Contrast Optimization for Size Invariant Visual Cryptography Scheme

Visual cryptography scheme (VCS) serves as an effective tool in image security. Size-invariant VCS (SI-VCS) can solve the pixel expansion problem in traditional VCS. On the other hand, it is anticipated that the contrast of the recovered image in SI-VCS should be as high as possible. The investigation of contrast optimization for SI-VCS is carried out in this article. We develop an approach to optimize the contrast by stacking
$t$
(
$k \le t \le n$
) shadows in
$(k, n)$
-SI-VCS. Generally, a contrast-maximizing problem is linked with a
$(k, n)$
-SI-VCS, where the contrast by
$t$
shadows is considered as an objective function. An ideal contrast by
$t$
shadows can be produced by addressing this problem using linear programming. However, there exist
$(n-k+1)$
different contrasts in a
$(k, n)$
scheme. An optimization-based design is further introduced to provide multiple optimal contrasts. These
$(n-k+1)$
different contrasts are regarded as objective functions and it is transformed into a multi-contrast-maximizing problem. The ideal point method and lexicographic method are adopted to address this problem. Additionally, if the Boolean XOR operation is used for secret recovery, a technique is also provided to offer multiple maximum contrasts. The effectiveness of the proposed schemes is verified by extensive experiments. Comparisons illustrate significant advancement on contrast is provided.