A Generalized Image Interpolation-based Reversible Data Hiding Scheme with High Embedding Capacity and Image Quality

Abstract

Jung and Yoo proposed the first image interpolation-based reversible data hiding algorithm. Although their algorithm achieved superior interpolation results, the embedding capacity was insufficient. Lee and Huang proposed an improved algorithm to enhance the embedding capacity and the interpolation results. However, these algorithms present limitations to magnify the original image to any resolution and pixels in the boundary region of the magnified image are poorly manipulated. Furthermore, the capacity and the image quality can be improved further. This study modifies the pixel mapping scheme and adopts a bilinear interpolation to solve boundary artifacts. The modified reference pixel determination and an optimal pixel adjustment process can effectively enhance the embedding capacity and the image quality. The experimental results show our proposed algorithm achieves a higher embedding capacity under acceptable visual distortions, and can be applied to a magnified image at any resolution. Our proposed technique is feasible in reversible data hiding.

1. Introduction

The development of personal computers and the advancement of digital technology have dramatically altered human behavior. The majority of traditional media have been digitalized to improve their portability and storability. Further, digital media can be cost-efficiently transmitted over the Internet. However, the Internet is an open platform that presents concerns on certain issues such as copyright infringement, message modification, and interception of private communications. Therefore, approaches to designing an appropriate mechanism that ensures the privacy of transmitted messages have become an urgent research problem.

Cryptographic algorithms employ a secret key that is used to encode messages into meaningless characters prior to transmission over the Internet. Although a malicious user cannot derive any information from an encoded message, they can potentially corrupt or destroy the transmitted message before forwarding it to the intended receiver. Data hiding algorithms [1] conceal a secret message inside a digital cover media, and this stego media with the embedded message is subsequently transmitted over the Internet. Any third party monitoring a transmission would be under the impression that a common form of media is being transmitted. Consequently, the privacy of the transmitted message is considerably improved. Current data hiding algorithms [2-10] use still images, audio, video, 3D models or high-dynamic-range images as their cover media. However, still images remain the most commonly used media because they are easily accessible. Therefore, embedding secret messages into images has been a thoroughly studied research area.

However, after a secret message has been embedded using any of the aforementioned algorithms, the pixel values of an image are permanently distorted and cannot be restored to their original values. For medical or military applications, any distortion is unacceptable. Therefore, numerous researchers have focused specifically on reversible data hiding algorithms [11-17]. The primary objective of reversible data hiding algorithms is the extraction of a secret message without the occurrence of any errors, and lossless recovery of the original pixel values.

Data hiding algorithms can be regarded as a type of image processing. Therefore, other image processing operations are typically integrated into data hiding algorithms to improve their efficiency. Image interpolation [18] is a common example. According to our research, two schemes [19, 20] have applied image interpolation to propose a different concept on reversible data hiding applications. However, each algorithm has corresponding shortcomings that are detrimental to their performance, either less embedding capacity or low image quality. In this study, we modify the pixel mapping technique of previous algorithms and apply bilinear interpolation to the original image. Thus, our algorithm can be applied to a magnified image at any resolution without producing any artifacts in the boundary region of the cover image. We also modify the reference pixel determination algorithm proposed by Lee and Huang to further increase the embedding capacity. The image quality of stego images is also raised through an optimal pixel adjustment process [21]. The experimental results support the feasibility of our algorithm.

The remainder of this paper is organized as follows. Section 2 provides a review of image interpolation-based reversible data hiding algorithms, Section 3 details the proposed technique, Section 4 presents a discussion on the experimental results, and Section 5 offers a conclusion and directions for future research.

 

2. Image Interpolation-Based Reversible Data Hiding Algorithms

Fig. 1 shows a flowchart of image interpolation-based reversible data hiding algorithms. The algorithm first scales up the original image to the cover image based on the user-determined magnifying factors. Subsequently, the algorithm embeds the secret message into the cover image to obtain a stego image. Because the pixels mapping from the original image to the cover image are not modified during the embedding process, they can be recovered losslessly from the stego image. Note that the algorithm scales down the input image and subsequently scales it up to the cover image using different interpolation methods. Thus, a comparison between the input and cover images can evaluate the efficiency of various interpolation methods. In the following sections, we introduce the core technologies of two previous algorithms, containing pixel mapping, image interpolation, reference pixel determination, and data embedding, with the magnifying factor equaling 2.

