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Visual cryptography scheme is initiated to securely encode a secret image into multiple shares. The secret can be reconstructed by overlaying the shares, making it perceptible to the human visual system. Random grid visual cryptography offers key advantages over traditional visual cryptography such as avoiding pixel expansion and the requirement for intricate codebook design. This paper is intended to conduct a critical analysis and implementation of various algorithms in random grid visual cryptography from 2011 to 2022. The focal parameters of this study are theoretical contrast, experimental contrast and visual quality. Experiments were done on binary images for (k, n) algorithms considering different values of threshold. By implementing and analysing the results, the scheme which gives the optimal result is identified. [ABSTRACT FROM AUTHOR]

Quantum visual secret sharing scheme combines the traditional visual secret sharing scheme with quantum properties to improve the security of secret information. However, all existing quantum visual secret sharing schemes encode a single pixel as a quantum superposition state. Each pixel requires n qubits for encoding. The number of qubits required grows proportionally to the number of pixels, which is unfavorable when the secret image is large. To reduce the number of qubits used, we propose a (n, n)-threshold quantum visual secret sharing scheme based on position superposition. In the secret sharing phase, the position and the encoded color corresponding to the position of the image are encoded as a quantum superposition state simultaneously. The whole secret image is encoded only once instead of encoding individual pixels. Only 2 m + n qubits are required for a secret image of size 2 m × 2 m . Then, the qubits encoding the position and the color of the secret image are distributed to n participants. In the recovery phase, n participants work together to recover the secret image by a quantum XOR operation on the qubits encoding the color. Simulations have been carried out to verify the practical feasibility of this scheme. Our scheme reduces the number of qubits used in the secret sharing process compared to previous quantum visual secret sharing schemes. In addition, there is no need to design the codebook in advance and the secret image can be fully recovered. [ABSTRACT FROM AUTHOR]

Visual cryptography (VC) is a cryptographic technique that allows the encryption of a secret image into multiple shares. When the shares of a qualified subset are superimposed, the original secret image can be visually recovered. Region incremental visual cryptography (RIVC) is a class of visual cryptography; it encrypts a single image into a shared image with multiple levels of secrecy, and when decrypted, the secret image of each region can be gradually recovered. Traditional VC encrypts two black-and-white images, and its recovery method is equivalent to a logical OR operation. To obtain a better recognizability of the restored image, the XORoperator becomes a simple and efficient method of encryption and decryption. Because the XOR operation needs extra cost or equipment, if the equipment cannot be obtained, the scheme can be more flexible if the secret can still be restored by using OR decryption (superimpose). In this paper, we propose a novel RIVC that allows encoding multiple secret regions of a secret image into n random grids. Both the OR operation and the XOR operation can be used as operations during decryption. The proposed scheme is evaluated by simulation, and the experimental result shows its correctness, effectiveness and practicability. [ABSTRACT FROM AUTHOR]

Visual cryptography scheme is a method of encrypting secret image into n noiselike shares. The secret im)age can be reconstructed by stacking adequate shares. In the past two decades, many schemes have been proposed to realize the cheating prevention visual cryptography scheme (CPVCS). Significantly, Ren et al. [9] first introduced the idea of CPVCS with the help of Latin square. Inspired by their work, in this article, a new reliable scheme is proposed. More precisely, to facilitate the certification process, we embed meaningful characters into the randomly chosen authentication patterns in each divided blocks. Furthermore, we fix the security vulnerability in the stacked results of share Sд and verification Verд, where 1 ≤ д ≤ n. Since the improved scheme encrypts the secret image by utilizing random grids, the generated shares have no pixel expansion. Finally, theoretical analysis and experimental results are conducted to evaluate the efficiency and security of the proposed scheme. [ABSTRACT FROM AUTHOR]

Visual cryptography (VC) is a cryptographic technique that allows the encryption of a secret image into multiple shares. When the shares of a qualified subset are superimposed, the original secret image can be visually recovered. Region incremental visual cryptography (RIVC) is a class of visual cryptography; it encrypts a single image into a shared image with multiple levels of secrecy, and when decrypted, the secret image of each region can be gradually recovered. Traditional VC encrypts two black-and-white images, and its recovery method is equivalent to a logical OR operation. To obtain a better recognizability of the restored image, the XORoperator becomes a simple and efficient method of encryption and decryption. Because the XOR operation needs extra cost or equipment, if the equipment cannot be obtained, the scheme can be more flexible if the secret can still be restored by using OR decryption (superimpose). In this paper, we propose a novel RIVC that allows encoding multiple secret regions of a secret image into n random grids. Both the OR operation and the XOR operation can be used as operations during decryption. The proposed scheme is evaluated by simulation, and the experimental result shows its correctness, effectiveness and practicability.

