### HALFTONE VISUAL CRYPTOGRAPHY VIA ERROR DIFFUSION PDF

Request PDF on ResearchGate | Halftone visual cryptography via error diffusion. | Halftone visual cryptography (HVC) enlarges the area of visual cryptography. Request PDF on ResearchGate | Halftone Visual Cryptography Via Error Diffusion | Halftone visual cryptography (HVC) enlarges the area of. Halftone visual cryptography (HVC) enlarges the area of visual cryptography by the addition of digital halftoning techniques. In particular, in.

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Skip to main content. Log In Sign Up. In particular, in visual secret sharing schemes, a secret image can be encoded into halftone shares taking meaningful visual information. In this paper, HVC construction methods based on error diffusion vizual proposed. The secret image is con- currently embedded into binary valued shares while these shares are halftoned by error diffusion—the workhorse standard of halftoning algorithms. Error diffusion has low complexity and provides cryptograpuy shares with good image quality.

A reconstructed secret image, obtained by stacking qualified shares together, does not suffer from cross interference of share images. Factors affecting the share image quality and the contrast of the recon- structed image are discussed. Simulation results show several Fig. In a 2-out-of-2 scheme, a secret pixel is encoded into two subpixels in each of the two shares. Particularly in a -out-of- visual secret sharing VSS scheme, a secret image is cryptographically encoded into shares.

Crytography share resembles a random binary pattern.

## Halftone Visual Cryptography Through Error Diffusion

haoftone The shares are then copied onto transparencies, respectively, and distributed among participants.

The secret images can be vi- sually revealed by stacking together any or more transparen- Fig. Example of 2-out-of-2 scheme. The secret image is encoded into two cies of the shares and no cryptographic computation is needed. However, by inspecting less than shares, one cannot gain any information about the secret image, even if infinite computa- tional power is available. Then, the first copyright protection [2], watermarking [3], visual authentica- two subpixels in that column are assigned to share 1 diffuskon the tion, and identification [4].

Independent To illustrate the principles of VSS, consider a simple of whether is black ha,ftone white, is encoded into two subpixels 2-out-of-2 VSS scheme shown in Fig. Each pixel taken of black—white or white—black with equal probabilities. Thus from a secret binary image is encoded into a pair of black and an individual share gives no clue as whether is black or white [5], [6].

Now consider the superposition of the two shares as white subpixels in each of the two shares. If the pixel is black, the pixel in Fig. The selection is random such that superposition of the two shares outputs two black subpixels corresponding to a halgtone level 1.

If is white, it results in one white and one black subpixel, corresponding to a gray level Manuscript received June 24, ; revised April 22, First published June 16, ; current version published August 14, The associate halftons information of the secret image.

According to the encoding rule shown in Fig. Superimposing the two shares cordia Technologies Inc. The decoded Digital Object Identifier In the proposed HVC secret image since each pixel is expanded to two subpixels in methods, pixels that carry the secret image information are each share. These pixels The 2-out-of-2 VSS scheme demonstrated above is a special are then naturally embedded into the halftone shares when the case of the -out-of- VSS scheme [1].

Error diffusion, a simple and an optimal contrast -out-of- scheme to alleviate the problem widely used halftone method that yields a good compromise of contrast loss in the reconstructed images [7]. An access structure is a specification algorithm.

### Halftone Visual Cryptography Through Error Diffusion – Semantic Scholar

Error diffusion then halftones the input grayscale of all bisual qualified and forbidden subsets of shares. The partic- images but does not change the predetermined pixels. The concept of away the quantization error into the neighboring grayscale VSS has also been extended such that the secret image can be a pixels so that a visually pleasing halftone image is obtained.

In our approach, encoding of the secret information vvisual The aforementioned VC methods all have the disadvantage extra constraints on the error diffusion. However, the additional that the shares consisting of random pixel patterns do not take quantization error introduced by the encoding of the secret any visual information and may lead to suspicion of secret in- information is diffused away by error diffusion halfyone the neigh- formation encryption.

Shares showing meaningful images are boring grayscale pixels. Thus, visually pleasing halftone shares more desirable in terms of the steganography aspect. To al- can still be obtained. In EVC, the shares not image immune to the interference from the share images. The only cruptography the secret information, but are also themselves first method employs a complementary halftone image pair. Secret images can still be decoded The second method deliberately introduces homogeneously when qualified shares are stacked together.

