Backward-Forward Distortion Minimization for Binary ... - IEEE Xplore
Backward-Forward Distortion Minimization for Binary Images Data Hiding Huijuan Yang and Alex C. Kot School of Electrical & Electronic Engineering, Nanyang Technological University. Email: {ehjyang, eackot}@ntu.edu.sg Abstract— In our previous paper [1], we propose to use the morphological transform for binary images data hiding for authentication purpose. We view flipping an edge pixel in binary images as shifting the edge location one pixel horizontally and vertically. Based on this observation, we propose an interlaced morphological binary wavelet transform to track the shifted edges. The two processing cases that flipping the candidates of one does not affect the flippability conditions of another are employed such that a large capacity can be achieved. However, employing double processing cases sacrifices the visual quality of the watermarked image. In this paper, we further investigate and propose a novel effective Backward-Forward Minimization method to minimize the visual distortion for double processing cases. Experimental results demonstrate its superior performance.
I. INTRODUCTION Data hiding for digital binary images has received great interest recently due to the wide applications of binary images [1]-[9], [10]. Most data hiding techniques for binary images are based on spatial domains, for example, choosing data hiding locations by employing pairs of contour edge patterns [2], visual distortion tables [3], [4], defining visual qualitypreserving rules [5] and edge pixels [6], [7]. Localization of tamperings for binary images are addressed in [4], [8]. Generally speaking, data hiding in real-valued transform domain does not work well for binary images due to the quantization errors introduced in the pre/post-processing [9]. In addition, embedding data using real-valued coefficients requires more memory space. We observe that the morphological binary wavelet transform [11] can be used to track the transitions in binary images by utilizing the detail coefficients. One rather intuitive idea in employing the morphological binary wavelet transform for data hiding is to use the detail coefficients as a location map to determine the data hiding locations. However, this makes it difficult to achieve blind watermark extraction due to the fact that once a pixel is flipped, the horizontal, vertical and diagonal detail coefficients will change correspondingly. The idea of designing an interlaced transform to identify the embeddable locations is motivated by the fact that some transition information is lost during the computation of a single transform and there is a need to keep track of transitions between two and three pixels for binary images data hiding. Specifically, we process the images based on 2 × 2 pixel blocks and combine two different processing cases that the flippability conditions of one are not affected by flipping the candidates of another for data embedding,
978-1-4244-1684-4/08/$25.00 ©2008 IEEE
namely “orthogonal embedding”. As a result, significant gains in capacity can be achieved, which also improves the efficiency of utilizing the flippable pixels. Implementing the transforms by the “Exclusive OR (XOR)” operation addresses the quantization error issue in a DCT-based approach [10]. In general, the larger the capacity, the higher the visual distortion. The increase in capacity by employing double processing cases unavoidably sacrifices the visual quality of the watermarked images, hence minimization of the distortion is needed. In this paper, we propose a novel Backward-Forward Minimization (BFM) method to further minimize the distortions of the watermarked images by employing double processing cases. This paper is organized as follows. The orthogonal embedding by employing double processing case is discussed in Section II, in which minimization of the distortion by the proposed Backward-Forward Minimization is presented. Experimental results are presented in Section III and Section IV concludes the paper. II. H IGH C APACITY DATA H IDING U SING O RTHOGONAL E MBEDDING A. Double Processing Let us now review the double processing cases proposed in [1]. The capacity of a Single Processing Case (SPC) is determined by the number of pixels that satisfy the flippability condition, in which the flippability condition is defined such that the shifted edges can be tracked. For example, the flippability conditions of a SPC for the even-even and oddodd processing cases are given by fee (i, j) foo (i, j)
= =
(hee (i, j) ⊕ hoe (i, j)) ∧ (vee (i, j) ⊕ veo (i, j)) (1) (voo (i − 1, j − 1) ⊕ voe (i − 1, j)) ∧ (2) (hoo (i − 1, j − 1) ⊕ heo (i, j − 1))
where the candidate pixels are s(2i + 1, 2j + 1) and s(2i, 2j), respectively; i ≥ 1 and j ≥ 1 for foo (i, j). In terms of pixel values, Eqs. (1) and (2) can be further expressed as fee (i, j)
=
(s(2i + 1, 2j) ⊕ s(2i + 1, 2j + 2)) ∧ (3) (s(2i, 2j + 1) ⊕ s(2i + 2, 2j + 1))
foo (i, j)
=
(s(2i, 2j − 1) ⊕ s(2i, 2j + 1)) ∧ (s(2i − 1, 2j) ⊕ s(2i + 1, 2j))
(4)
It can be observed from Eqs. (3) and (4), the flippability condition of the even-even processing case (i.e., fee (i, j)) is not affected by flipping the candidates of the odd-odd processing case (e.g., s(2i, 2j)) and vice versa, as illustrated
404
in Fig. 1, where (i, j) is the index of the 2 × 2 block. This “nonintersection” property of the two processing cases
Fig. 2.