Essential Secret Image Sharing (ESIS) is a method to decompose a secret image into two groups of shares, where one group is essential and the other group is non-essential. In this method, recovery of secret image is possible only if threshold number of shares along with all essential shares will be present. Existing state of art has some limitations such as different share size, complex computation, random pattern (meaningless) share, explicit codebook requirement, pixel expansion and constraint on image type. These limitations restrict the applications of the secret image sharing. In this paper, a novel approach of generating shares of similar size as that of the secret image has been proposed. The proposed "essential secret image sharing approach with same size of meaningful shares" (ESISMS) scheme produces meaningful shares based on bitwise XORing. This proposed approach resolves all the above stated issues and the advantages and applicability of this approach have been demonstrated by the theoretical analysis and experimental results. [ABSTRACT FROM AUTHOR]

Since Noar and Shamir introduced visual cryptography scheme (VCS), the cheating problem of VCS has absorbed much attention of scholars. The current researches on cheating immune have one or more of these serious disadvantages: (1) each share has extra pixel expansion, (2) some methods need extra verification shares to determine the share is genuine or not, (3) some schemes require a higher encryption/decryption overhead, and (4) the authentication procedure needs a trusted third party. In order to establish a novel cheating immune visual cryptography scheme (CIVCS) without pixel expansion, this paper generates n original shares by using random grid based visual cryptography scheme (RG-based VCS) and stamps authentication patterns on original shares to obtain verifiable shares, where the authentication patterns are three adjacent and non-intersect concentric solid black rings. In authentication phase, the authentication patterns can be revealed respectively by stacking any two verifiable shares in several ways, including rotating one of the two shares by 90 ∘ , 180 ∘ , and 270 ∘ counterclockwise. The main contribution of this paper is that we propose a novel CIVCS without the above deficiencies. Furthermore, experimental results and theoretical proofs are provided for illustrating the effectiveness of the proposed CIVCS. [ABSTRACT FROM AUTHOR]

Traditional visual secret sharing (VSS) encodes the original secret image into n shares, and each share is of equal importance. However, in some scenarios, we need to make a difference between the participants according to the levels of their importance. Therefore, the capability of each share to recover the original secret image will be different. In this paper, we proposed a weighted (k,n)-threshold random grid VSS(RG-VSS) with multiple decrytions and lossless recovery. When we get k or more shares for decryption, we will recover different levels of the original image because of the different weights of the shares. More importantly, the secret information can be recovered by OR and XOR operations in our scheme. When we get all the n shares and using the XOR operation to recover the image, we can recover the secret information losslessly. The experimental results and analyses show that our scheme outperforms the related schemes.

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As in recent years digital data transmission and image application have been increasing, maintaining secure transmission of image is of high importance. Image Encryption is implemented to achieve security on image applications. This paper exhibits a survey on various existing image encryption techniques. The paper mainly focuses on two types: Image encryption with Key(s) and Image Encryption without Key(s). In addition it also describes several properties of a good image encryption technique. The paper presents a survey of most popular algorithms and research papers that are related with different image encryption techniques.

This article points out the fallacies in the theory and its implementation proposed by Kaur and Khanna. They have set out a cancelable biometric-based template protection method to address the security and privacy concerns emerging from the use of biometric systems. There are three major issues associated with the method proposed in their study. The first issue relates to the mathematical fallacy in the proof of the random distance method. The second issue concerns the claim of dimension-reduction by 50%, despite the fact that RDM does not preserve inter- and intra-user variations. The third issue is in salting the feature vectors using the OR operation between the feature vectors and random grid (RG), which is incorrect. As it will result in revealing partial information only and will not increase entropy. Furthermore, they have stated that their approach results in noninvertibility using the median filtering. However, its implementation is flawed. [ABSTRACT FROM AUTHOR]

