Research Information: My Ph.D. thesis, Relative Critical Sets in Rn and Applications to Image Analysis, characterizes the local geometric structure of smooth real valued functions using "relative" critical information about the function. That is I studied a set that consists of critical points along with points that are almost critical points in a very well defined sense. To understand the structure of these sets, I used techniques in real analysis, partial differential equations, differential topology, abstract algebra (e.g., transformation groups), and singularity theory. I am interested in continuing work with these sets and showing how they can be used in data analysis and processing, and in particular, medical image analysis. Other interest include computer graphics, game theory, and writing. Here is some eye-candy related to ridge-theory, created by Mathematica and gifsicle: One-Parameter Families of Ridges.

List of Publications ``The Maximal Scale Ridge: Incorporating scale into the ridge definition.'' (with J.Furst). Scale-Space Theory in Computer Vision: Proceedings of the Second International Conference, Space-Space 1999. Springer-Verlag. Lecture Notes in Computer Science 1682: 93-104. Relative Critical Sets in Rn and Applications to Image Analysis. Ph.D. Dissertation, University of North Carolina. August 1998. ``Image Loci are Ridges in Geometric Spaces'' with J. Furst, R.Keller, and S. Pizer. Scale-Space Theory in Computer Vision: Proceedings of First International Conference, Scale-Space '97, Lecture Notes in Computer Science 1252: 176-187 ``Shape Based Mathematical Modeling of the Human Nasal Passages'' Len Brin, Jackie Huband, Jason Miller, Laura Kay Potter, and Monica Price. In 1996 Industrial Mathematics Modeling Workshop for Graduate Students. Center for Research in Scientific Computation, NCSU, Technical Report CRSC-TR97-8.

Presentations "Relative Critical Sets and Ridge Sets of Functions." Contributed talk at the Institute for Mathematics and its Applications's workshop on Image Analysis and High Level Vision. Part of the program on Vision, Speech, and Language. November 15, 2000. ``The Maximal Scale Ridge: Incorporating scale into the ridge definition.'' (with J.Furst). Invited talk at Scale-Space Theory in Computer Vision: Proceedings of the Second International Conference, Space-Space 1999.

People: colleagues of the past, present, and future Jacob Furst, at DePaul's School of Computer Science, Telecommunications, and Information Systems Rob Keller, Assistant Professor of Mathematics, Loras College, Dubuque, Iowa. Rob Katz, at the University fo North Carolina (CS Dept) MIDAG, Medical Image and Display Analysis Group, at the University fo North Carolina (CS Dept)

Web Resources The European Singularities Network: For the latest results in Singularity Theory coming out of Europe. Rob Keller's Ridge Page: A page with pictures of ridges of function and a nutshell description of some theory concerning the maximal convexity ridge and parameterized families of maximal convexity ridges. David Eberly's MAGIC image processing plus software. His RVCExtractor.

Journal Pages Cambridge University Press Bulletin of the London Mathematical Society Journal of the London Mathematical Society Proceedings of the London Mathematical Society Kluwer Academic Publishing International Journal of Computer Vision Journal of Mathematical Imaging and Vision Multidimensional Systems and Signal Processing Machine Graphics and Vision IEEE transactions on Pattern Analysis and Machine Intelligence