Fig. 1.A flowchart of image interpolation-based reversible data hiding algorithms

2.1 Pixel Mapping and Image Interpolation

Jung and Yoo [19] proposed the neighbor mean interpolation (NMI), which is a novel image interpolation method. The pixel mapping and the image interpolation methods are expressed in Equation 1. For example, if the magnifying factor equals 2, the pixel p located at position (m,n) in the original image is mapped to position (i,j) in the cover image, where i=2m and j=2n (i.e. the pixels with the gray background in Fig. 2). Thereafter, pixels p' in the cover image that have not yet been assigned a pixel value (i.e. the pixels with the white background in Fig. 2) are interpolated based on Equation 1. However, the pixels in the hatched area in Fig. 2 are inappropriately interpolated because of insufficient neighboring pixels, which may result in artifacts appearing gradually as the magnifying factor is increased. Lee and Huang [20] proposed the neighboring pixels interpolation (NPI) as an alternative image interpolation method. The pixel mapping technique employed in this method is identical to that proposed by Jung and Yoo. The only difference is the interpolation method for the pixels with the white background shown in Fig. 2. The example for Lee and Huang’s algorithm is shown in Equation 2 and Fig. 3.

Fig. 2.Pixel mapping and image interpolation proposed by Jung and Yoo [19]

Fig. 3.Pixel mapping and image interpolation proposed by Lee and Huang [20]

2.2 Reference Pixel Determination

Prior to data embedding, both of the discussed algorithms calculate the embedding capacity for each embeddable pixel. The embeddable pixel is defined as all pixels in the cover image except for the pixels derived from the original image. The embedding capacity is determined by the difference between the embeddable and the reference pixels. The reference pixels for both algorithms are selected from the pixels in the original image. Jung and Yoo subdivided the cover image into non-overlapping blocks, each with 2×2 pixels, and the reference pixel is located at (⌊i/2⌋×2,(⌊j/2⌋×2). However, Lee and Huang subdivided their cover image into overlapping blocks, each with 3×3 pixels, and the reference pixel was determined by maximal value MV among the corner pixels in the overlapping blocks (Equation 3). For example, in Fig. 4, the pixels with the blue background are used to determine the reference pixel, the pixels with the blue background and red bold text are the final reference pixel, and those with the green background are prepared for data embedding.

Fig. 4.An example for reference pixel determination

2.3 Data Embedding Method

Except for the pixels derived from the original image, each embeddable pixel in the cover image is prepared for data embedding. Both algorithms derive their embedding capacity from the difference between each embeddable and reference pixel (Equations 4 and 5). Finally, the secret message is embedded into the embeddable pixel based on Equation 6, where SM10n(i,j) is a decimal value converted from a binary value with length n(i,j).

2.4 Data Extraction Method

Once the stego image has been received by the intended recipient, the data extraction process is initiated to extract the secret message. First, pixel p" located at (2m,2n) is extracted, and the image interpolation is repeated to produce an image that is identical to the cover image. Except for the pixels derived from the original image, embedding capacity n(i,j) is calculated based on the difference between the embeddable and the reference pixels. The secret message can subsequently be derived from the difference between the cover and stego pixels by converting the decimal value to a binary value with length n(i,j). The original image can then be recovered by extracting the pixel at location (2m,2n) in the stego image.

 

3. The Proposed Method

Both algorithms present limitations to the magnification of the original image to any resolution, and artifacts may appear in the boundary area of the cover image because of insufficient neighboring pixels. Additionally, the data embedding method causes large visual distortions and the embedding capacity can also be improved. These factors affect the efficiency of the discussed algorithms.

In this study, we offer a potential solution to avoid the shortcomings discussed above. First, we modify the previous pixel mapping techniques to allow the scheme to support magnified images at any resolution. Second, the stego image quality is raised by applying an optimal pixel adjustment process. Finally, the embedding capacity can be increased by selecting the proper reference pixel. The following sections detail each process of the proposed scheme.

3.1 Data Embedding Procedure

In this section, we detail the differences between our proposed algorithm and the two discussed algorithms, containing pixel mapping, image interpolation, reference pixel determination and data embedding.

3.1.1 Pixel Mapping and Image Interpolation

To raise the visual quality of the boundary area in the cover image, we propose a new pixel mapping technique. Assume the original image is of rw×rh pixels, where mw and mh are the magnifying factors for width and height, respectively. The pixel at position (m,n) in the original image is mapped to position (i,j) in the cover image based on Equation 7, where 1≤m≤rw, 1≤n≤rh, 1≤i≤⌊rw×mw⌋, 1≤j≤⌊rh×mh⌋ . The remaining pixels are interpolated using a traditional bilinear interpolation scheme based on the nearest four corner pixels. For example, Fig. 5 shows the results for pixel mapping and image interpolation. The original image is of 2×2 pixels, where both mw and mh equal 2. The pixels in Fig. 5, with the gray background, are obtained from the original image, whereas the pixels with the white background are interpolated from the four corner pixels using the bilinear interpolation scheme. The difference between this approach and previous algorithms can be seen by comparing Fig.s 2, 3, and 5.

