M-lattice: from morphogenesis to image processing

Author

Sherstinsky, Alexander S. ; Picard, Rosalind W.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA

Volume

5

Issue

7

fYear

1996

fDate

7/1/1996 12:00:00 AM

Firstpage

1137

Lastpage

1149

Abstract

The paper is based on reaction-diffusion, a nonlinear mechanism first proposed by Turing in 1952 to account for morphogenesis, the formation of shape and pattern in nature. One of the key limitations of reaction-diffusion systems is that they are generally unbounded, making them awkward for digital image processing. In this paper we introduce the “M-lattice”, a system that preserves the pattern-formation properties of reaction-diffusion and is bounded. On the theoretical front, we establish how the M-lattice is closely related to the analog Hopfield network and the cellular neural network, but has more flexibility in how its variables interact. Like many “neurally inspired” systems, the bounded M-lattice also enables computer or analog VLSI implementations to simulate a variety of partial and ordinary differential equations. On the practical front, we demonstrate two novel applications of reaction-diffusion formulated as the new M-lattice. These are adaptive filtering, applied to the restoration and enhancement of fingerprint images, and nonlinear programming, applied to image halftoning in both “faithful” and “special effects” styles

Keywords

VLSI; adaptive filters; fingerprint identification; image enhancement; image restoration; lattice theory; neural nets; nonlinear differential equations; nonlinear dynamical systems; nonlinear programming; partial differential equations; M-lattice; VLSI implementations; adaptive filtering; analog Hopfield network; cellular neural network; enhancement; faithful styles; fingerprint images; image halftoning; image processing; morphogenesis; nonlinear mechanism; nonlinear programming; ordinary differential equations; partial differential equations; pattern-formation properties; reaction-diffusion; restoration; special effects styles; Analog computers; Application software; Cellular neural networks; Computational modeling; Computer simulation; Differential equations; Digital images; Image processing; Shape; Very large scale integration;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.502393

Filename

502393