To reduce the pixel expansion problem in color–black-and-white visual cryptography schemes (CBW-VCSs) and to provide flexible sharing strategy simultaneously, a random grid based CBW-VCS (RG-CBW-VCS) for general access structure (GAS) is proposed in this paper. First of all, the concept of random grid is extended to color pixel domain, and the XOR operation for color pixels is defined. By adopting this operation, a scheme for RG-CBW-VCS which implements the GAS is introduced. The proposed method is further extended to realize the generalized GAS (GGAS), where implementing complicated sharing strategy becomes available. Theoretical analysis on the proposed method are given to prove the security and contrast conditions, as well as the calculation of contrast. Experimental results are exhibited to show that optimal pixel expansion is achieved by the proposed method. • The concept of random grid is extended to color image domain, and XOR operation for color pixels is defined. • A scheme of RG-CBW-VCS for GAS is proposed based on the XOR operation for color pixels. • The proposed RG-CBW-VCS for GAS is extended to realize generalized GAS (GGAS). [ABSTRACT FROM AUTHOR]

Random grid (RG) is an alternative approach to realize a visual secret sharing (VSS) scheme. RG-based VSS has merits such as no pixel expansion and no tailor-made matrix requirement. Recently, many investigations on RG-based VSS are made. However, they need further improvements. In this paper, we obtain some improvements on RG-based VSS. Actually, two improved schemes are proposed, namely RG-based VSS for general access structure (GAS) with improved contrast and extended RG-based VSS with improved access structure. The first scheme can achieve better contrast than previous schemes. The second scheme reduces the chance of suspicion on secret image encryption by generating meaningful shares instead of noise-like shares in the first scheme, and improves the access structure from (k, k) to GAS while maintaining the property that the contrast of the recovered image is traded with that of share images by setting a certain parameter from small to large. Finally, theoretical analyses and experimental results are provided to demonstrate the effectiveness and advantages of the proposed schemes. [ABSTRACT FROM AUTHOR]

Visual secret sharing (VSS) technology encodes a secret image into some share images for sharing some classified information. Only when the participants gather and stack their share pictures the secret image would be reconstructed and recognizable by the human visual system. Two well-known encoding ways of VSS, visual cryptography (VC) and random grid (RG), have been developed in recent years. As both VC and RG have been considered as a secure way for communicating with high security, they have been pointed out with cheating problems. In this paper, we propose two RG-based VSS schemes with fraud prevention for the cases of (2,n) and (k,n). The experimental results and the analysis of security and contrast show that the proposed method is efficient and practical. [ABSTRACT FROM AUTHOR]

Visual secret sharing is a method used to secure images by converting a secret image into multiple shares so that the original image cannot be recognized from individual shares, and no calculations are required during the image decryption, but the original image can be visually seen by stacking the shares. However, one of the significant challenges in this method is the increased size of the shares and the recovered image, which is called pixel expansion. Researchers have proposed several methods to solve this problem, but many of them are limited to binary images, and they cannot handle gray and color images without converting them to binary. This study proposes a novel fuzzy random grid-based method to directly encrypt gray and color images without any pixel expansions. In this method, fuzzy random grids with decimal values between 0.0 to 1.0 are generated during the encryption stage, and fuzzy operators are used for the decryption stage. The evaluation results demonstrate the ability of the proposed solution in encrypting gray and color images without converting them to binary and without any pixel expansions. The individual shares of the proposed method do not reveal any information from the original image, making it a secure method. The quality of the decrypted images has been evaluated using both subjective and objective evaluation methods such as PSNR and SSIM metrics, which show state-of-the-art results. • Visual Secret Sharing is developed for encrypting gray and color images. • Visual cryptography of gray and color images without pixel expansion and without binary conversion. • Secure encrypted and acceptable-quality encrypted gray and color images using fuzzy random grids. • Introducing an extendable fuzzy OR operator for fuzzy random grids. [ABSTRACT FROM AUTHOR]

A visual cryptography scheme (VCS) allows one to decrypt images without any knowledge of cryptography and computational efforts. VCS allows secret image sharing such that we can divide the original image into meaningful or nonmeaningful shares. The shares are distributed among participants; during decryption, the original secret image is recovered through stacking all or some of the shares by the human visual system. Various techniques of visual cryptography were constructed mainly for binary images but later, they were enhanced to handle gray-scale or color images. This article focuses on the study of various visual cryptographic schemes and analyses the performance on the basis of various parameters such as, pixel expansion, type of shares generated, image format, number of secret images, encryption method, etc.. In the proposed work, we give a precise and complete review of various visual cryptographic schemes based on different research works related to this area and cite the relevant literature. [ABSTRACT FROM AUTHOR]

