Experimental Results

A series of experiments have been conducted to test the proposed method using many secret and target images with sizes 1024768 or 7681024. To show that the created mosaic image looks like the pre-selected target image, the quality metric of root mean square error (RMSE) is utilized, which is defined as the square root of the mean square difference between the pixel values of the two images.

An example of the experimental results is shown in Figure 2.5, where Figure 2.5(c) shows the created mosaic image using Figure 2.5(a) as the secret image and Figure 2.5(b) as the target image. The tile image size is 88. The recovered secret image using a correct key is shown in Figure 2.5(d) which looks nearly identical to the original secret image shown in Figure 2.5(a) with RMSE = 0.948 with respect to the secret image. It is noted by the way that all the other experimental results shown in this paper have small RMSE values as well, as seen in Figure 2.10(c).

Moreover, Figure 2.5(e) shows the recovered secret image using a wrong key, which is a noise image. Figures 2.5(f) through 2.5(i) show more results using different tile image sizes. It can be seen from the figures that the created mosaic image retains more details of the target image when the tile image is smaller. It can also be seen that the blockiness effect is observable when the image is magnified to be large; but if the image is observed as a whole, it still looks like a mosaic image with its appearance similar to the target image. Figure 2.10(a) also shows this fact in another way  a mosaic image created with smaller tile images has a smaller RMSE value with respect to the target image. On the other hand, the number of required bits embedded for recovering the secret image will be increased when the tile image becomes smaller, as can be seen from Figure 2.10(b).

Figure 2.6 shows a comparison of the results yielded by the proposed method with those by Lai and Tsai [39], where Figure 2.6(a) is the input secret image, Figure 2.6(b) is the selected target image, Figure 2.6(c) is the mosaic image created by Lai and Tsai [39], and Figure 2.6(d) is that created by the proposed method. It can be seen from these results that the mosaic image yielded by the proposed method has a smaller RMSE value with respect to the target image, implying that it is more similar to the target image in appearance. The other results of our experiments also show the same conclusion. And more importantly, the proposed method allows users to select their favorite images for uses as target images.

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 2.5. An experimental result of mosaic image creation. (a) Secret image. (b) Target image. (c) Mosaic image created with tile image size 88. (d) Recovered secret image using a correct key with RMSE = 0.948 with respect to secret image (a). (e) Recovered secret image using a wrong key.

(f)-(i) Mosaic images created with different tile image sizes 1616, 2424, 3232, and 4040.

Figure 2.7 shows two other experimental results of mosaic image creation, where the utilized secret images both contain many structures (Figure 2.7(a) is a stained-glass window painting and Figure 2.7(d) is a document image) and Figures 2.7(b) and 2.7(e) are the target images; Figures 2.7(c) and 2.7(f) are the created mosaic images with image sizes 88; and Figures 2.7(g) and 2.7(h) are the zoom-out images of the red square regions of Figures 2.7(c) and 2.7(f), respectively. It can be seen from Figures 2.7(c) and 2.7(f) that each created mosaic image still has the visual

appearance of the pre-selected target image even when the secret image contains many structural elements. Especially, the secret image of Figure 2.7(d) is a nearly black-and-white document image, which means that the proposed method can be utilized for secure transmissions of confidential document images as well. Moreover, it can be seen from Figures 2.7(g) and 2.7(h) that each generated mosaic image has a blocky appearance which comes from the mosaic effect because the mosaic image is composed by changing the color characteristics of the fragments of the secret image and rearranging the resulting fragments. To show the flexibility of the proposed method for a user to choose any target image as the reference of a secret image, we selected one secret image as shown in Figure 2.8 and two target images as shown in Figures 2.7(b) and 2.7(e), and transformed the former to have the visual appearance of each of the latter ones. The results are shown in Figures 2.8(b) and 2.8(c) from which we can see that the created mosaic images look similar to the respective target images even though the secret image is quite different from the target images in appearance.

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(c) (d)

Figure 2.6. Comparison of results of Lai and Tsai [39] and proposed method. (a) Secret image. (b) Target image. (c) Mosaic image created from (a) and (b) by [39] with RMSE = 47.651. (d) Mosaic image created from (a) and (b) by proposed method with RMSE = 33.935.

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(d) (e) (f)

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Figure 2.7. Two other experimental results of mosaic image creation. (a) and (d) Secret images. (b) and (e) Target images. (c) and (f) Mosaic images created from (a) and (b), and (d) and (e), respectively, with tile size 88.

(g) and (h) Zoom-out images of red square regions of (c) and (f), respectively.

However, since the mosaic image is yielded by dividing the secret image into tile images and transforming their color characteristics to be those of the corresponding target blocks, the global color characteristics of a transformed tile image and its corresponding target block are the same but the color distributions of them may be quite different. Hence, although the mosaic image has the visual appearance of the target image, the details of each fragment in the mosaic image may have low similarity to those of its corresponding target block. To measure this mosaic effect, we adopt the metric of mean structural similarity (MSSIM) to compare the

similarity of the created mosaic image and the target image [47]. Figure 2.10(d) shows the MSSIM values of the created mosaic images with respect to the target images versus different tile image sizes, where the window size for computing the MSSIM is set to be the same as the size of the tile image. We can see from Figure 2.10(d) that the MSSIM value of the created mosaic image with respect to the target image varies from 0.2 to 0.8, which shows that the similarity of the details of the created mosaic image to those of the target image is not good enough. But, this is not the main concern of the proposed method because our goal is to create a globally visually-similar mosaic image, which contains a secret image of the same size, for the purpose of secure image transmission.

(a) (b) (c)

Figure 2.8. Created mosaic images with the same secret image. (a) Secret image. (b) Mosaic image created from (a) and Figure 2.7(b) with RMSE = 26.067. (c) Mosaic image created from (a) and Figure 2.7(e) with RMSE = 33.102.

A limitation of the proposed method is that the sizes of available target images should match those of possible input secret images. Specifically, if we have a very large secret image but only small target images for selections, then any selected target image should be enlarged before mosaic image creation in order to match the size of the secret image, and the created mosaic image will become blurred. An experimental result showing this blurring effect is presented in Figure 2.9.

(a) (b) (c)

Figure 2.9. Created mosaic images with the same secret image shown in Fig. 5(a) and small-sized target images. (a) Created image for target image shown in Fig. 5(b) with size 768×1024. (b) Created image for target image shown in Fig. 5(b) but with size reduced to (1/5)×(1/5). (c) Created image for target image shown in Fig. 5(b) but with size reduced to (1/10)×(1/10).

Furthermore, as shown in Figure 2.10, we have drawn plots of the trends of various parameters versus different tile image sizes, including those for the parameters of 1) the RMSE values of the created mosaic images with respect to the target images; 2) the numbers of required bits embedded for recovering the secret images; 3) the RMSE values of the recovered secret images with respect to the original ones; and 4) the MSSIM values of created mosaic images with respect to target images.

In addition, we have conducted experiments on a set of 12 images from which a total of 1211 = 132 secret-target image pairs are selected without repetitions, and the averages of the parameters of the 132 mosaic image creation results were also plotted in Figure 2.10 as the orange curves for comparisons.