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.

A new content‐based image retrieval (CBIR) scheme is proposed based on the optimised combination of the colour and texture features to enhance the image retrieval precision. This work focuses on a uniform partitioning scheme which is applied in the Hue, Saturation and Value (HSV) colour space to extract dominant colour descriptor (DCD) features. In the proposed CBIR scheme, the DCD features are initially extracted as the colour features, and then an appropriate similarity measure is applied. Also, several wavelet and curvelet features are defined as texture features to overcome the noise and the problem of image translation. Finally, the colour and texture features are optimally combined by using the particle swarm optimisation algorithm. The findings show that not only the proposed colour, wavelet and curvelet features outperform the existing ones but also their optimum combination has a better accuracy in comparison with several contemporary CBIR systems. The performance analysis shows that the proposed method improves the average precision metric from 67.85 to 71.05% for DCD, 58.90 to 65.43% for wavelet and 53.18 to 56.00% for curvelet using Corel dataset. In addition, the optimum combination presents the average precision of %76.50 which is significantly higher than the other state‐of‐the‐art methods.