Fig. 1. Checking of the flippability conditions for even-even and odd-odd processing cases of IMBWT.
renders the processing of the even-even and odd-odd cases can be done together. The same applies to the even-odd and odd-even processing cases. The capacity can be increased significantly by combining the two single processing cases, namely, Double Processing Case (DPC). For convenience, we call the two combined processing cases as a “Pair Case”. As evidenced from the increase in the number of candidate pixels, i.e., from 14 × M × N to 12 × M × N for an image of size M × N , the capacity can be approximately doubled by combining the two processing cases. This idea is motivated by the quantization index modulation based data hiding method [12]. The even-even and odd-odd processing cases can be viewed as two orthogonal sets of embedders indexed at the 2 × 2 blocks starting from even-even and odd-odd coordinates, denoted as Qee and Qoo , respectively. In this paper, the embedders are an ensemble of the embedding functions of a “Pair Case”, e.g., the embedding functions of even-even and odd-odd cases. Unlike [12], there is no quantization involved to embed the information by employing a pair case in the present approach. We define a designated 2 × 2 block Db (i, j) as the 2 × 2 block that contains the two candidate pixels for a pair case, which is shown in Fig. 2. The designated 2 × 2 block can be chosen from one of the two processing blocks of a pair case, but only one candidate pixel is chosen to hide data in each Db (i, j). Hence, the maximum capacity Cζ is upper bounded by Cζ ≤ 14 × M × N . To achieve higher security, the choice of an embedder Qk in each Db (i, j) using DPC can rely on a random key Rs , where Rs ∈ {0, 1}. For example, for the mth Db (i, j) block, we choose Qee when Rs (m) = 1 and choose Qoo when Rs (m) = 0. By choosing Qee , we check fee (i, j) first, mark the current candidate pixel as embeddable if fee (i, j) = 1 and proceed to the next Db (i, j). Otherwise, foo (i, j) will be checked (i.e., when fee (i, j) = 1). Similarly, foo (i, j) is checked first by choosing Qoo . From the above
Designated 2 × 2 blocks.