The phase ambiguity is the main difficulty in the phase unwrapping of three-step phase-shifting. In this paper, a novel three-step phase-shifting phase unwrapping method based on sparse depth map is proposed. The sparse depth map is an auxiliary in phase unwrapping for depth acquisition. Firstly, a novel random grid pattern is proposed based on the random speckle and Delaunay triangulation in this algorithm. Secondly, the sparse depth can be calculated based on the proposed random grid. Finally, the phase unwrapping sequence is designed based on proposed quality of relative phase map (quality map). The calculated sparse depth is used as an auxiliary to solve the absolute phase according to designed phase unwrapping sequence. The depth can be acquired based on proposed phase unwrapping algorithm. In the experiment, the reliability of the proposed phase unwrapping algorithm has been verified in simple and complex scenes respectively. The phase ambiguity can be avoided by this method. Experiments show that this method has advantages in both accuracy and resolution. [ABSTRACT FROM AUTHOR]

This study proposes a user‐friendly XOR‐based visual secret sharing scheme using random grids. In some visual secret sharing schemes, problems such as pixel expansion or noisy and meaningless shares may be encountered. In the proposed scheme, different regions in the shared image will have different brightness levels depending on the cover image's pixel values so that the generated shares contain information regarding the cover image and are not just a meaningless noisy image. This can overcome the difficulty in recovering the secret image in cases wherein the shares were mixed up by mistake. Furthermore, the dimension of the share is the same as the secret image and there are no pixel expansion problems. The size of the recovered secret image is consistent with the size of the original secret image, and there are no changes in scaling. Lastly, although one of the generated share is a complementary cover image, the image quality of the recovered secret image is still favourable when the secret image is recovered. The experimental and analysis results demonstrate that the proposed scheme is more effective than other schemes. [ABSTRACT FROM AUTHOR]

Pixel expansion and contrast are two major performance parameters for visual cryptography scheme (VCS), which is a type of secret image sharing. Random Grid (RG) is an alternative approach to solve the pixel expansion problem. Chen and Tsao proposed the first (k, n) RGbased VCS, and then Guo et al., Wu et al., Shyu, and Yan et al. significantly improved the contrast in recent years. However, the investigations on improving the contrast of threshold RG-based VCS are not sufficient. In this paper, we develop a contrast-improved algorithm for (k, n) RG-based VCS. Theoretical analysis and experimental results demonstrate that the proposed algorithm outperformers the previous threshold algorithms with better visual quality and a higher accuracy of contrast. [ABSTRACT FROM AUTHOR]

Two visual models of image secret sharing have been studied: visual cryptography schemes (VCS), introduced by Naor and Shamir, and visual cryptograms of random grids (VCRG), introduced by Kafri and Keren. VCRG has gained much attention in academia than before to avoid the pixel expansion of VCS. Although there is a strict relation between VCRG and VCS, VCRG can still be improved to achieve a better result. In this paper, based on new insight into linear algebraic technique to construct VCS, where we are able to construct VCS by solving a linear system of more equations at a time, we put forward a new construction of VCRG for general access structures. The effectiveness and advantage of the proposed construction are formally analyzed and experimentally demonstrated. With theoretical and practical interests, our construction exposes new possibilities to the researches of visual models of image secret sharing. [ABSTRACT FROM AUTHOR]

Conventional (k, n)-threshold visual secret sharing of random grids (VSSRG) schemes generate n shares having the same average light transmission from a secret image to be shared, and any information related to the secret image cannot be identified externally from a single share held by one participant. In addition, the secret image can be recovered only by collecting k shares individually held by participants, and every share has the same capability of recovering the secret image. In fact, participants’ priority levels vary in certain conditions, and therefore their shares’ capabilities to recover the secret image are different. The priority-based (k, n)-threshold VSSRG scheme proposed in this study enables the assignment of different priority weights to each share to create different priority levels. During decryption, the stacking of shares with different priority levels recovers the secret image at different levels. Moreover, shares individually held by each participant have the same average light transmission, and consequently the shares’ priority levels cannot be identified externally. [ABSTRACT FROM AUTHOR]

