"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.
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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