Space-Varying Cellular Neural Networks with Fuzzy Inference and RGB Component

Cellular Neural Networks (CNN) [1] were introduced by Chua and Yang in 1988. The idea of CNN was inspired from the architecture of the cellular automata and the neural networks. A different point from the conventional neural networks is that CNN has local connectivity property. Since the structure of CNN resembles the structure of animals’ retina, CNN can be used for various image processing applications [2]-[6]. CNN is composed of the basic circuit units called cells. The cell contains linear and nonlinear circuit elements which are typically linear capacitors, linear resistors, linear and nonlinear controlled sources. Wiring weights of the cells are established by parameters called the template. The performance of the CNN is decided by the template. If the templates of all the cells in the CNN are identical, the system is called space-invariant, while if the templates of all the cells in the CNN are not identical, the system is called space-varying. Typically, the space-invariant system is mainly used in the studies of the CNN because the implementation cost is low. However, the performance of the space-invariant system may be limited because the essential processing dynamics are identical for every position. On the other hand, the performance of space-varying system can be better although the design of the template and implementation are much more difficult. The research of the space-varying system is an interesting subject for developing a new direction of CNN. In particular, the design method of CNN is important problem because the design method influences on the performance of CNN. In the previous study, we have proposed the spacevarying CNN designed by Hopfield Neural Network (Hopfield NN) [7]. We prepare some existing templates and the Hopfield NN as associative memory to which some patterns are embedded. In that method, the templates of CNN was chosen according to the retrieved pattern in each cell. By using this method, we design the space-varying CNN and could perform better image processing depending on the local information of input images. We have confirmed that this system is effective for some tasks. However, we have to prepare some patterns for designing space-varying CNN. These patterns are one of the parameter of this system. Also, this method does not include the fuzziness like a human. We consider that the fuzziness like a human is necessary to design the space-varying CNN for applying still more suitable template. In this study, we propose the space-varying CNN designed by Fuzzy inference and the RGB component of an input image. We apply some existing templates to each cell by using Fuzzy inference and the RGB component of an input image. In 1965, L. A. Zadeh has introduced the Fuzzy set as an extension of the classical notion of set [8]. This method has performed for applying the fuzziness to computer. Fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems and computer vision. Then, L. O. Chua et al have proposed the Fuzzy CNN [9], [10] which build the Fuzzy component into the cell. This CNN carry out the normal processing and Fuzzy processing in parallel. The performance is decided own template. They have confirmed that this CNN has characteristic performances. As the new space-varying design method, we apply one of templates to each cell according to the position of a barycenter in Fuzzy inference. In fact, we substitute Hopfield Networks for Fuzzy inference and RGB component for designing the space-varying CNN. We apply some existing templates to each cell by considering the barycenter from Fuzzy inference. To calculate the barycenter, we focus on the RGB component of an input image. We show the performance of this system by color noise removing. In Sec. II, we describe the structure of the space-varying CNN designed by Fuzzy inference and RGB component. In Sec. III, simulation results about the color noise removing are shown. In Sec. IV, we investigate the results numerically. Section V, concludes this article.