Traditional visual cryptography schemes presented pixel expansion and could only share one secret image. This paper proposed a multi-level visual cryptography scheme without pixel expansion. The scheme processed multiple secret images based on random grids and XOR operation. Using XOR operation on each level could recovery all secrets respectively. It could realize lossless recovery of binary secret image，and could be extended to the gray image and color image. Image transfer process introduced error correction encoding mechanism to improve the reliability of the program. Simulation experiments demonstrate that the share images have no pixel expansion and the recovery images are the same as the original images. The analysis shows the scheme meets the security requirement. [ABSTRACT FROM AUTHOR]

To evaluate the visual quality in visual secret sharing schemes, most of the existing metrics fail to generate fair and uniform quality scores for tested reconstructed images. We propose a new approach to measure the visual quality of the reconstructed image for visual secret sharing schemes. We developed an object detection method in the context of secret sharing, detecting outstanding local features and global object contour. The quality metric is constructed based on the object detection-weight map. The effectiveness of the proposed quality metric is demonstrated by a series of experiments. The experimental results show that our quality metric based on secret object detection outperforms existing metrics. Furthermore, it is straightforward to implement and can be applied to various applications such as performing the security test of the visual secret sharing process. [ABSTRACT FROM AUTHOR]

We consider 2D Principal Component Analysis (2DPCA) for optimal target tracking strategy for UAVs based on random grid regression Monte Carlo. We perform the best coordination for target tracking of UAVs based on visual observation and propose to improve its effect though optimum combination of unpredictable ground targets. First, the random target for optimal coordination and control of double UAVs is presented based on analysis of dynamics of UAV and target dynamics. Second, the Monte Carlo solution scheme for the control target is combined with a random grid to overcome the problems of standard Monte Carlo scheme of: 1) the state space having relatively high dimension, ii) the computation is complex, and iii) the accuracy is not high. Third, the optimal coordination control of UAVs is realized. Finally, the effectiveness of the method is proved through simulation experiments. [ABSTRACT FROM AUTHOR]

Compared with the visual-cryptography-based visual secret sharing, the random-grid-based visual secret sharing (RGVSS) has some technical advantages, such as no pixel expansion and no need of codebooks. Designed based on RGVSS, the user-friendly random-grid-based visual secret sharing (UFRGVSS) not only inherits the advantages of RGVSS but also overcomes the data management problem in RGVSS by taking meaningful images as shares. Unfortunately, up to now, the existing threshold UFRGVSS schemes are only (2, 2) ones, which should use two meaningful images with complementary colors as shares. What's more, there is no feasible method to construct UFRGVSS schemes for more general threshold access structures excluding (2, 2) threshold, let alone for general access structures (GASs). Motivated by these concerns, in this paper, by stamping the gray-scale images with the shares generated from the traditional RGVSS, a novel method was proposed to design the UFRGVSS scheme for GASs, in which the resulting shares can be any meaningful gray-scale images. Experimental results show the feasibility of the proposed method by assessing its performance under different situations. Literature retrieval shows that our work may be the first attempt to construct the UFRGVSS scheme for GASs. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Visual secret sharing (VSS) schemes are classified into two categories—visual cryptography-based (VC) and random grid-based (RG)—with the purpose of encoding a secret into several meaningless shared images that can be superimposed to reveal the secret again. VC-based VSS suffers from the problems of pixel expansion and difficulty in alignment. Although the first problem has been solved by RG-based VSS, the latter remains. This paper proposes a new deviation-tolerant RG-based VSS method without pixel expansion. To demonstrate its feasibility, experiments are conducted to show that the reconstructed secret image is still recognizable visually when one shared image shifts by one or more pixels. Compared with related works, the proposed scheme not only has higher misalignment tolerance but also avoids the significant drawbacks in the related work. [ABSTRACT FROM AUTHOR]

Visual cryptography encrypts a secret image into two meaningless random images, called shares, such that it can be decrypted by human vision without any calculations. However, there would be problems in alignment when these two shares are staked by hand in practice. Therefore, this paper presents the fault-tolerant schemes of stacking two shares that are acquired from secret image encryption without pixel expansion. The main idea of these schemes is to combine several pixels as a unit and then to encrypt each unit into a specific combination of pixels. Both theoretical analysis and simulation results demonstrate the effectiveness and practicality of the proposed schemes. [ABSTRACT FROM AUTHOR]

