A Framework for Hexagonal Image Processing Using Hexagonal Pixel-Perfect Approximations in Subpixel Resolution

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.