A. Petrosino (Ed.): ICIAP 2013, Part II, LNCS 8157, pp. 532–541, 2013. © Springer-Verlag Berlin Heidelberg 2013 Integral Spiral Image for Fast Hexagonal Image Processing Sonya Coleman 1 , Bryan Scotney 2 , and Bryan Gardiner 1 1 School of Computing and Intelligent Systems, University of Ulster, Magee, BT48 7JL, Northern Ireland 2 School of Computing and Information Engineering, University of Ulster, Coleraine, BT52 1SA, Northern Ireland Abstract. A common requirement for image processing tasks is to achieve real- time performance. One approach towards achieving this for tradition rectangu- lar pixel-based images is to use an integral image that enables feature extraction at multiple scales in a fast and efficient manner. Alternative research has intro- duced the concept of hexagonal pixel-based images that closely mimic the hu- man visual system: a real-time visual system. To enhance real time capability, we present a novel integral image for hexagonal pixel based images and associ- ated multi-scale operator implementation that significantly accelerates the fea- ture detection process. We demonstrate that the use of integral images enables significantly faster computation than the use of conventional spiral convolution or the use of neighbourhood address look-up tables. 1 Introduction Motivated by the real-time processing capabilities of the human vision system, we consider the use of hexagonal pixel-based images in order to reduce computational effort when implementing low-level image processing algorithms. We consider the way in which humans capture visual information: a small region, the fovea, within the retina, contains photoreceptor cones that are arranged in a densely packed hexagonal structure. Correspondingly, we consider digital images in which the pixels are hex- agonal. In [8] a spiral architecture is designed which enables a hexagonal pixel-based image to be stored as a one dimensional vector. This is a fundamental characteristic that can be utilized to target real-time processing. One of the most popular ways of applying edge detection operators at multiple scales is through the use of image pyramids [4]. An image pyramid is constructed by first smoothing the image with an appropriate filter and then sub-sampling the smoothed image. This process is repeated a number of times on the subsequently generated images resulting in a set of increasingly smoothed images. Edge detection, for example, is then performed by applying a gradient-based operator such as the Sobel operator to each image in the pyramid. However one issue with this method is that it is difficult to relate features at higher levels of the image pyramid to those at lower levels of the pyramid due to the fact that the spatial locations of the detected features do not relate directly. An alternative method to applying edge detection oper- ators at multiple scales is to use is to use a set of differently sized operators applied to