Visual secret sharing (VSS) schemes providing secret communication services are classified into two categories depending on the method of encoding the secret: visual cryptography (VC)-based and random grid (RG)-based schemes. A friendly progressive version of the VC-based VSS scheme was presented in 2008; however, it is marred by pixel expansion, which is the innate deficiency of conventional VC-based VSS schemes. This paper proposes a suitable user-friendly RG-based VSS scheme with progressive secret reconstruction and without pixel expansion. The experimental results of the developed scheme validated its feasibility, and a theoretical analysis demonstrated its visual quality and security. [ABSTRACT FROM AUTHOR]

In recent years, various visual secret sharing schemes have been proposed to protect digital images from malicious behavior with comprehensive properties such as ( $$k, n$$ ) threshold, simple recovery, no pixel expansion, meaningful shadow images, alternative order of shadow images, and avoiding codebook design. However, to the best of our knowledge, no previous secret sharing scheme achieves almost all the above properties. In this paper, a visual secret image sharing threshold scheme is proposed based on random grids and error diffusion. It has several performances to other schemes such as ( $$k, n$$ ) threshold, simple computation (stacking recovery), alternative order of shadow images in recovery, no codebook design, and avoiding the pixel expansion problem. In addition, it has meaningful shadow images, at the price of possible degrading of images' quality. Experiments are conducted to show the security and efficiency of the proposed scheme. Comparisons with previous approaches show the performances of the proposed scheme. [ABSTRACT FROM AUTHOR]

The basic concept of secret image sharing is to encrypt a secret image into a number of meaningless share images. Except for all the images, no information should leak out from any of the share images. The original secret image is printed onto transparencies, and stacking these transparencies directly reveals the original image. The advantage lies in the fact that no computational cost is encountered, and only the human visual system is required to decode the secret image. The visual secret sharing scheme is to encrypt a secret image into a set of share images to increase the encryption capacity. However, the schemes available use a codebook, and used pixel expansion to encrypt secret images into share images. In general, pixel expansion of twice the original order is seen. It is neither practical nor the best solution when secret images are more in number. This paper proposes a novel visual secret sharing scheme that can share a binary secret image on two share images with no codebook requirement. The experimental result reveals that the proposed approach has high contrast and also has an excellent recovery quality of the secret image. The recovered secret image type is lossless. [ABSTRACT FROM AUTHOR]

Using a ray tracing technique, we investigate the dependence of the moiré effect on the crossing angles between touch screen panels (TSPs) and display panels, the metal grid structures (spacing and width), and metal grid shapes (non-uniform and random grids). Of those design parameters, adjusting the crossing angle (∼45°), reducing the grid width (∼1 μm), and employing a random grid in the shape of irregular hexagon are found to suppress the moiré phenomenon to a great extent. We also provide the simulation scheme that can capture the moiré patterns observed experimentally and useful design guidelines for metal grids. [ABSTRACT FROM AUTHOR]

The meaningful share in visual cryptography (VC) is a desired feature because it can increase the efficiency of management and decrease the suspicion of secret image encryptions. Although the traditional user-friendly random grid (RG)-based VC can produce meaningful shares, with the advantages of no pixel expansion and no need for codebook design, current user-friendly RG-based VCs fail to support the general ( k , n ) threshold and the complementary shares might be required. In this paper, a generalized RG-based VC with meaningful shares is proposed. Besides inheriting the good features of no pixel expansion and no codebook design, the proposed scheme can support ( k , n ) threshold and provide adaptive visual quality, at the cost of slightly decreasing visual quality of shared images. Our main contribution is to propose a meaningful VC for case ( k , n ) with no pixel expansion and codebook design. To the best of our knowledge, the proposed scheme is the first method with all of these good features. Both the theoretical analysis and simulation results demonstrate the effectiveness and security of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper discusses a random-grid-based nonexpanded visual cryptography scheme for generating both meaningful and noise-like shares. First, the distribution of black pixels on the share images and the stack image is analyzed. A probability allocation method is then proposed that is capable of producing the best contrast in both the share images and the stack image. With our method, not only can different cover images be used to hide the secret image, but the contrast can be adjusted as needed. The most important result is the improvement of the visual quality of both the share images and the stack image to their theoretical maximum. Our meaningful visual secret sharing method is shown in experiments to be superior to past methods. [ABSTRACT FROM PUBLISHER]