Fig. 5.Pixel mapping and image interpolation in this study

3.1.2 Reference Pixel Determination

For the reference pixel determination, we modified the algorithm proposed by Lee and Huang to select the proper reference pixel to increase the embedding capacity. The Lee and Huang’s algorithm determined the reference pixel by the maximal value MV among the corner pixels in the overlapping blocks. Instead, we simultaneously consider both maximal value MV and minimal value mV among the corner pixels in the overlapping blocks. After comparing the difference between (MV-p'(i,j)) and (p'(i,j)-mV) , the value of the reference pixel is set based on the value that produces the largest difference. Finally, the embedding capacity can be also derived using Equation 8.

3.1.3 Data Embedding Method

Except for the pixels derived from the original image, each pixel is prepared for data embedding. To raise the stego image quality, we employed the optimal pixel adjustment process to perform the data embedding. First, we extracted n(i,j) -bit binary value SM2n(i,j) from the secret message stream in binary form. SM2n(i,j) was subsequently embedded into the embedding pixel by applying a simple least-significant-bit substitution method based on Equation 9, where SM10n(i,j) is a decimal value derived from the binary-to-decimal conversion of SM2n(i,j) . Finally, an adjustment process based on Equation 10 is performed to derive the final value for the embedding pixel.

3.2 Data Extraction Procedure

Once the intended receiver obtains the stego image, the data extraction process is initiated to extract the secret message. First, the original resolution rw and rh can be calculated with the assistance of magnifying factors mw and mh . The position for pixels in the original image can be extracted based on Equation 7, and the remaining pixels are interpolated again to obtain the cover image. We subsequently calculate the embedding capacity for each embeddable pixel. Finally, we extract the modulus of 2n(i,j) for each embeddable pixel, and represent it in binary form with length n(i,j). The secret message can be extracted without error after processing each pixel.

 

4. Experimental Results

This section presents the experimental results to show the feasibility of the proposed method. Fig. 6 depicts the visual effects of our test images. The proposed algorithm was implemented using Matlab on a personal computer fitted with an Intel Xeon E3-1230V2 3.3GHz processor and 16 GB of RAM. We also re-implemented the previous algorithms. The embedded secret message is a randomly generated 0/1-bit string. The experimental results show there is no error in the extracted secret message and the original image can be recovered completely from the stego image. The distortion between the two images is measured based on the peak signal-to-noise ratio (PSNR) shown in Equation 11, where MSE is the mean squared error, and represents the difference between the first image C and second image S , with size of M×N . Ci,j and Si,j are pixels located in the ith row and the jth column of the first and second images, respectively (see Equation 12). Further, we also adopt a full reference metric, structural similarity index measure (SSIM), to measure the similarity between cover and stego images. Equation 13 shows the formula of SSIM, where x and y represent the luminance of pixels in a window with common size 8×8 in the cover and stego images, respectively. μx and μy are the average of x and y; σ2x and σ2y are the variance of x and y; σxy is the covariance of x and y. Two constants c1=(k1L)2 and c2=(k2L)2 are used to stabilize the division with weak denominator, where L is the dynamic range of a pixel (255 for a gray-scale images with 8 bits/pixel), k1 = 0.01, and k2 = 0.03 by default.

Fig. 6.The visual effects of our test images

This section first presents the experimental results of our proposed algorithm, including the visual distortion and the embedding capacity. We also show the embedding capacity under different magnifying factors. Finally, we show the feasibility of the proposed algorithm by comparing it with the previous algorithms.

Fig. 7 shows the visual effects for the stego images of the proposed algorithm. The PSNR values of our stego images compared to those of the cover images range from 32.60 to 42.55, which indicates that the image quality is acceptable. Observing the SSIM values, our scheme shows a value from 0.96 to 0.98. This implies our scheme can achieve a significant fidelity between the cover image and the data-embedded stego image. The average embedding capacities for the stego images range from 1.26 to 2.58 bits per pixel (bpp) and from 1.68 to 3.43 bits per embeddable pixel (bpep). These factors prove the effectiveness of our proposed algorithm.

