Fast Pattern Detection Using Normalized Neural Networks and Cross-Correlation in the Frequency Domain
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Fast Pattern Detection Using Normalized Neural Networks and Cross-Correlation in the Frequency Domain Hazem M. El-Bakry Multimedia Devices Laboratory, University of Aizu, Aizu Wakamatsu 965-8580, Japan Email: [email protected]
Qiangfu Zhao Multimedia Devices Laboratory, University of Aizu, Aizu Wakamatsu 965-8580, Japan Email: [email protected] Received 12 January 2004; Revised 20 December 2004 Neural networks have shown good results for detection of a certain pattern in a given image. In our previous work, a fast algorithm for object/face detection was presented. Such algorithm was designed based on cross-correlation in the frequency domain between the input image and the weights of neural networks. Our previous work also solved the problem of local subimage normalization in the frequency domain. In this paper, the effect of image normalization on the speedup ratio of pattern detection is presented. Simulation results show that local subimage normalization through weight normalization is faster than subimage normalization in the spatial domain. Moreover, the overall speedup ratio of the detection process is increased as the normalization of weights is done offline. Keywords and phrases: fast pattern detection, neural networks, cross-correlation, image normalization.
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INTRODUCTION
Pattern detection is a fundamental step before pattern recognition. Its reliability and performance have a major influence in a whole pattern recognition system. Nowadays, neural networks have shown very good results for detecting a certain pattern in a given image [1, 2, 3]. But the problem with neural networks is that the computational complexity is very high because the networks have to process many small local windows in the images [4, 5]. Some authors tried to speed up the detection process of neural networks [6, 7, 8]. They proposed a multilayer perceptron (MLP) algorithm for fast object/face detection. They claimed that applying crosscorrelation in the frequency domain between the input image and the neural weights is much faster than using conventional neural networks. They stated this without any conditions and introduced formulas for the number of computation steps needed by conventional neural networks and their proposed fast neural networks. Then, they established an equation for the speedup ratio. It was proved in [9] that their equations contain many errors which lead to an invalid speedup ratio. Moreover, a symmetry condition is necessary and must be found either in the input image or in the neural weights so that those fast neural networks can give the same
correct results as conventional neural networks for detecting a certain pattern in a given image. Recently, we succeeded in accelerating the behavior of neural networks during the search process [10]. The speedup of the detection process is achieved by converting the input image into a symmetric one and applying cross-correlation in the frequency domain between the new symmetric image and the neural weights. Mathematical proof and simulation results for fast te
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