discussion, it is noticed that there may be two candidate pixels being flipped in some 2 × 2 blocks (not Db (i, j)), e.g., the OOBs in Fig. 2. B. Backward-Forward Minimization for Double Processing The “nonintersection” property of the even-even and oddodd, or even-odd and odd-even processing cases renders the possibility to combine the two processing cases to minimize the distortion, namely, Double Processing with Distortion Control (DPDC) [1]. Embedding data using either DPC or DPDC is described as orthogonal embedding. To process the mth Db (i, j) using DPDC, an index k is chosen such that the distortion between the original pattern Po (m) and watermarked pattern Pw (m) with respect to embedder Qk is minimized by k = arg min Pw (m)(Qk , k) − Po (m)(Qk , k)
k
(5)
where m ∈ {(i, j)} and · represents the distortion measures such as the visual distortion tables [3], [4], k ∈ {ee, oo}∨ k ∈ {eo, oe}. Note that k is subsequently used to choose the corresponding embedder Qk to determine the embeddable location. Pw (m)(Qk , k) represents the function that gives the watermarked 3 × 3 pattern for the mth Db (i, j) by choosing the embedder Qk . To compare the visual distortion caused by employing different embedders, the list of patterns that satisfy the flippability conditions should be ranked first. Minimization by only considering the two candidates determined by the two embedders in each Db (i, j) for DPDC, namely, DPDCMTC, may cause the increase in distortion to the neighboring flippable candidates [1], which ultimately may consume the reduced distortion gained by minimization. To minimize the overall distortion, we consider those neighboring processed embeddable candidates (e.g., C, D and E of EEBs in Fig. 2 which are affected by flipping A in OOB) for backward minimization; Whereas we consider those unprocessed flippable candidates (e.g., F, G and H of OOBs in Fig. 2 which are affected by flipping B in EEB) for forward minimization, namely, Backward-Forward Minimization for DPDC (DPDC-BFM). Let Qr be the embedder in the nth
405
neighboring 2 × 2 blocks to be considered, here r only takes one value from {ee, oo, oe, oo}; Ir () is an indicator function to represent whether Qr is chosen (“1”) or not (“0”) in the processed neighboring 2 × 2 blocks for backward minimization, or flippable (“1”) or not (“0”) in the unprocessed neighboring 2 × 2 blocks for forward minimization. Further, let Pw (n) and Po (n), and Pw (n) and Po (n) be the watermarked and original patterns, before and after flipping the candidate in the nth Db (i, j) by choosing Qk , respectively. The accumulated change in distortion Dc (k) in the neighboring 2 × 2 blocks because of choosing Qk is given by
=
−−DPC/DPDC Versus SPC
95
Capacity Increase (%)
Dc (k)
100
Ir (n) × ( Pw (n)(Qr , r) − Po (n)(Qr , r) (6)
n∈Np
− Pw (n)(Qr , r) − Po (n)(Qr , r) )
90 85 80 75 70 65 60
where Np ∈ {(i − 1, j − 1), (i − 1, j), (i, j − 1)} and Np ∈ {(i, j + 1), (i + 1, j), (i + 1, j + 1)} for backward and forward minimization, respectively. Dc (k) is subsequently employed to update the distortion generated by choosing embedder Qk , Eq. (5) thus becomes
55 50
10
20
30
40
50
60
70
80
90
100
Image Index Number Fig. 3. Capacity increase using DPC or DPDC compared with that of SPC.
k = arg min Pw (m)(Qk , k) − Po (m)(Qk , k) + Dc (k)
k
To summarize, an embedder in DPC is chosen based on a random key, whereas it is chosen to minimize the distortion for each flipping in DPDC.
Average Per Pixel Distortion
0.7
III. E XPERIMENTAL R ESULTS A. Capacity and Visual Quality To show the capacity increase by employing DPC and DPDC compared with that of SPC, 100 images of a variety of sizes are used. These images are of different types (e.g., cartoons, tables, handwritten and text in different languages) and resolutions (e.g., 300dpi, 200dpi and 150dpi). The image sizes vary from 100 × 100 to 512 × 512. The visual distortion table [3] is used to quantitatively evaluate the visual quality of the watermarked image, which is defined in [5]. The increase in capacity represented in percentage from SPC to DPC or DPDC is shown in Fig. 3. The results further reinforce our observations that capacity has increased significantly using DPC or DPDC versus SPC, e.g., increase from 56% to 95% for the 100 test images. The average per pixel distortion (APPD) obtained for DPC, DPDC-MTC and DPDC-BFM is shown in Fig. 4. From the figure, it is not difficult to see that the average per pixel distortion has been further reduced with the use of DPDC-BFM. With appropriate selection of the lower distortion pixel to flip for both DPDC-MTC and DPDC-BFM, the achieved APPD is lower than that obtained by using DPC. It should be noted that Da can be high for those images of low resolutions such as 150dpi, as observed for the last several images in Fig. 4. This is due to the fact that there are few good patterns exist in thin strokes. Noticeably, with the use of DPC or DPDC, more than one pixel may be flipped in each 3 × 3 block. In this case, the main 2 × 2 block is timely reconstructed once a candidate is processed. The pattern used for distortion evaluation is taken as the reconstructed
−−DPC −−DPDC−MTC −−DPDC−BFM 0.65
0.6
0.55
0.5 10
20
30
40
50
60
70
80
90
100
Image Index Number Fig. 4. Comparisons of Average Per Pixel Distortion for DPC,DPDC-MTC and DPDC-BFM.
