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Visual secret sharing (VSS) is one of the cryptographic techniques of Image secret sharing scheme (ISSS) that performs encoding of secret message image (text or picture) into noise like black and white images, which are called as shares. Shares are stacked together and secret message image is decoded using human visual system. One of the major drawbacks of this scheme is its poor contrast of the recovered image, which improves if computational device is available while decoding. In this paper, we propose to improve poor contrast of classical VSS schemes for text or alphanumeric secret messages and low entropy images. Initially, stacked image is binarized using dynamic threshold value. A mathematical morphological operation is applied on the stacked image to enhance contrast of the reconstructed image. Moreover, a method is proposed that allows the size of the structuring element to change according to the contrast and the size of a stacked image. We perform experiments for different types of VSS schemes, different share patterns, different share types (rectangle and circle), and low entropy images. Experimental results demonstrate the efficacy of the proposed scheme.

An image secret sharing scheme (ISSS) is a cryptographic technique to hide secret message image into meaningless images, which reveal no information about the secret message; called as shares. Typically, the secret message image contains text or picture where text is short alphanumeric message or password. Super- imposition of all shares reveals secret message. There are two major categories in ISSS: one is the visual secret sharing (VSS) scheme and the other is the polynomial-based ISSS (PISSS). VSS scheme is also known as visual cryptography scheme (VCS) [

Another category of VSS scheme proposed with two decoding options, where the secret image is revealed both by stacking the shares and by computation. This scheme is called as Two-in-one image secret sharing scheme (TiOISSS) [

In this paper, we propose a mathematical morphology based scheme to achieve almost ideal contrast of classical VSS schemes for text message image. Here, image after stacking at receiver is considered as an input. Otsu’s method is utilized to convert grayscale image into binary image. Further, image contrast enhances by mathematical morphological operation using appropriate size of square structuring element (SE). Notably, the proposed method computes size of SE from given input image itself.

Typically, for a given stacked text message image, impulse noise (pepper) is present. Briefly describing, few popular techniques to remove this impulse noise are isolated pixel removal technique, and adaptive median filter. Here, isolated pixel removal algorithm removes only isolated pixels, whereas probability of two or more pixels in a cluster is very high. Same way, adaptive median filter works well if the spatial density of the impulse noise is not very large. Hence, mathematical morphological opening operation is employed to remove impulse noise.

A possible application scenario of two options decoding as described in [

The rest of this paper is organized as follows: Section 2 describes the proposed scheme. Section 3 shows experimental results and further discussion of the proposed scheme, and in Section 4, we conclude this paper.

Analogous to second step of TiOISSS, stacked image is considered as an input image. Stacked grayscale image has mainly foreground message and noisy background. Primarily, image is required to be converted into binary using optimum threshold value. Though histograms of the different input images represent bi-modal behavior, resultant threshold values vary in wide range. Hence, Otsu’s method [

where

Set erosion and dilation are formulated based on structuring elements (SEs). SE is a small set or subimage, used to probe an image under study for properties of interest. Here, we employ standard symmetric square binary SE of value 1. However, optimum SE width (W) is required to select for generalized solutions, as higher W of SE eliminates message content whereas lower W of SE keeps noise elements. Therefore, probability of noise cluster is calculated for the optimum value of W. Here, input stacked result has typically white background (value 0) with pepper noise with black foreground message (value 1), whereas SE of width W eliminates W ´ W noise cluster. In stacked image, probability of black pixel is defined as,

Whereas, probability of noise cluster of square W elements is,

While, possibility of occurrence of such noise cluster in M ´ N size image is,

The probability of noise cluster in computed image reduces exponentially with increasing dimension of SE. This is explained as follows. Here, as image size increases, _{n}), which is very high compared to the

where k = number of attempts to generate noise cluster

Using Equation (3) and Equation (4),

If we solve Equation (5) for exact solution, we get

Since P(B) is always < 1, denominator turns to positive value and as W is always positive integer, we do not consider the negative solution. Additionally, for float valued W, next odd value is selected. Here, small change in P(B) makes larger change in W, whereas numerator terms comparatively affects less. Logically, P(B), probability of black pixels, is related to contrast, so as it changes, W changes rapidly. Whereas for same P(B) value, size of image is not much effected comparatively. Practically, for highly noisy images, W has large values. Very large value of W erodes secret message. Hence, cut-off value of W is set to 9. This cut-off can be increased provided secret message width allows.

Experiments are conducted for different stacked messages [

Here,

Lastly, results showed for (2, 4) VSS using OR and XOR decryptions [

Results show that the proposed scheme works well for different types of VSS schemes, different share patterns, and different share types. Where

Stacked Image Size (M ´ N) | Threshold Value | Structuring Element Size (Calculated) | Structuring Element Size (Experimental) | Probability of Black Pixels P (B) | |
---|---|---|---|---|---|

228 × 228 | 112 | 5.57 | 7 | 0.56 | |

228 × 228 | 112 | 5.55 | 7 | 0.56 | |

392 × 419 | 64 | 13.6 | 9 | 0.9 | |

272 × 272 | 107 | 5.67 | 7 | 0.57 | |

272 × 272 | 107 | 5.72 | 7 | 0.58 | |

240 × 120 | 112 | 6.11 | 7 | 0.63 | |

240 × 120 | 96 | 8.87 | 9 | 0.8 | |

270 × 270 | 64 | 5.42 | 7 | 0.54 | |

270 × 270 | 64 | 5.36 | 7 | 0.53 | |

360 × 255 | 80 | 4.98 | 5 | 0.48 | |

221 × 221 | 143 | 3.98 | 5 | 0.33 | |

221 × 221 | 46 | 4.28 | 5 | 0.38 | |

540 × 360 | 86 | 9.42 | 9 | 0.81 |

Additionally, we compare proposed method with the Wu et al. [

In this paper, we propose a generalized solution using mathematical morphological opening operation to remove noise clusters from the stacked message image of VSS. Stacked grayscale image is converted to binary image with distinct threshold value using Otsu’s algorithm. Mathematical morphological opening operation is applied on resultant image. Width of square SE is formulated from the stacked image with higher cut-off value of 9. Here, contrast of the stacked image plays significance role compared to size. Even small difference in contrast value makes large variation in SE size whereas for the similar contrast values, SE varies little. The removal of noise from the image improves the contrast and reconstructs received image from recognizable to almost ideal contrast. Here, secret message will be eroded if the width of the secret message is less than the experimental SE. The proposed method works well for the application scenario of two options decoding techniques. Additionally, proposed scheme can be implemented for handheld devices like mobile phone.

Yogesh K.Meghrajani,Himanshu S.Mazumdar, (2015) Enhanced Contrast of Reconstructed Image for Image Secret Sharing Scheme Using Mathematical Morphology. Journal of Information Security,06,273-279. doi: 10.4236/jis.2015.64027