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-diffusion model, first proposed be 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 Hopfield network and the cellular neural network, but has more flexibility in how its variables interact. In particular, the model is well-suited to a variety of applications formulated as constrained nonlinear optimization. The present study demonstrates the use of this model for two different image halftoning examples. The first example synthesizes a halftone of Einstein in the “hand-drawn” style of the Wall Street Journal portraits; it illustrates how a more flexible 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