watermarked image (some neighboring candidates possibly have been flipped) with the center pixel taken from the original image so that better visual quality of the watermarked images can be preserved. The good visual quality of the watermarked images obtained by employing DPC and DPDCBFM is shown in Fig. 5, in which Da is 0.5852 and 0.5747, respectively. The results demonstrate that better visual quality of the watermarked image can be achieved using DPDC-BFM compared with that of DPC. IV. CONCLUSIONS In our previous paper [1], we have presented a high capacity data hiding scheme for binary images authentication based on the interlaced morphological binary wavelet transforms. Two
406
(a)
(b)
(c)
(d)
(e)
Fig. 5. Hiding Effects. (a) the original image of size 360 × 376 and 300dpi; (b) and (c) the watermarked image with 4036 bits embedded by employing DPC and DPDC-BFM, respectively. (d) and (e) the enlarged difference images, which are generated from the original image (a) and the watermarked image of (b) and (c), respectively. Note that the foreground of the image is painted in light gray; the black and dark gray dots are the pixels that are flipped from white to black and from black to white.
processing cases that are not intersected with each other are employed for orthogonal embedding in such a way that the capacity can be significantly increased. In this paper, we further propose a Backward-Forward Minimization method to minimize the distortion caused by employing double process case, which considers both those neighboring processed embeddable candidates and those unprocessed flippable candidates that may be affected by flipping the current pixel. In this way, the total visual distortion can be minimized. Experimental results validate the effectiveness of the proposed method. R EFERENCES [1] Huijuan Yang, Alex C. Kot and Susanto Rahardja and Xudong Jiang, “High Capacity Data Hiding for Binary Images in Morphological Wavelet Transform Domain”, Proc. of the IEEE Int. Conf. on Multimedia & Expo. (ICME’2007), pp. 1239-1242, 2-5 July 2007. [2] Q. Mei, E. K. Wong and N. Memon, “Data Hiding in Binary Text Document,” Proceedings of SPIE, vol. 4314, pp. 369-375, 2001. [3] Min Wu, and Bede Liu, “Data Hiding in Binary Images for Authentication and Annotation”, IEEE Trans. on Multimedia, vol. 6, no. 4, pp. 528-538, August 2004. [4] H. Y. Kim and de Queiroz, R. L., “Alteration-Locating Authentication Watermarking for Binary Images,” Proc. Int. Workshop on Digital Watermarking, pp. 125-136, 2004.
