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Many algorithms exist for the halftoning of digital images. These algorithms all suffer well studied defects, which are especially apparent in the case where the resulting image is to be displayed at the marginally sampled resolution and viewed at the critical pixel merge distance. Recently, it has been shown that neural network approach may be useful for halfton ing [KA91]. Here, the feasibility of using neural networks in a practical application is considered. The Cellular Neural Network (CNN) architecture is chosen for its proven implementibility in VLSI, high speed, and programmability [CC91b]. Since both the CNN and halftoning have a geometrically local character, the CNN provides a natural implementation. The CNN template weights are derived by analogy to the well known error diffusion algorithm for halftoning. Some limitations of the neural network approach are analyzed providing an advance in designing template weights over previous methods. These limitations are shown to be especially critical in the case of the small interconnec tion neighborhoods needed for efficient implementation. Our design criteria are validated by direct simulation. The resulting halftones are shown to be more faithful reproductions of the original than those produced by the error diffusion algorithm. It is suggested that a CNN with optical inputs could provide a high-speed scanner/halftoner for applications such as FAX.

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This paper presents analytic criteria for local activity in one-port Cellular Nonlinear Network (CNN) cells [Chua, 1997, 1999], and gives the applications to the Oregonator CNN defined by the kinetic chemical reaction model of morphogenesis first introduced in [Field & Noyes, 1974]. Locally active domains, locally passive domains, and the edge of chaos are identified in the cell parameter space. Computer simulations of the dynamics of several Oregonator CNN's with specific selected cell parameters in the above-mentioned domains show genesis and the emergence of complexity. Furthermore, a novel phenomena is observed that "extremely high energy" is concentrated only on a few cells in the dynamic patterns of some Oregonator CNN's whose cell parameters are located in active domains; furthermore, relaxation oscillations and "transient oscillations" can exist if the cell parameters of the Oregonator CNN are located nearby or on the edge of chaos. This research illustrates once again the effectiveness of the local activity theory in choosing the system parameters for the emergence of complex patterns (static and dynamic) in a homogeneous lattice formed by coupled cells.