April 18, 2002 - VIGRE Presentations
Debbie Hinck, Jocelyn Renner, Alejandro Cantarero, Moorea Brega, Corry Lee, Ashok Basawapatna, Patricia Orendorff, and Robert Thornton

IMAGE ENHANCEMENT FOR FINGERPRINT IDENTIFICATION
Debbie Hinck
(Research under Dr. Curry and Dr. Doughterty)

Personal identity recognition is a crucial part of today's society. We rely on identity verification to protect personal information, find and prosecute criminals, and identify missing persons. The FBI uses a digital database of over 300 million fingerprint images to make identifications. It would be impossible for one person or even a team of people to search through a database of 300 million fingerprints; a matching program must be used to search through the database and return possible matches for an unidentified print.

A variety of image enhancement techniques have been applied to digital fingerprint images, but an optimal method has not yet been determined. This is largely due to the fact that a metric to quantify the quality of the enhancement does not exist. In this talk, I will be discussing the development of a set of standard images that represent fingerprints, methods of noise addition that model common imperfections in fingerprint images, and the non-linear thresholding image enhancement technique.

MATHEMATICAL MODEL OF DISPERSION USING LYAPUNOV EXPONENTS
Jocelyn Renner
(Research under Dr. Julien and Paul Mullowney)

Understanding the dynamics of systems involving dispersion of passive scalars is important in many fields of engineering and science. Dispersion can include the transport of particles such as contaminants or represent a property of the system such as heat. Ocean dynamics, weather patterns, engines, reactors, and rocket boosters all undergo mixing in different forms, and understanding the dynamics behind these systems is important for prediction of the behavior of the system. A valid mathematical model of transport processes is essential to understanding the physics behind these complex systems. Good models allow scientists and engineers to provide more accurate predictions of ocean currents and weather patterns as well as allowing them to build more efficient reactors and engines. With Dr. Keith Julien and Paul Mullowney, I am studying ways to numerically measure dispersion in dynamic systems using Lyapunov exponents with the aim of applying the method to a new class of analytic three-dimensional flows for rotating fluids.

APPROXIMATION, STANDARDIZATION AND OTHER APPLICATIONS OF NON-NEGATIVE MATRIX FACTORIZATION
Alejandro Cantarero, Moorea Brega, and Corry Lee
(Research under Dr. Curry)

There exists a factorization method for non-negative matrices such that V is approximately equal to WH. When applied to a set of digital images, this factorization produces a set of basis images. It is then possible to reconstruct other faces not in the original set in terms of these basis images. We explore the "standardization" which occurs when the original image set is sufficiently homogeneous. In such cases, deviant images, when recreated from the basis set, lose "non-standard" features.

THE TRIG IDENTITY OF THE FUTURE
Ashok Basawapatna, Patricia Orendorff and Robert Thornton
(Research under Dr. Mohlenkamp and Lucas Monzón)

An effort to discover ways to reduce the cost of working with functions of several dimensions by using separable functions produced an unexpected discovery: a new trigonometric identity that allows us to write the sine of a sum of N variables as a sum of N separable functions. We are considering what happens if we take a sine of a sum of N distinct variables, such as sin(x+y+z) and multiply it by a sine of a sum of N different variables, such as sin(u+v+w). Simply multiplying out would result in a sum of N^2 terms, but we can now write it with 4N terms and it may be possible to reduce the sum to 2N, or even N terms.