[5] Huijuan Yang and Alex C. Kot, “Pattern-Based Date Hiding for Binary Images Authentication by Connectivity-Preserving”, IEEE Trans. On Multimedia, vol. 9, no. 3, pp. 475-486, April 2007. [6] Y. C. Tseng and H.-K. Pan, “Data Hiding in 2-Color Images,” IEEE Trans. on Computers, vol. 51, no. 7, pp. 873-878, July 2002. [7] K.-F. Hwang and C.-C. Chang, “A Run-length Mechanism for Hiding Data into Binary Images,” Proc. of Pacific Rim Workshop on Digital Steganography, pp. 71-74, Kitakyushu, Japan, July 2002. [8] Huijuan Yang and Alex C. Kot, “Binary Image Authentication With Tampering Localization By Embedding Cryptographic Signature and Block Identifier”, IEEE Signal Processing Letters, vol. 13, no. 12, pp. 741-744, Dec. 2006. [9] Y. Liu, J. Mant, E. Wong and S. H. Low, “Marking and Detection of Text Documents Using Transform-domain Techniques”, Proc. of SPIE, Electronic Imaging (EI’99) Conf. on Security and Watermarking of Multimedia Contents, vol. 3657, pp. 317-328, San Jose, CA, 1999. [10] H. Lu, X. Shi, Yun Q. Shi, Alex C. Kot and L. Chen, “Watermark Embedding in DC Components of DCT for Binary Images,” Proc., IEEE Workshop on Multimedia Signal Processing, pp. 300-303, 9-11, Dec. 2002. [11] Henk J. A. M. Heijmans, and J. Goutsias, “Nonlinear Multiresolution Signal Decomposition Schemes-Part II: Morphological Wavelets” IEEE Trans. on Image Processing, vol. 9, no. 11, pp. 1897-1913, Nov. 2000. [12] B. Chen and G. W. Wornell, “Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding,” IEEE Trans. on Information Theory, vol. 47, no. 4, pp. 1423-1443, May 2001.
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I. INTRODUCTION Data hiding for digital binary images has received great interest recently due to the wide applications of binary images [1]-[9], [10]. Most data hiding techniques for binary images are based on spatial domains, for example, choosing data hiding locations by employing pairs of contour edge patterns [2], visual distortion tables [3], [4], defining visual qualitypreserving rules [5] and edge pixels [6], [7]. Localization of tamperings for binary images are addressed in [4], [8]. Generally speaking, data hiding in real-valued transform domain does not work well for binary images due to the quantization errors introduced in the pre/post-processing [9]. In addition, embedding data using real-valued coefficients requires more memory space. We observe that the morphological binary wavelet transform [11] can be used to track the transitions in binary images by utilizing the detail coefficients. One rather intuitive idea in employing the morphological binary wavelet transform for data hiding is to use the detail coefficients as a location map to determine the data hiding locations. However, this makes it difficult to achieve blind watermark extraction due to the fact that once a pixel is flipped, the horizontal, vertical and diagonal detail coefficients will change correspondingly. The idea of designing an interlaced transform to identify the embeddable locations is motivated by the fact that some transition information is lost during the computation of a single transform and there is a need to keep track of transitions between two and three pixels for binary images data hiding. Specifically, we process the images based on 2 × 2 pixel blocks and combine two different processing cases that the flippability conditions of one are not affected by flipping the candidates of another for data embedding,
978-1-4244-1684-4/08/$25.00 ©2008 IEEE
