Fadaei Sadegh, Rashno Abdolreza
IEEE Trans Image Process. 2021;30:4555-4570. doi: 10.1109/TIP.2021.3073328. Epub 2021 Apr 27.
Image processing in hexagonal lattice has many advantages rather than square lattice. Researchers have addressed benefits of hexagonal structure in applications such as binarization, rotation, scaling and edge detection. Approximately all existing hardwares for capturing and displaying images are based on square lattice. Therefore, the best way for using advantages of hexagonal lattice is to find a proper software approach to convert square pixels to hexagonal ones. This paper presents a hexagonal platform based on interpolation which addresses three existing hexagonal challenges including imperfect hexagonal shape, inaccurate intensity level of hexagonal pixels and lower resolution in hexagonal space. The proposed interpolation is computed by overlaps between square and hexagonal pixels. Overlap types are formulated mathematically in 8 separate cases. Each overlap case is detected automatically and used to compute final gray-level intensity of hexagonal pixels. It is mathematically and experimentally shown that the proposed method satisfies necessary conditions for square-to-hexagonal conversion. The proposed scheme is evaluated on synthetic and real images with 10 different levels of noise in interpolation and edge detection applications. In synthetic images, the proposed method achieves the best figure of merit (FOM) 99.92% and 98.67% in high and low SNRs 100 and 20, respectively. Also, the proposed method outperforms existing state of the art hexagonal lattices with interclass correlation coefficient (ICC) 84.18% and mean rating 7.7 (out of 9) in real images.
六边形晶格中的图像处理比正方形晶格具有许多优势。研究人员已经探讨了六边形结构在诸如二值化、旋转、缩放和边缘检测等应用中的优势。几乎所有现有的图像采集和显示硬件都是基于正方形晶格的。因此，利用六边形晶格优势的最佳方法是找到一种合适的软件方法将正方形像素转换为六边形像素。本文提出了一种基于插值的六边形平台，该平台解决了现有的三个六边形挑战，包括不完美的六边形形状、六边形像素强度水平不准确以及六边形空间分辨率较低。所提出的插值通过正方形像素和六边形像素之间的重叠来计算。重叠类型在数学上被公式化为8种不同的情况。每种重叠情况都会被自动检测并用于计算六边形像素的最终灰度强度。从数学和实验上都表明，所提出的方法满足从正方形到六边形转换的必要条件。在插值和边缘检测应用中，对具有10种不同噪声水平的合成图像和真实图像对所提出的方案进行了评估。在合成图像中，所提出的方法在高信噪比100和低信噪比20时分别达到了最佳品质因数（FOM）99.92%和98.67%。此外，在所提出的方法在真实图像中，类间相关系数（ICC）为84.18%，平均评分7.7（满分9分），优于现有的六边形晶格技术水平。