Fig. 7.The PSNR value, SSIM value, and embedding capacity for different test images

This section next presents a comparison between the proposed algorithm and the previous algorithms, including the interpolation results, embedding capacity, and the stego image quality. Fig. 8 shows the PSNR and SSIM values for the interpolation results using NMI [19], NPI [20], and our proposed method. The obtained experimental results are identical to those obtained by Lee and Huang; that is, based on the obtained PSNR and SSIM values, the cover images of the NMI and NPI methods have a substantially better image quality than those of the bilinear interpolation scheme. Because our proposed algorithm is based on the bilinear interpolation scheme, the PSNR and SSIM values of our cover image is the lowest, except for the Tiffany image. Fig. 9 shows a close-up view of the interpolated cover images to provide a better comparison of the visual artifacts. As shown in the Fig., the interpolation results of the previous algorithms produce a “zipper effect”, whereas our cover images result in a considerable level of blurring. Thus, each interpolation method produces different artifacts. Specifically, our pixel mapping method can support the magnified images at any resolution, whereas previous algorithms have not considered this issue.

Fig. 8.The PSNR and SSIM values comparison for the interpolation results between our and previous algorithm

Fig. 9.A close-up view of interpolation results for our and previous algorithms

We next compare the embedding capacity of the proposed and previous algorithms. Fig. 10 shows that, with a magnifying factor set at 2, the algorithm proposed by Jung and Yoo provides an embedding capacity ranging from 0.43 to 1.32 bpp for different test images, whereas the embedding capacity of the algorithm proposed by Lee and Huang can provide from 1.00 to 2.11 bpp. Our algorithm provides the highest embedding capacity, which ranges from 1.26 to 2.58 bpp. Furthermore, in Fig. 11, we also show the embedding capacity distribution for each embeddable pixel of the Lena, Baboon, and F16 images. The remaining images achieved similar results. The Fig. shows that the embedding capacity of our proposed algorithm can effectively achieve a higher bpp value by modifying the reference pixel determination.

Fig. 10.The embedding capacity comparison for our and previous algorithms

Fig. 11.The embedding capacity distribution for each embeddable pixel for the test images

Table 1 shows the amount of embedding capacity under different magnifying factors. Given two magnifying factors mw and mh , the algorithm first calculates the resulting image resolution with ⌊mwrw⌋×⌊mhrh⌋ pixels. Subsequently, the algorithm maps the pixels in the original image to the ones in the cover image using Equation 7. Bilinear interpolation is then performed to obtain a final cover image. Obviously, with the increasing magnifying factors, more pixels can be with data embedded and the amount of embedding capacity is increasing. However, previous algorithm cannot support magnified images at any resolution.

Table 1.The amount of embedding capacity under different magnifying factors

Finally, Fig. 12 shows a comparison of the cover and stego image quality for the proposed and previous algorithms after the secret message has been embedded. The Lena, Baboon, and F16 images have been selected as our test images because they differ in image complexity. Because of the high level of image distortions resulting from high embedding capacity values, the image quality of our proposed algorithm is lower than that obtained by Jung and Yoo. However, by applying an optimal pixel adjustment process, the image quality of our proposed algorithm is superior to that of Lee and Huang’s. Fig. 13 shows the difference between the visual modifications of the pixel intensity of each image (magnified by a factor of eight). The images in the Fig. show the absolute difference between the corresponding pixels of the cover and the stego images. We flip the black and white expressions to improve the visualization effects. Therefore, a brighter region in the difference image indicates that the corresponding pixel values of the cover and stego images are similar, whereas a darker region indicates dissimilar pixel values. The darker region appears at the edge area of each test image because of the large difference in data embedding. The algorithm proposed by Lee and Huang produces difference images with edge areas that are the darkest. We assert that the highest pixel distortion causes this phenomenon. However, our proposed algorithm generates a similar image quality for the stego images, and improves the embedding capacity from 94.75% to 198.87%.

Fig. 12.The image quality comparison for our and previous algorithms

Fig. 13.The difference image between the cover and the stego images for our and previous algorithms

 

5. Conclusion

This study proposes a novel image interpolation-based reversible data hiding scheme. The proposed algorithm is reversible, and achieves a high embedding capacity, while maintaining acceptable image quality. The combination of the modified pixel mapping technique and bilinear interpolation schemes enable the proposed algorithm to support magnified images at any resolution. Simultaneously, the artifacts for the boundary regions in the cover image have also been eliminated. Furthermore, an optimal pixel adjustment process was employed to substantially raise the image quality. Finally, the embedding capacity is increased based on the modified reference pixel determination. The experimental results show that our technique is feasible for image interpolation-based reversible data hiding. Future studies can extend on the interpolation concepts to support 3D models or high-dynamic-range images as cover media. Furthermore, additional data embedding schemes that further improve image quality are also worthy of examination.