namely “orthogonal embedding”. As a result, significant gains in capacity can be achieved, which also improves the efficiency of utilizing the flippable pixels. Implementing the transforms by the “Exclusive OR (XOR)” operation addresses the quantization error issue in a DCT-based approach [10]. In general, the larger the capacity, the higher the visual distortion. The increase in capacity by employing double processing cases unavoidably sacrifices the visual quality of the watermarked images, hence minimization of the distortion is needed. In this paper, we propose a novel Backward-Forward Minimization (BFM) method to further minimize the distortions of the watermarked images by employing double processing cases. This paper is organized as follows. The orthogonal embedding by employing double processing case is discussed in Section II, in which minimization of the distortion by the proposed Backward-Forward Minimization is presented. Experimental results are presented in Section III and Section IV concludes the paper. II. H IGH C APACITY DATA H IDING U SING O RTHOGONAL E MBEDDING A. Double Processing Let us now review the double processing cases proposed in [1]. The capacity of a Single Processing Case (SPC) is determined by the number of pixels that satisfy the flippability condition, in which the flippability condition is defined such that the shifted edges can be tracked. For example, the flippability conditions of a SPC for the even-even and oddodd processing cases are given by fee (i, j) foo (i, j)
= =
(hee (i, j) ⊕ hoe (i, j)) ∧ (vee (i, j) ⊕ veo (i, j)) (1) (voo (i − 1, j − 1) ⊕ voe (i − 1, j)) ∧ (2) (hoo (i − 1, j − 1) ⊕ heo (i, j − 1))
where the candidate pixels are s(2i + 1, 2j + 1) and s(2i, 2j), respectively; i ≥ 1 and j ≥ 1 for foo (i, j). In terms of pixel values, Eqs. (1) and (2) can be further expressed as fee (i, j)
=
(s(2i + 1, 2j) ⊕ s(2i + 1, 2j + 2)) ∧ (3) (s(2i, 2j + 1) ⊕ s(2i + 2, 2j + 1))
foo (i, j)
=
(s(2i, 2j − 1) ⊕ s(2i, 2j + 1)) ∧ (s(2i − 1, 2j) ⊕ s(2i + 1, 2j))
(4)
It can be observed from Eqs. (3) and (4), the flippability condition of the even-even processing case (i.e., fee (i, j)) is not affected by flipping the candidates of the odd-odd processing case (e.g., s(2i, 2j)) and vice versa, as illustrated
404
in Fig. 1, where (i, j) is the index of the 2 × 2 block. This “nonintersection” property of the two processing cases
Fig. 2.
Fig. 1. Checking of the flippability conditions for even-even and odd-odd processing cases of IMBWT.
renders the processing of the even-even and odd-odd cases can be done together. The same applies to the even-odd and odd-even processing cases. The capacity can be increased significantly by combining the two single processing cases, namely, Double Processing Case (DPC). For convenience, we call the two combined processing cases as a “Pair Case”. As evidenced from the increase in the number of candidate pixels, i.e., from 14 × M × N to 12 × M × N for an image of size M × N , the capacity can be approximately doubled by combining the two processing cases. This idea is motivated by the quantization index modulation based data hiding method [12]. The even-even and odd-odd processing cases can be viewed as two orthogonal sets of embedders indexed at the 2 × 2 blocks starting from even-even and odd-odd coordinates, denoted as Qee and Qoo , respectively. In this paper, the embedders are an ensemble of the embedding functions of a “Pair Case”, e.g., the embedding functions of even-even and odd-odd cases. Unlike [12], there is no quantization involved to embed the information by employing a pair case in the present approach. We define a designated 2 × 2 block Db (i, j) as the 2 × 2 block that contains the two candidate pixels for a pair case, which is shown in Fig. 2. The designated 2 × 2 block can be chosen from one of the two processing blocks of a pair case, but only one candidate pixel is chosen to hide data in each Db (i, j). Hence, the maximum capacity Cζ is upper bounded by Cζ ≤ 14 × M × N . To achieve higher security, the choice of an embedder Qk in each Db (i, j) using DPC can rely on a random key Rs , where Rs ∈ {0, 1}. For example, for the mth Db (i, j) block, we choose Qee when Rs (m) = 1 and choose Qoo when Rs (m) = 0. By choosing Qee , we check fee (i, j) first, mark the current candidate pixel as embeddable if fee (i, j) = 1 and proceed to the next Db (i, j). Otherwise, foo (i, j) will be checked (i.e., when fee (i, j) = 1). Similarly, foo (i, j) is checked first by choosing Qoo . From the above
Designated 2 × 2 blocks.
