2008 10th Intl. Conf. on Control, Automation, Robotics and Vision Hanoi, Vietnam, 17–20 December 2008 An Approach of Canny Edge Detection with Virtual Hexagonal Image Structure Xiangjian He, Wenjing Jia and Qiang Wu Centre for Innovation in IT Services and Applications (iNEXT) University of Technology, Sydney, Australia {sean,wejia, wuq}@it.uts.edu.au Abstract— Edge detection plays an important role in the areas of image processing, multimedia and computer vision. Gradient- based edge detection is a straightforward method to identify the edge points in the original grey-level image. It is intuitive that, in the human vision system, the edge points always appear where the gradient magnitude assumes a maximum. Hexagonal structure is an image structure alternative to traditional square image structure. 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, an approach that uses bilinear interpolation and tri-linear interpolation is applied for conversion between square and hexagonal structures. Based on this approach, an edge detection method is proposed. This method performs Gaussian filtering to suppress image noise and computes gradients on the hexagonal structure. The pixel edge strengths on the square structure are then estimated before Canny’ edge detector is applied to determine the final edge map. The experimental results show that the proposed method improves the edge detection accuracy and efficiency. Keywords—Edge detection, image interpolation, hexagonal structure, Canny edges, Gaussian filtering I. INTRODUCTION During the last three decades, many algorithms have been developed for edge detection [1-4], among which the most popular one is Canny's computational approach [1] by formulating the task as a numerical optimization problem. Since 1996, there have been many papers on edge detection based on hexagonal image structure where an image is represented by a collection of hexagons of the same size. The importance of the hexagonal representation is that it possesses special computational features that are pertinent to the vision process. Although hexagonal image structure has numerous advantages such as higher degree of circular symmetry, uniform connectivity, greater angular resolution, and a reduced need of storage and computation in image processing operations (see [5-7]), a problem that limits the its use is the lack of hardware for capturing and displaying hexagonal-based images [8]. The edge detection methods as presented in [9] are based on a mimic hexagonal structure that uses four square pixels to represent a single hexagonal pixel and hence has a loss of image resolution. The methods as shown in [8] are based on simple pixel interpolation algorithms for simulation of hexagonal structure. The computation cost for edge detection using these methods is expensive because its edge values are based on the intensity values of all sub-pixels (see Section 2 for detail) used for simulation. In this paper, a scheme to simulate a hexagonal grid on a regular rectangular grid device as presented in [10] is adopted. In this scheme, each of the original square pixels and simulated hexagonal pixels is regarded as a collection of sub- pixels. The light intensities of all sub-pixels constituting a hexagonal pixel are computed using a bi-linear interpolation technique. On the other hand, the light intensities of all sub- pixels constituting a square pixel are computed using a tri- linear interpolation technique. We will use experimental results to show the improvement in edge detection in terms of accuracy and efficiency. The contributions of this paper are listed in the following: • A fast edge detection algorithm on a hexagonal image structure is proposed. Unlike the work done in [11], the algorithm does not require the computation of light intensities at individual sub- pixels and hence greatly increases the computation speed. The proposed approach is different from the work in [8] in the way that it is based on a new hexagonal structure on which images have much higher resolution than the hexagonal structure introduced in [8]. This results in higher accuracy of edge detection. • The work presented in [10] has shown the superior performance of using bi-linear and tri- linear interpolation approach compared with other interpolation methods. This paper further demonstrates the advantages of the linear interpolation algorithms using the edge detection outcomes for image processing. The rest of this paper is organized as follows. In Section II, we briefly review the simulation of hexagonal structure together with bilinear interpolation and tri-linear interpolation schemes as shown in [10]. In Section III, an edge detection scheme is presented. The experimental results are demonstrated in Section IV. We conclude in Section V. 879 978-1-4244-2287-6/08/$25.00 c  2008 IEEE ICARCV 2008