Essay: Improved block Encoding method for An Image Self-Recovery Approach

Abstract—The paper proposes a modified self-embedding watermarking scheme of the Fan Chen & Hongjie He [4] that improves the quality of the recovered image. The watermarking bits are of variable length that best approximates 5 MSB of the pixel values of a 2 x 2 block of original image compared to average intensity of the block. There are 7 different schemes that help to calculate the watermarking bits for a 2 x 2 block, including the average intensity of the block. That is, when the watermarking bits of a 2 x 2 block survive an attack, the greatest deviation of the recovered block from the original block is not greater than the deviation when the block is recovered using its average intensity. Thus the PSNR between the original and recovered image is relatively higher compared with the one when image recovery used only the average intensity of the block. The experimental results confirm this fact.

Keywords— self-embedding; fragile watermarking, self-recovery, Chaos.

I. INTRODUCTION

Self-embedding fragile watermarking methods help in authenticating the digital content, localizing the tampered parts if any and recovering the same by imperceptibly embedding additional data in the host image. They generally divide the host image into number of non-overlapping blocks of same size and generate for each one of the sub-blocks the watermarking bits. Part of the watermarking bits is used for restoration (called restoration/recovery bits) and the remaining is used for authenticating the block (called authentication bits). The restoration data are usually the quantized DCT[2] coefficients or VQ indices[8], or average intensity[2][4][6] etc., of the block. In general the length of the watermark of a block is of fixed length.

When average intensity is used to generate the restoration data of a block, it works well for the ‘smooth’ (homogeneous) blocks. That is, the difference between the original and recovered block is small. But for ‘rough’ (non-homogeneous) blocks, the difference between the original and recovered block is large and in turn can affect the quality of the recovered image. To overcome this problem, restoration data of variable length were proposed by classifying the blocks into various types.[3] But these schemes still lead to situations where they fail.

In [2] authors proposed the DCT-based alterable-capacity self-recovery fragile watermarking schemes. The image was divided into non-overlapping sub-blocks of size 8×8 and the sub-blocks were classified into various types according the block variance. The generated watermark has 3 parts: 20-bit significant-code, 3-bit type-code and detail-code with variable number of bits ranging from 0 to 78 and the watermark bits are embedded in 3 different blocks. The quality of recovered images improved as two copies of the significant-code of each block were embedded in different blocks, and the image inpainting method was used to recover the tampered blocks in the event two copies of significant-code embedded in other blocks had been destroyed. Since the block size is large, the tamper localization is affected and the quality of the recovered images is affected when the tampered region is large.

In [4] the authors proposed a chaos based self-embedding fragile watermarking with flexible watermark payload. The image is divided into non-overlapping blocks of size 2 x 2 and are classified as smooth or rough based on the difference between sum of the two largest values and sum of the two smallest values of the block. For a smooth block the watermark bits are given by the mean of the 5MSB of the values in the block while for a rough block the watermark bits consist of the mean of the 5MSB of the values in the block and detailed code (7 bits). That is, for a smooth block the length of the watermark is 5 where as for a rough block it is 12. As a result, the quality of the watermarked image, if the original image is smooth, will be high compared to that of a rough image. But the bits in the detailed code for a rough block help only in authenticating the block but not in recovery of the block. That is for both the smooth and rough blocks the recovery data is provided by the average block intensity of the 5MSB. Clearly when variance in the rough block is high the average intensity of the block does not properly recover the block.

In this paper we propose a self-embedding scheme with flexible watermark payload. The original image is divided into non-overlapping blocks of size 2 x 2. For each one of the blocks an appropriate watermark that can best approximate the 5 MSB of pixel values compared to block average is constructed. The security of the watermark is improved by its exclusive or operation with a sequence of random bits generated by a chaotic map and block map generated by sorting a chaotic sequence.

II. PROPOSED SCHEME

A. Self-embedding procedure

The proposed scheme has novel block encoding method but retains the block-neighbourhood tamper detection and recovery strategies from [4]. The self embedding procedure has the following steps.

1. Block Division: The original image X of size m x n is divided into non-overlapping blocks of size 2 x 2. The small block size generally enables better tamper detection. In our scheme it also enables better block encoding when the block is smooth. Let N= m/2 *n/2 be number of sub-blocks.

2. Block encoding:

We are using 7 different ways of constructing the compression code/restoration bits of the block including the block average intensity. We try to get closest values possible to the 5MSB of the pixels in the block. The details are as follows.

