#
Linear Pixel Shuffling and Neural Network

Peter G. Anderson

Department of Computer Science

Rochester Institute of Technology

pga@cs.rit.edu

## Synopsis of the Presentation

"Linear Pixel Shuffling" (LPS) originally
developed for image processing applications, is a
technique for generating all the pixel
coordinates in an image in a simple, linear,
uniform manner. In contrast to raster pixel
ordering, LPS ordering generates pixels spread
smoothly all over the image, so an initial
fraction of the pixels generated covers the
entire image quite uniformly. LPS uses a linear
rule, so it requires very little
computational overhead.

Character recognition is our first neural
network application of LPS . We use LPS to
select a subset of locations in a a hand
printed character image. This provides an
efficient placement of image features (e.g.,
stroke detectors). We used these features
for a perceptron-like network which uses
only integer operations. Our net's
character recognition performance matched
that of backprop-trained, multilayer
perceptrons, and it trained ten times
faster.

Infinite analogs of LPS generate points
uniformly in the unit cubes in n-dimensional
space, for n = 1, 2, 3, ... We can use
these real-valued vectors for the first
layer of weights (i.e., the low-level
feature-detection layer) of a multilayer
perceptron. We have applied this idea to
problems such as the well-known nested
spirals with excellent results. Our
hidden-layer transfer functions have
included continuous and piecewise linear
sigmoids and radial basis functions.

The resulting networks do have a very large
first hidden layer of nodes, and we have
developed a genetic algorithm approach to
locating good performing subsets of that.

## Bio

Peter G. Anderson, Ph.D., is a Computer Science
Professor at RIT. His teaching assignments
are in the areas of Neural Networks,
Genetic Algorithms, Computer Graphics,
and Computing Theory. He is the coordinator
of the C.S. M.S. program, and runs the
M.S. Projects-Theses seminar.
Peter is one of the external faculty members
in RIT's Center for Imaging Science. He is
actively pursuing research in digital halftoning
and character recognition.
Before joining RIT in 1980, he held academic
positions at Seton Hall University, the
New Jersey Institute of Technology, and
Princeton University. He worked for
RCA's Computer Division in its
Spectra/70 years.
Since re-joining academia in 1971, he has
been an active consultant at the RIT
Research Corporation, Kodak, Xerox, and RCA.
His degrees are in Mathematics (Algebraic Topology)
from MIT. Because of these math roots, Peter has
developed his theory of Linear Pixel Shuffling
and applied it to everything.

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