Bi-cubic interpolation for image conversion from virtual hexagonal to square structure

Hexagonal image structure represents an image as a collection of hexagonal pixels rather than square pixels in the traditional image structure. However, all the existing hardware for capturing image and for displaying image are produced based on square pixel image structure. Therefore, it becomes important to find a proper software approach to mimic the hexagonal structure so that images represented on the traditional square structure can be smoothly converted from or to the images on the hexagonal structure. For accurate image processing, it is critical to best maintain the image resolution during the image conversion. In this paper, we present an algorithm for bi-cubic interpolation of pixel values on a hexagonal structure when convert from the hexagonal structure to the square structure. We will compare with the results obtained through bi-linear interpolation for the conversion. Our experimental results show that the bi-cubic interpolation outperforms the bi-linear interpolation for most of testing images at the cost of slower and more complex computation

Bilinear interpolation on a virtual hexagonal structure

Spiral Architecture (SA) is a relatively new and powerful approach to machine vision system. The geometrical arrangement of pixels on SA can be described as a collection of hexagonal pixels. However, all the existing hardware for capturing image and for displaying image are produced based on rectangular architecture. Therefore, it becomes important to find a proper software approach to mimic SA so that images represented on the traditional square structure can be smoothly converted from or to the images on SA. For accurate image processing, it is critical to best maintain the image resolution during the image conversion. In this paper, we present an algorithm for bilinear interpolation of pixel values on a simulated SA. Our experimental results show that the bilinear interpolation improves the image representation accuracy while keeping the computation simple

Image translation and rotation on hexagonal structure

Image translation and rotation are becoming essential operations in many application areas such as image processing, computer graphics and pattern recognition. Conventional translation moves image from pixels to pixels and conventional rotation usually comprises of computation-intensive CORDIC operations. Traditionally, images are represented on a square pixel structure. In this paper, we perform reversible and fast image translation and rotation based on a hexagonal structure. An image represented on the hexagonal structure is a collection of hexagonal pixels of equal size. The hexagonal structure provides a more flexible and efficient way to perform image translation and rotation without losing image information. As there is not yet any available hardware for capturing image and for displaying image on a hexagonal structure, we apply a newly developed virtual hexagonal structure. The virtual hexagonal structure retains image resolution during the process of image transformations, and almost does not introduce distortion. Furthermore, images can be smoothly and easily transferred between the traditional square structure and the hexagonal structure. © 2006 IEEE

Basic transformations on virtual hexagonal structure

Hexagonal structure is different from the traditional square structure for image representation. The geometrical arrangement of pixels on hexagonal structure can be described in terms of a hexagonal grid. Hexagonal structure provides an easy way for image translation and rotation transformations. However, all the existing hardware for capturing image and for displaying image are produced based on square architecture. It has become a serious problem affecting the advanced research based on hexagonal structure. In this paper, we introduce a new virtual hexagonal structure. Based on this virtual structure, a more flexible and powerful image translation and rotation are performed. The virtual hexagonal structure retains image resolution during the process of image transformations, and does not introduce distortion. Furthermore, images can be smoothly and easily transferred between the traditional square structure and the hexagonal structure. © 2006 IEEE

Computation of the Euler Number of a Binary Image Composed of Hexagonal Cells

ABSTRACTMost of the proposals to compute the Euler number of a binary image have been designed to work with imagescomposed of squared cells. Only a few of these methods (in the case of images composed of hexagonal cells) havebeen reported in literature, although it is known that images composed of hexagonal cells do not suffer from theproblems of connectivity frequently found in the case of images composed of squared cells. In this paper, a new wayto compute the Euler number (E) of a binary image composed of hexagonal cells is presented. For this, the perimeterP of the isolated regions in the image, their contact perimeter c P and the type T of a cell are used to obtain thisimportant invariant. The proposal can be used alone or in combination with other features to describe any binaryplanar shape composed of hexagonal pixels for its further recognition

Hexagonal structure for intelligent vision

Using hexagonal grids to represent digital images have been studied for more than 40 years. Increased processing capabilities of graphic devices and recent improvements in CCD technology have made hexagonal sampling attractive for practical applications and brought new interests on this topic. The hexagonal structure is considered to be preferable to the rectangular structure due to its higher sampling efficiency, consistent connectivity and higher angular resolution and is even proved to be superior to square structure in many applications. Since there is no mature hardware for hexagonal-based image capture and display, square to hexagonal image conversion has to be done before hexagonal-based image processing. Although hexagonal image representation and storage has not yet come to a standard, experiments based on existing hexagonal coordinate systems have never ceased. In this paper, we firstly introduced general reasons that hexagonally sampled images are chosen for research. Then, typical hexagonal coordinates and addressing schemes, as well as hexagonal based image processing and applications, are fully reviewed. © 2005 IEEE

Hexagonal pixel-array for efficient spatial computation for motion-detection pre-processing of visual scenes

Article discussing hexagonal pixel-array for efficient spatial computation for motion-detection pre-processing of visual scenes

Hexagonal pixel-array for efficient spatial computation for motion-detection pre-processing of visual scenes

Article discussing hexagonal pixel-array for efficient spatial computation for motion-detection pre-processing of visual scenes

Reversible, fast, and high-quality grid conversions

A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations