Almost-aspect-ratio-invariant visual cryptography without adding extra subpixels

• We propose a (k,n)(k,n) almost aspect ratio invariant VCS (AAIVCS).
• Our (k,n)(k,n)-AAIVCS does not need extra subpixels.
• Our (k,n)(k,n)-AAIVCS does not find out a mapping pattern for arranging subpixels.
• We theoretically prove that our scheme has the smallest aspect ratio difference.

A visual cryptographic scheme is a method to decompose a secret image into shadow images by expanding a secret pixel into m subpixels. Only legitimate subsets of participants can reconstruct the original image by combining their shadows. Because the size of the subpixel is the same as that of the pixel, the shadow size is expanded m times. In cases where m is not a square number, the aspect ratio of the reconstructed image is distorted. Accordingly, an aspect ratio invariant VCS (ARIVCS) was proposed to address this distortion problem. However, ARIVCS requires extra subpixels and a mapping pattern showing how to arrange the subpixels. A large m creates a significant challenge when attempting to derive this pattern. In this paper, we propose the almost-aspect-ratio-invariant VCS (AAIVCS), which simulates the principle of a jigsaw puzzle. The proposed AAIVCS has the smallest loss of aspect ratio when we do not add extra subpixels.