Visual cryptography (VC) is a powerful technique with high security and requires no PC or device to reconstruct the secret information. Progressive visual cryptography (PVC) is a variation of the VC scheme in which the quality of the reconstructed image is improved by increasing the number of shared images. The previous study focused directly on maximizing the value of the quality in the completely reconstructed image; thus, there is a difference in the quality of the shared images. In this paper, we focus on the aforementioned issue and propose a new approach based on inductive reasoning. Our basic idea is to maximize the quality of the reconstructed images each time the number of shared images increases. We call this method the bottom-up approach. Moreover, hitherto, PVC has been evaluated based on the value of relative difference or by sight. Such evaluation methods are only subjective or difficult to execute without the knowledge of basis matrices. In addition, PVC users cannot easily confirm the effectiveness of their shared images. In this paper, we propose a new information-theoretic evaluation method for PVC, which only uses shared images, to solve the aforementioned problems. Our proposed method can objectively and quantitatively evaluate PVC based on the numerical value, and PVC users can easily confirm the effectiveness of their shared images.

中文翻译：

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渐进式视觉密码的改进方案及评估方法

视觉密码（VC）是一种强大的技术，安全性高，不需要PC或设备来重建秘密信息。渐进式视觉密码术 (PVC) 是 VC 方案的一种变体，其中通过增加共享图像的数量来提高重建图像的质量。之前的研究直接集中在最大化完全重建图像中的质量值；因此，共享图像的质量存在差异。在本文中，我们关注上述问题，并提出了一种基于归纳推理的新方法。我们的基本思想是每次共享图像的数量增加时都最大化重建图像的质量。我们称这种方法为自下而上的方法。此外，迄今为止，PVC的评价是根据相对差值或目视进行的。如果没有基本矩阵的知识，这种评估方法只是主观的或难以执行。此外，PVC 用户无法轻易确认其共享图像的有效性。在本文中，我们提出了一种新的 PVC 信息论评估方法，该方法仅使用共享图像来解决上述问题。我们提出的方法可以根据数值客观定量地评估 PVC，PVC 用户可以轻松确认其共享图像的有效性。解决上述问题。我们提出的方法可以根据数值客观定量地评估 PVC，PVC 用户可以轻松确认其共享图像的有效性。解决上述问题。我们提出的方法可以根据数值客观定量地评估 PVC，PVC 用户可以轻松确认其共享图像的有效性。