Shares in an EVC distributed black pixels into each share, which has the advan- scheme, however, provide very low quality visual information tage that complementary image pairs are not needed. The diffuskon and suffer from low contrast between hypergraph black and method exploits the fact that the halftoning of the grayscale im- white pixels. Nakajima extended the EVC approach to natural ages alone may generate a sufficient number of cryptogra;hy pixels to grayscale images to improve the image quality [13].

Fu and Au satisfy the contrast condition of image decoding. A black pixel generated halftone shares that carry visual information by using is deliberately introduced only when a sufficient number of joint visual cryptography and watermarking [3]. Thus, complementary proposed a method to generate meaningful halftone haldtone by shares are also not required. With fewer constraints on error using threshold arrays [14]. The crhptography shortcomings with these diffusion, the third method has the potential to obtain shares methods are that either the security property is not strictly guar- showing natural images with fine details.

The proposed cryptography HVC based on the principle of void and visyal halftone VSS construction methods are computationally effi- dithering [5], [6], [15].

Compared with EVC, the image quality of cient and, as verified by extensive simulations, can produce vi- the shares is greatly eiffusion and the reconstructed image con- sually pleasing halftone shares. The security of the produced tains much less cross interference from the share images.

Our proposed halftone VSS methods, while information into preexisting uncoded halftone shares. While this exemplified for the VSS scheme, apply to visual encryption and method is effective at generating shares with pleasing visual re- visual authenticaiton.

Moreover, using the void The remaining sections of this paper are organized as follows. The image quality of the image may bear residual features of the original halftone images. Topics including improvement cryptograph share image of complimentary shares is required to prevent the share visual quality, comparison of different methods, and recovery of con- information from showing on the decoded image.

To show the effective- To further improve the image quality of the halftone shares ness of our proposed methods, simulation results are presented and completely remove the cross interference of the share images in Section VIII.

Finally, conclusions are presented in Section IX. Instead of modifying halftone images II. Please refer to [1] and [8] for more details on VSS. An introduction of error diffusion is also provided. Visual Secret Sharing Scheme Fig. Block diagram for binary error diffusion.

Errog pixel f m; n is passed Let be a set of elements called participants. The difference between these two pixels is diffused to halfttone neighboring pixels by A VC scheme for a set of participants is a method to encode means of the filter h k; l.

Let denote the set of all subsets of and let andIf the given secret pixel is black whiteis randomly where. We refer to members of as selected from. The cryptograhy collections can be obtained qualified sets and call members of forbidden sets. The by permuting the columns of the halftlne basis matrix pair is called the access structure of the scheme or in all possible ways [18].

Two matrices and are called basis ma- Any qualified set of participants can visually de- trices, if and satisfy the following two conditions [18]: Ifthe formation of [8], [18]. A visual recovery for a set row vectors andobtained by performing OR opera- consists of copying the shares given to the participants in tion on rows of andrespectively, sat- onto transparencies and then stacking them together. The par- isfy and. Ifone forming any cryptographic computation.

VSS is characterized of the two matrices, formed, respectively, by ex- by two parameters: See [7] for construction structed image [7]. As an For each secret binary pixel that is encoded into subpixels example, the and in a 2-out-of-2 scheme are shown as in each of the shares, these subpixels can be described as an follows: Boolean matrixwhere a value 0 corresponds to a white subpixel and a value 1 corresponds to a black subpixel.

The gray level of the reconstructed pixelobtained by superimposing the transparencies in a participant corresponds to the encoding of a white secret pixel and subsetis proportional to the Hamming corresponds to the encoding of a black secret pixel. Error diffusion is a simple, yet efficient algorithm to halftone Definition 2. Let be an access structure on a grayscale image. The quantization error at each pixel is fil- a set of participants. Two collections of Boolean ma- tered and fed back to a set of future input samples.

Any qualified subset and is the output quantized pixel value [16], [19]. The first the secret image by stacking the corresponding trans- component is the thresholding block where the output parencies. Formally, for a matrixis given by the row vectors. It holds that for all if and for all.

The second the reconstructed pixel as black or white. Any forbidden subset difference between and. Finally, we can com- has no information of the se- pute as cret image.

Formally, the two collectionsobtained by extracting rows from each matrix 3 inare indistinguishable.

The weights are given by: As an example, the widely used Floyd—Steinberg error filter is shown in Fig. The weights of the filter are given by,and.