视觉密码学对比度与安全方案分析

1、解释NS对比度的物理意义，并将其与其他定义进行比较。

NS对比度（αNS）的定义为：

αNS = (h - l) / m

其中参数 *m*、*h* 和 *l* 分别是像素扩展、黑度和白度界限。

其物理意义在于反映恢复的秘密图像的清晰度。因为对比度仅与恢复的秘密图像相关，所以它是一个以 *m*、*h* 和 *l* 为参数的函数。

与其他对比度定义如：

- αVV = (h - l) / [m(h + l)]
- αES = (h - l) / (m + l)
- α(m,h,l) = [(h - l) · m] / [h · (m - h) + l · (m - l) + m²]

相比，不同的定义在反映图像对比度方面有不同的特点。

通过对 (2, 4)-VCS 的例子分析表明，α(m,h,l) 能更恰当地反映不同 VCS 的对比度。例如，对于 Droste 的 (2, 4)-VCS 和 Blundo 的 (2, 4)-VCS，只有 α(m,h,l) 能合适地反映这两种 VCS 的对比度，说明 NS 对比度等其他定义在某些情况下可能无法准确反映图像的实际对比度情况。

2、How are the thin line problems generated in SIVCS? How to resolve the relevant thin line problems?

Generation of thin line problems in SIVCS

1. First type thin line problem (TLP - 1) :
   In P-SIVCS, the thin lines in the secret image are usually unclear and misrepresented in the recovered secret image. There are many chaotic pixels in the recovered secret image, especially in the white-background areas, making it hard to identify the thin lines from the white background. This is because the thin lines are represented with a certain probability in the recovered secret image.

2. Second type thin line problem (TLP - 2) :
   In Construction 2.2, although TLP-1 is avoided as it has a smaller variance of the darkness level of each block of two secret pixels, because every $ m $ of $ B_{m,b} $ blocks are encrypted by $ b $ of $ M_1 $ and $ m - b $ of $ M_0 $ alternatively, it is possible that the patterns in the secret image can be falsely recovered. For images only consisting of thin lines, the blocks on a thin line may be always encrypted by $ M_0 $ (resp. $ M_1 $), which means the thin line may be mis