Fast Painting with Different Colors Using Cross Correlation in the Frequency Domain Hazem M. El-Bakry Abstract—In this paper, a new technique for fast painting with different colors is presented. The idea of painting relies on applying masks with different colors to the background. Fast painting is achieved by applying these masks in the frequency domain instead of spatial (time) domain. New colors can be generated automatically as a result from the cross correlation operation. This idea was applied successfully for faster specific data (face, object, pattern, and code) detection using neural algorithms. Here, instead of performing cross correlation between the input input data (e.g., image, or a stream of sequential data) and the weights of neural networks, the cross correlation is performed between the colored masks and the background. Furthermore, this approach is developed to reduce the computation steps required by the painting operation. The principle of divide and conquer strategy is applied through background decomposition. Each background is divided into small in size sub- backgrounds and then each sub-background is processed separately by using a single faster painting algorithm. Moreover, the fastest painting is achieved by using parallel processing techniques to paint the resulting sub-backgrounds using the same number of faster painting algorithms. In contrast to using only faster painting algorithm, the speed up ratio is increased with the size of the background when using faster painting algorithm and background decomposition. Simulation results show that painting in the frequency domain is faster than that in the spatial domain. Keywords—Fast Painting, Cross Correlation, Frequency Domain, Parallel Processing I. INTRODUCTION AINTING in real time is an important issue for many different applications [57]. In this article, a new idea for fast painting is presented. Painting with colored masks is equivalent to cross correlation with these masks and background. It was proved that performing cross correlation in the frequency domain is faster that time domain [1-54]. Fast cross correlation has been applied successfully for many different applications [1-53]. Manuscript received March31, 2006. H. M. El-Bakry, is assistant lecturer with Faculty of Computer Science and Information Systems – Mansoura University – Egypt. Now, he is PhD student in University of Aizu, Aizu Wakamatsu City, Japan 965-8580 (phone: +81-242-37-2760, fax: +81-242-37-2743, e-mail: d8071106@u-aizu.ac.jp). A faster searching algorithm for face/object detection using neural networks and fast cross correlation was presented in [6,27,29,30,32,33,34,35,38,42,48,50,51,52,53]. Faster sub- image detection was achieved using fast cross correlation [16,20,25,36,39]. Very fast iris detection using fast cross correlation was introduced in [31,41,43,44,45,46,47,49]. A general fast pattern detection using fast cross correlation was presented in [2,7,8,9,10,14,15,21,22,23,24]. Furthermore, a real time fast code detection for communication applications using fast cross correlation was introduced in [18,37,40]. In addition, a new time delay artificial neural network was invented using fast cross correlation as introduced in [1,5,12,19]. As well as, an interesting mathematical application by using fast cross correlation was presented [17,26,28]. A quick algorithm for fast Principle Component Analysis (PCA), applied in many artificial intelligent algorithms, using fast cross correlation was introduced in [3]. Moreover, an Internet application for fast searching on web pages using fast cross correlation was presented in [4]. Finally, high speed data processing using fast cross correlation was introduced in [12]. Here, fast painting is implemented in the frequency domain using different masks. Each mask can have a single color or mixed colors. In addition, new colors can be generated after performing the cross correlation operation. In section II, a new fast painting algorithm using cross correlation is presented. A faster painting algorithm that reduces the number of the required computation steps through background decomposition is presented in section III. Accelerating the new approach using parallel processing techniques is also introduced. II. A NEW THEORY FOR FAST PAINTING WITH COLORED MASKS USING CROSS CORRELATION IN THE FREQUENCY DOMAIN In this new approach, we are interested in increasing the speed of the painting process. By the words “fast painting” we mean reducing the number of computation steps required to perform the painting process. In the proposed model, each sub- background in the background is painted with one or more colors. At each position in the background each sub- background is dot multiplied by a mask (window) of a certain P International Journal of Computer Science Volume 1 Number 2 145