extraction phase. The average extraction time for Scheme 1,Scheme 2 and proposed scheme was observed to be 190, 90 and 20 ms, respectively. It is also noticed that unlike the twoSVDbased schemes, the extraction time in our proposed scheme does not depend on the host image. Scheme 2 is fasterthan Scheme 1 because of absence of rank calculation and selection of blocks based on rank.The putational advantage of the proposed scheme is derived from the fact that CRT involves only modular operationswhich are putationally e?cient pared to SVD. In the SVDbased Schemes 1 and 2, the basic operations involved inthe embedding phase are given by: (i) given a matrix A, generate the three matrices, U, V and D, (ii) manipulate someelements of U or V matrix, and (iii) obtain the matrix?A through SVD using modified U, V and D. In our proposed scheme,the basic operations in the embedding stage are given by: (i) given an integer Z, using CRT determine the residues R1. Patra et al. / Digital Signal Processing 20 (2020) 442–453 449Fig. 5. Quality of watermarked image in PSNR for different host images.and R2, (ii) check the embedding conditions, and (iii) modify Z until embedding conditions are satisfied. We simulatedthese operations in an Intel Duo P8600based CPU with GHz clock and 4 GB RAM using JAVA programming language.The average putation time for one run of the SVD and CRT based basic operations were found to be 37 ms and 92 ns,respectively. This shows that the CRTbased putations are much faster than SVD putations. The relative timingsshown in Fig. 4 are much higher because they were based on a different PC specification and are meant for pleteembedding and extraction phases.. Quality of watermarked imagesThe