M-lattice: a novel non-linear dynamical system and its application to halftoning

This paper presents a novel non-linear dynamical system called the \M-lattice system". This system is rooted in the reaction-diiusion model, rst proposed by Turing in 1952 to explain the formation of animal patterns such as zebra stripes and leopard spots. The M-lattice system is closely related to the analog Hoppeld network and the cellular neural network, but has more exibility in how its variables interact. In particular, the model is well-suited to a variety of applications formulated as constrained non-linear optimization. The present study demonstrates the use of this model for two diierent image halftoning examples. The rst example synthesizes a halftone of Einstein in the \hand-drawn" style of the Wall Street Journal portraits ; it illustrates how a more exible quality metric can be used when the binary requirement is stated as an explicit constraint. The second example synthesizes halftones free of correlated artifacts; it illustrates the noise-shaping capability of the M-lattice system.