M-Lattice: A System For Signal Synthesis And Processing Based On
Reaction-Diffusion
OR:
M-Lattice: From Spots and Stripes on Animals to Signal Processing
Sc.D. Thesis
Alex Sherstinsky
MIT EECS & Media Lab
Abstract
This research begins with reaction-diffusion, first proposed by Alan
Turing in 1952 to account for morphogenesis, such as the formation of
hydranth tentacles, leopard spots, and zebra stripes.
Reaction-diffusion systems have been researched primarily by
biologists working on theories of natural pattern formation and by
chemists modeling dynamics of oscillating reactions. The past few
years have seen a new interest in reaction-diffusion spring up within
the computer graphics and image processing communities. However,
reaction-diffusion systems are generally unbounded, making them
impractical for many applications. In this thesis we introduce a
bounded and more flexible non-linear system, the ``M-lattice,'' which
preserves the natural pattern-formation properties of
reaction-diffusion.
On the theoretical front, we establish relationships between
reaction-diffusion systems and paradigms in linear systems theory and
certain types of artificial ``neurally-inspired'' systems. 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. The bounded M-lattice enables computer or analog VLSI
implementations to serve as simulation ``engines'' for a wide variety
of systems of partial and ordinary differential equations.
On the practical front, we have developed new applications of
reaction-diffusion (formulated as the new M-lattice). These include the
synthesis of visual and sound textures, restoration and enhancement of
fingerprints, non-linear programming, and digital halftoning of images.
Halftones were synthesized in the creatively hand-drawn ``special-effects''
style of the Wall Street Journal portraits as well as in the
``faithful-rendition'' style of error-diffusion.
Thesis Supervisor: Professor Rosalind W. Picard
To obtain: ftp whitechapel.media.mit.edu anonymous anonymous cd pub/shers
get thesis.ps.Z
Enjoy!
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|Alexander Sherstinsky|shers at mit.edu|To become as refined a person as possible.|
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