Abstract

In this research, a novel Collatz conjecture-based image transformation and a modified logistic map are used for digital image watermarking. The proposed modified logistic map is utilized as a pseudo-random number generator (PRNG) to select the pixel to be watermarked. The host image is divided into nonoverlapping blocks, for instance, 2 × 2, 3 × 3, 4 × 4, 8 × 8, and 10 × 10 size blocks. A Collatz transformation is used on the selected pixel to generate a Collatz value because watermark embedding and extraction processes are implemented on the Collatz values. Evaluation criteria, such as visual quality, payload capacity, robustness, and execution time have been used to measure the performance of the proposed method. The results obtained and calculated clearly show that the proposed Collatz-based watermarking method has high visual quality, high payload capacity, and shorter execution time. Also, the proposed method has a basic mathematical structure and it can be programmed basically. This situation shows that the proposed method can be used in real-time applications. Collatz values can be changed with minimal distortions; therefore, this method is not robust against attacks. Finally, a successful image watermarking method is presented in this method using Collatz conjecture.

摘要

在这项研究中，一种新颖的基于 Collat​​z 猜想的图像变换和改进的逻辑图被用于数字图像水印。所提出的修改后的逻辑图被用作伪随机数生成器（PRNG）来选择要加水印的像素。宿主图像被分成不重叠的块，例如，2×2、3×3、4×4、8×8和10×10大小的块。对选定像素使用 Collat​​z 变换以生成 Collat​​z 值，因为水印嵌入和提取过程是在 Collat​​z 值上实现的。评估标准，如视觉质量、有效载荷容量、鲁棒性和执行时间已被用于衡量所提出方法的性能。所得结果和计算结果清楚地表明，所提出的基于 Collat​​z 的水印方法具有较高的视觉质量，高负载容量和更短的执行时间。此外，所提出的方法具有基本的数学结构，并且基本上可以编程。这种情况表明所提出的方法可以用于实时应用。Collat​​z 值可以以最小的失真进行更改；因此，该方法对攻击不鲁棒。最后利用Collat​​z猜想提出了一种成功的图像水印方法。