discussion, it is noticed that there may be two candidate pixels being flipped in some 2 × 2 blocks (not Db (i, j)), e.g., the OOBs in Fig. 2. B. Backward-Forward Minimization for Double Processing The “nonintersection” property of the even-even and oddodd, or even-odd and odd-even processing cases renders the possibility to combine the two processing cases to minimize the distortion, namely, Double Processing with Distortion Control (DPDC) [1]. Embedding data using either DPC or DPDC is described as orthogonal embedding. To process the mth Db (i, j) using DPDC, an index k is chosen such that the distortion between the original pattern Po (m) and watermarked pattern Pw (m) with respect to embedder Qk is minimized by k = arg min Pw (m)(Qk , k) − Po (m)(Qk , k)
k
(5)
where m ∈ {(i, j)} and · represents the distortion measures such as the visual distortion tables [3], [4], k ∈ {ee, oo}∨ k ∈ {eo, oe}. Note that k is subsequently used to choose the corresponding embedder Qk to determine the embeddable location. Pw (m)(Qk , k) represents the function that gives the watermarked 3 × 3 pattern for the mth Db (i, j) by choosing the embedder Qk . To compare the visual distortion caused by employing different embedders, the list of patterns that satisfy the flippability conditions should be ranked first. Minimization by only considering the two candidates determined by the two embedders in each Db (i, j) for DPDC, namely, DPDCMTC, may cause the increase in distortion to the neighboring flippable candidates [1], which ultimately may consume the reduced distortion gained by minimization. To minimize the overall distortion, we consider those neighboring processed embeddable candidates (e.g., C, D and E of EEBs in Fig. 2 which are affected by flipping A in OOB) for backward minimization; Whereas we consider those unprocessed flippable candidates (e.g., F, G and H of OOBs in Fig. 2 which are affected by flipping B in EEB) for forward minimization, namely, Backward-Forward Minimization for DPDC (DPDC-BFM). Let Qr be the embedder in the nth
405
neighboring 2 × 2 blocks to be considered, here r only takes one value from {ee, oo, oe, oo}; Ir () is an indicator function to represent whether Qr is chosen (“1”) or not (“0”) in the processed neighboring 2 × 2 blocks for backward minimization, or flippable (“1”) or not (“0”) in the unprocessed neighboring 2 × 2 blocks for forward minimization. Further, let Pw (n) and Po (n), and Pw (n) and Po (n) be the watermarked and original patterns, before and after flipping the candidate in the nth Db (i, j) by choosing Qk , respectively. The accumulated change in distortion Dc (k) in the neighboring 2 × 2 blocks because of choosing Qk is given by
=
−−DPC/DPDC Versus SPC
95
Capacity Increase (%)
Dc (k)
100
Ir (n) × ( Pw (n)(Qr , r) − Po (n)(Qr , r) (6)
n∈Np
− Pw (n)(Qr , r) − Po (n)(Qr , r) )
90 85 80 75 70 65 60
where Np ∈ {(i − 1, j − 1), (i − 1, j), (i, j − 1)} and Np ∈ {(i, j + 1), (i + 1, j), (i + 1, j + 1)} for backward and forward minimization, respectively. Dc (k) is subsequently employed to update the distortion generated by choosing embedder Qk , Eq. (5) thus becomes
55 50
10
20
30
40
50
60
70
80
90
100
Image Index Number Fig. 3. Capacity increase using DPC or DPDC compared with that of SPC.
k = arg min Pw (m)(Qk , k) − Po (m)(Qk , k) + Dc (k)
k
To summarize, an embedder in DPC is chosen based on a random key, whereas it is chosen to minimize the distortion for each flipping in DPDC.