Case (1): When 3MSB of all 4 pixels are same

A. If the mode of Later 2 MSB(2LMSB) in the 4 pixels of the block is 3, then

the recovery bits are constructed as

00 | 3MSB | 2LMSB | position(3bits) | 2LMSB@other position

1 2 3 4 5

1 code 00 indicates it’s the case in which 3MSB of all 4 pixels are same (2 bits)

23MSB of all 4 pixels that is same.(3 bits)

32LMSB that are same in 3 positions in block (2 bits)

4code to indicate the 3 positions at which 2LMSB in the block are same. (3 bits)

52LMSB at the remaining position (2 bits)

B. If the mode of 2LMSB in the 4 pixels of the block is 2, then the recovery bits are constructed as

00 | 3MSB | 2LMSB | position (3bits) | 2LMSB

1 2 3 4 5

1 code 00 indicates it’s the case in which 3MSB of all 4 pixels are same (2 bits)

23MSB of all 4 pixels that is same.(3 bits)

32LMSB those are same in 2 positions in block (2 bits)

4code to indicate the 2 positions at which 2LMSB in the block are same. The principle diagonal position is coded as 0. (3 bits)

5average of 2LMSB at the remaining 2 position (2 bits)

Observe that the position codes 0, 3 are common in the above two situations of the case(1). But the reconstruction in the second situation for the position codes 0 and 3 are done treating them as in first situation. This doesn’t hinder the authentication procedure.

Case (2): When 3MSB of any 3 out of 4 pixels are same

1 2 3 4 5

01| 3MSB | position | 3MSB@remaining location | 2LMSB (average of 2LMSB@3positions corresponding to pos.)

1 code 01 indicates it’s the case in which 3MSB of 3 out of 4 pixels are same (2 bits)

23MSB of the 3 out of 4 pixels that is same.(3 bits)

3position code of the 3 positions in block at which 3MSB are same (2 bits)

43MSB of the remaining pixel.(3 bits)

5average of 2LMSB at the 3 posit
ions (2 bits)

While reconstructing we take the 2LMSB at the remaining position to be 01 so as to optimize the reconstruction value.

Case (3): When 3MSB of any 2 out of 4 pixels are same

10 | 3MSB | position | 3MSB | 4thMSB

1 2 3 4 5

1 code 10 indicates it’s the case in which 3MSB of 2 out of 4 pixels are same (2 bits)

23MSB of the one pair out of 2pairs of pixels that is same.(3 bits)

3position code of the pair of positions in block at which 3MSB are same (3 bits)

4average of 3MSB of the remaining pair of pixel. .(3 bits)

5optimized bit for the 4th bit of all 4 pixels (1 bits) considering 4th and 5th bits of all 4 pixels.

We may observe that we are trying to nearest values of the 4 pixels using 4MSB of the 4 pixels.

Case (4): This case is a general case that is calculated for every block and contains 4 sub-cases of which the block average intensity is one.

A. 11 | 00 | 5MSB of average intensity of the block

1 2 3

1code 11 indicates that it’s different from all above cases (2 bits)

2code 00 indicates that it’s the block average intensity (2 bits)

3The 5MSB of the block average intensity (5 bits)

B. 11| XX | AA |AA | AA | AA

1 2 3

1code 11 indicates that it’s different from all above cases (2 bits)

2code 01/10/11 indicates the divisor 12/16/19 respectively (2 bits)

3The optimizing multiples of 36/48/57 according to the code in 2 (8 bits)

Of all these schemes we pick the best one i.e. the one that can reconstruct the closest values for the 5MSB in the block. So, except the block average intensity case, all schemes generate the watermark of length 12.

S.No Block 5MSB Best case Restored Mean intensity Difference against block average

1 1 164 16

2 2 110 52

3 3 124 192

4 4 168 80

Table.1. Examples of block encoding scheme compared with block mean intensity.

3. Chaotic sequence generation: We use a chaotic map and generate a pseudo random sequence. Then according to the length of the optimal watermark of the block, we select the same number of bits from the chaotic sequence and perform the exclusive operation between the watermark and the selected chaotic sequence bits.

4. Block Mapping: With a different set of initial parameters we generate a chaotic sequence R= of length N, sort it to get an ordered index set A= such that for i=1, 2,..N. Now using the set A we define the block mapping as . i.e. ith block is mapped to block.

5. Watermark embedding: Once the encrypted watermark is ready, the watermark is embedded into the 3LSB of the mapped block.

B. Watermark extraction and tamper detection:

The watermark extraction is reverse process of watermark embedding. For ith 2 x 2 block of the received image, the watermark bits Wi= 1} are generated and the embedded watermark bits Ei= 1} from the LSB of its mapped block are extracted. We construct the watermark validation mark (WVM) , D = N } for each block as follows.

