272 IEEE zyxwvutsrq TRANSACIIONS ON NEURAL NETWORKS, VOL. 3, NO. zyxwv 2, MARCH 1992 Rotation-Invariant Neural Pattern Recognition System with Application to Coin Recognition Minoru Fukumi, Associate Member, IEEE, Sigeru Omatu, Member, IEEE, Fumiaki Takeda, and Toshihisa Kosaka Abstruct- In pattern recognition, we must often deal with problems to classify a transformed pattern. In this paper, we propose a neural pattern recognition system which is insensitive to rotation of input pattern by various degrees. The system consists of a fixed invariance network with many slabs and a trainable multilayered network. To illustrate the effectiveness of the system, we apply it to a rotation-invariant coin recognition problem to distinguish between a 500 yen coin and a zyxwvuts 500 won coin. The results show that our neural network approach works well for variable rotation pattern recognition problem. I. INTRODUCTION neural network have been the focus of active research A since Rumelhart et zyxwvutsrqpon al. [l] presented the error back- propagation (BP) method. The BP is a training algorithm for a layered feedforward network and a generalized version of the delta rule [2]-[4]. During the last several years, the BP has been applied to many problems [5], [6]. Conventional pattern recognition methods require an input pattern to be presented in a standard position, orientation, size, etc. In practice, however, the input pattern may be shifted in position, rotated, or scale-changed in relation to its standard form. Furthermore, the patterns can be corrupted by noise. Conventional pattern recognition methods, for example, pattern matching, do not work well under these conditions. Many pattern recognition systems insensitive to transfor- mation of an input pattern by neural networks have now been presented. Fukushima [7] presented the neocognitron, which is insensitive to translation and deformation of input pattern. Carpenter [SI proposed a self-organizing system which can classify patterns by adaptive resonance theory. Widrow [9] proposed a pattern recognition system made up of ADALINE networks, which is insensitive to translation and rotation by every 90" of input pattern. Koch [lo] also described a method similar to Widrow's [9]. The present authors [11]-[13] presented a noise-tolerant system which is an extended version of Widrow's. In this system, sigmoidal neuron units are adopted and trained by the BP. Reid [14] constructed a system which is invariant to translation, rotation, and the scale of the input pattern by using a high-order neural network as a preprocessor. However, it resulted in a combinatorial explosion of units. Although several other invariant pattern recognition systems have been proposed [15], [16], there is Manuscript received May zyxwvutsrqponm 14, 1991; revised October 9, 1991. M. Fukumi and S. Omatu are with the Faculty of Engineering, University F. Takeda and T. Kosaka are with Glory Ltd., 3-1, Shimoteno 1-Chome, IEEE Log Number 9105238. of Tokushirna, 2-1 Minami-Josanjima, Tokushima 770 Japan. Himeji, 670 Japan. still no useful system insensitive to translation, rotation, and scale. Another approach to invariant pattern recognition is to use the similarity criterion defined in terms of certain mathematical transformation functions, e.g., the Fourier transform [8], [ 171, the Hough transform [MI, and moment invariance [19], [20], as a preprocessor. The transformed feature vector can be input to feedforward neural networks. However, if an input pattern is a gray scale image with many levels, edge detection would be required as a preprocessor in many cases [SI. Furthermore, in cases where functions such as the Fourier transform are used as preprocessors followed by the feedforward network, a large-scale network would then be required, which would result in an explosion of training time. The object of this paper is to achieve automatic recognition of various coins, and for this purpose a rotation-invariant pattern recognition system involving neural networks is con- sidered. In coin recognition, one can easily distinguish one coin from another on the basis of size. However, one must discriminate them by surface design in cases where several coins are of the same size; then an input image from an image scanner can be rotated by any random number of degrees in many cases. In order to recognize such an image, a pattern recognition architecture which is insensitive to rotation would be required. Effective measures for this kind of problem, however, have not yet been arrived at. This paper presents a neural pattern recognition system which is insensitive to rotation by any number of degrees. As such a system is useful in problem related to coin recognition, we apply this algorithm to classify a 500 yen coin and a 500 won coin, which have the same shape and size, the same thickness, and a similar pattern structure. zyxw 11. A ROTATION-INVARIANT PAITERN RECOGNITION SYSTEM This section describes a method which constructs a rotation- invariant pattern recognition system by neural networks. In principle, it is possible to construct a system that is insensitive to translation, rotation, and scale. However, if the input pattern is an image (e.g., 256*256 pixels), it is difficult to deal with it by computer because of the huge preprocessor in the system [21]. Moreover, normalization of coin image on position (detection of center of the coin) can be easily done, and there is no variation in size because the images in this paper are obtained from those by an automatic coin classifying machine. Consequently, this paper considers a method which constructs a pattern recognition system insensitive only to rotation by neural networks. 1045-9227/92$03.00 zyxwvutsrq 0 1992 IEEE