An Approach to Edge Detection on a Virtual Hexagonal Structure Xiangjian He 1 , Wenjing Jia 1 , Jianmin Li 2 , Qiang Wu 1 and Tom Hintz 1 1 Faculty of Information Technology University of Technology, Sydney Australia {sean,wejia,wuq,hintz}@it.uts.edu.au 2 School of Computer and Mathematics Fuzhou University Fujian 320002, China lijianm_9@hotmail.com Abstract Hexagonal structure is another image structure alternative to traditional square image structure for image processing and computer vision. The geometrical arrangement of pixels on a hexagonal structure can be described as a collection of hexagonal pixels. Because all the existing hardware for capturing image and for displaying image are produced based on square structure, it becomes important to find a proper software approach to mimic hexagonal structure so that images represented on the traditional square structure can be smoothly converted from or to the images on hexagonal structure. For accurate image processing, it is critical to best maintain the image resolution during the image conversion. In this paper, a bilinear interpolation algorithm that is used to convert an image from square structure to hexagonal structure is presented. Based on this, an edge detection method is proposed. Our experimental results show that the bilinear interpolation improves the edge detection accuracy. 1. Introduction The advantages of using a hexagonal grid to represent digital images have been investigated for more than thirty years [1-5]. The importance of the hexagonal representation is that it possesses special computational features that are pertinent to the vision process [4]. Its computational power for intelligent vision has pushed forward the research in areas of image processing and computer vision. The hexagonal image structure has features of higher degree of circular symmetry, uniform connectivity, greater angular resolution, and a reduced need of storage and computation in image processing operations [6-7]. In spite of its numerous advantages, a problem that limits the use of hexagonal image structure is the lack of hardware for capturing and displaying hexagonal- based images. In the past years, there have been various attempts to simulate a hexagonal grid on a regular rectangular grid device [1-5]. The use of these techniques provides a practical tool for image processing on a hexagonal structure and makes it possible to carry out research based on a hexagonal structure using existing computer vision and graphics systems. A new simulation scheme as presented in [8] was developed. In this scheme, each of the original square pixels and simulated hexagonal pixels is regarded as a collection of smaller components, called sub-pixels. The light intensities of all sub-pixels constituting a square pixel (or hexagonal) are assigned the same value as that of the square pixel (or hexagonal) pixel in the square (or hexagonal) structure. This simple assignment method does not give accurate enough intensity interpolation of sub-pixels, and hence affects the results of edge detection. In this paper, we present a new assignment scheme using the simple bilinear interpolation algorithm [9] which can be easily and fast implemented. We will use experimental results to show the improvement in edge detection. The rest of this paper is organized as follows. In Section 2, we briefly review the simulation of hexagonal structure and its bilinear interpolation as shown in [8]. In Section 3, an edge detection scheme is presented. The experimental results are demonstrated in Section 4. We conclude in Section 5. Digital Image Computing Techniques and Applications © 2007 IEEE DOI 10.1109/DICTA.2007.25 340