Average Per Pixel Distortion
0.7
III. E XPERIMENTAL R ESULTS A. Capacity and Visual Quality To show the capacity increase by employing DPC and DPDC compared with that of SPC, 100 images of a variety of sizes are used. These images are of different types (e.g., cartoons, tables, handwritten and text in different languages) and resolutions (e.g., 300dpi, 200dpi and 150dpi). The image sizes vary from 100 × 100 to 512 × 512. The visual distortion table [3] is used to quantitatively evaluate the visual quality of the watermarked image, which is defined in [5]. The increase in capacity represented in percentage from SPC to DPC or DPDC is shown in Fig. 3. The results further reinforce our observations that capacity has increased significantly using DPC or DPDC versus SPC, e.g., increase from 56% to 95% for the 100 test images. The average per pixel distortion (APPD) obtained for DPC, DPDC-MTC and DPDC-BFM is shown in Fig. 4. From the figure, it is not difficult to see that the average per pixel distortion has been further reduced with the use of DPDC-BFM. With appropriate selection of the lower distortion pixel to flip for both DPDC-MTC and DPDC-BFM, the achieved APPD is lower than that obtained by using DPC. It should be noted that Da can be high for those images of low resolutions such as 150dpi, as observed for the last several images in Fig. 4. This is due to the fact that there are few good patterns exist in thin strokes. Noticeably, with the use of DPC or DPDC, more than one pixel may be flipped in each 3 × 3 block. In this case, the main 2 × 2 block is timely reconstructed once a candidate is processed. The pattern used for distortion evaluation is taken as the reconstructed
−−DPC −−DPDC−MTC −−DPDC−BFM 0.65
0.6
0.55
0.5 10
20
30
40
50
60
70
80
90
100
Image Index Number Fig. 4. Comparisons of Average Per Pixel Distortion for DPC,DPDC-MTC and DPDC-BFM.
watermarked image (some neighboring candidates possibly have been flipped) with the center pixel taken from the original image so that better visual quality of the watermarked images can be preserved. The good visual quality of the watermarked images obtained by employing DPC and DPDCBFM is shown in Fig. 5, in which Da is 0.5852 and 0.5747, respectively. The results demonstrate that better visual quality of the watermarked image can be achieved using DPDC-BFM compared with that of DPC. IV. CONCLUSIONS In our previous paper [1], we have presented a high capacity data hiding scheme for binary images authentication based on the interlaced morphological binary wavelet transforms. Two
406
(a)
(b)
(c)
(d)
(e)
Fig. 5. Hiding Effects. (a) the original image of size 360 × 376 and 300dpi; (b) and (c) the watermarked image with 4036 bits embedded by employing DPC and DPDC-BFM, respectively. (d) and (e) the enlarged difference images, which are generated from the original image (a) and the watermarked image of (b) and (c), respectively. Note that the foreground of the image is painted in light gray; the black and dark gray dots are the pixels that are flipped from white to black and from black to white.
processing cases that are not intersected with each other are employed for orthogonal embedding in such a way that the capacity can be significantly increased. In this paper, we further propose a Backward-Forward Minimization method to minimize the distortion caused by employing double process case, which considers both those neighboring processed embeddable candidates and those unprocessed flippable candidates that may be affected by flipping the current pixel. In this way, the total visual distortion can be minimized. Experimental results validate the effectiveness of the proposed method. R EFERENCES [1] Huijuan Yang, Alex C. Kot and Susanto Rahardja and Xudong Jiang, “High Capacity Data Hiding for Binary Images in Morphological Wavelet Transform Domain”, Proc. of the IEEE Int. Conf. on Multimedia & Expo. (ICME’2007), pp. 1239-1242, 2-5 July 2007. [2] Q. Mei, E. K. Wong and N. Memon, “Data Hiding in Binary Text Document,” Proceedings of SPIE, vol. 4314, pp. 369-375, 2001. [3] Min Wu, and Bede Liu, “Data Hiding in Binary Images for Authentication and Annotation”, IEEE Trans. on Multimedia, vol. 6, no. 4, pp. 528-538, August 2004. [4] H. Y. Kim and de Queiroz, R. L., “Alteration-Locating Authentication Watermarking for Binary Images,” Proc. Int. Workshop on Digital Watermarking, pp. 125-136, 2004.
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