Initially, if the generated watermark of a block did not match with that of the extracted then we do not immediately conclude that it’s a tampered block. To ascertain further if the block is tampered or not, we construct a tamper detection mark for each block based on the initial tamper detection mark

Let TiD denote the number of non-zero neighbours in 3 x 3 neighbourhood of ith element in the binary matrix D.

The initial tamper detection mark Tinitial = {tio} is constructed as follows.

The final tamper detection mark Tfinal= fi} is constructed based on both the initial tamper detection mark as follows..

III. EXPERIMENTAL RESULTS

Extensive experiments were conducted to test the effectiveness of the scheme and the results were compared with the schemes proposed in [4] and [2]. We use the same tamper detection procedure as in [4] and demonstrate the effectiveness of the proposed block encoding scheme. The parameters used for comparison are as follows.

1. Code quality: PSNR between reconstructed image and original one.

2. Invisibility: (a) Quality of watermarked image: PSNR between watermarked image and original one. (b) Watermark payload.

3. Tamper detection performance: (a) Probability of False Acceptance (PFA) is the probability of classifying the tampered block as not tampered. (b) Probability of False Rejection (PFR) is the probability of classifying the non-tampered block as tampered. Clearly, the higher the PFR, the lower the PSNR between the recovered and original image.

4. Recovery performance: PSNR between original image and recovered image.

The table 2 shows the comparison of code quality for different images of different methods. We observe that the code quality of proposed method is superior. That is because the code length is smaller for smooth blocks and for rough it’s longer.

The table: 3 gives the comparison of quality of various watermarked image and the watermark payload. The watermark payload of the methods [4][2] is variable. The shortest being provided by [2]. The PSNR value of the watermarked image of the proposed method is around 37.9 for all the images.

Image Code Quality (dB)

Proposed [ 4 ] [ 2 ]

Lena 33.16 33.04 33.96

Peppers 33.10 32.21 32.74

Gold hill 32.37 31.79 32.47

Barbara 31.13 29.92 26.57

Man 32.42 31.21 30.44

Flintstones 30.44 28.86 25.19

Baboon 30.79 27.48 25.56

Boat 31.99 30.32 33.41

Table 2: Comparison of coding efficiency for different images

Image Watermark payload Watermarked image Quality (dB)

Ours [ 4 ] [ 2 ] Ours [ 4 ] [ 2 ]

Lena 2.66 1.63 0.93 37.95 44.12 48.0

Peppers 2.67 1.62 0.94 37.92 43.81 48.01

Gold hill 2.70 1.70 1.03 37.91 43.2 47.27

Barbara 2.71 1.93 1.06 37.94 41.73 47.10

Man 2.68 1.77 1.09 37.94 42.82 46.90

Flintstones 2.74 1.94 1.14 37.88 41.90 46.54

Baboon 2.76 2.19 1.28 37.93 39.79 45.81

Boat 2.74 1.62 0.82 37.92 44.2 48.59

Table 3: Performance comparison of invisibility and watermark payload for different images.

To test the effectiveness of the proposed method, we applied the scheme to the rough image baboon, moderately rough image boat and smooth image Lena, all of size 512 x 512. The baboon image was tampered with 48.07% tampering ratio, the boat image tampered with 26.5% tamper ratio with 20 rectangles of size 6 x 432 pixels evenly spaced by 10 pixels, and the Lena image was tampered with 13.6% tamper ratio with the portion of the Flintstones image at the same region (collage attack). Since we used the same tamper detection scheme as [4], we have the same detected tampered region. Also the PFA and PFR are same.

The scheme in [2] though detected the tampered region with 97% accuracy its PFR (probability of false rejection) is quite high (see (c) and (f) of Fig: 3). The PFR of the scheme[2] is 53.5% for the boat tampering and hence the quality of the recovered image is relatively poor as can be observed from the figures (c) (f) (i) in Fig:4. The reason is that their basic blocks are of size 8 x 8. In contrast the PFR of the proposed scheme is about 3.5%, because we have the block sizes to be 2 x 2.

S.No TR PFA % PFR % PSNR

Ours [2] Ours [2] Ours [ 4 ] [2 ]

1 48.07% 0.01 0.93 0.36 32.94 26.32 24.79 21.74

2 26.5% 1.5 2.34 3.5 53.5 29.64 27.72 18.23

3 13.6% 1.31 2.48 0.16 1.89 38.45 35.81 32.42

Table 4: Performance comparison of tamper detection and recovery

A. Abbreviations and Acronyms

IV CONCLUSION

In this paper we proposed novel method of constructing the compression code that takes into consideration the roughness of a 2 x 2 image block. Then the compression code is encrypted to improve the security and embedded into block using block mapping function. The effectiveness of the method in terms of the quality of the recovered image was demonstrated under same tamper detection method and also against a different method.

REFERENCES

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