Dept. of Mathematics & Computer Science

 

Raif M. Rustamov

Undergraduate Research

Benefits of doing research as undergraduate include:

 

— Increased marketability for graduate school and employment (thanks to a stronger resume and professors who will know you well );

— Opportunity to apply theories which have been learned to practical, real-life situations;

— Improved skill set which includes life-long learning, making connections between theory and practice, critical thinking, problem-solving, etc;

— Enhanced professionalization/socialization through working with a faculty mentor.

(adapted from http://www.weber.edu/OUR/benefits.html, retrieved July, 2008)

 

In addition, by registering for MATH 155 — Independent Study in Mathematics  or CSCI 199 — Independent Study in Computer Science, you can get up to 4 credits for doing research on your favorite topic!

 

You will also be able to present your work at conferences such as The National Conference of Undergraduate Research, Posters on the Hill, Washington, D.C.; participate in contests like the ACM Student Research Competition; publish in journals including The College Mathematics Journal, SIAM Undergraduate Research Online, Involve — a Journal of Mathematics, RHIT Undergraduate Math Journal.

 

Requirements

 

Main requirements to succeed in research are motivation and perseverance. To work with me you will also need to have a strong mathematics background, a genuine interest in practical applications, some programming experience and a firm determination to learn MATLAB.

 

 

My Research Interests

My research interests lie in concrete applications of manifold learning, differential geometry, topology and partial differential equations to processing of images and three-dimensional data. The recent focus of my research has been developing algorithms and numerical methods for geometry processing and modeling of three-dimensional deformable shapes. Such shapes arise in protein bioinformatics, computer-aided medical diagnosis, electron cryomicroscopy, 3D face recognition and animation. Classification, retrieval, correspondence, segmentation, registration, symmetry detection, and modeling of deformable shapes are of great practical importance. My goal has been to develop necessary theoretical foundations and build reliable tools to effectively achieve some of these tasks.

 

 

Possible Topics

 

My research provides an abundance of industry-oriented research projects: image and 3D data processing arise in so many fields, that it will be easy to tailor projects according to your interests. If you have in mind working at Pixar, our project will concentrate on developing tools for character animation; Google – we will work on methods for searching shape databases; Philips Medical – we can concentrate on registration of images obtained using different imaging modalities; ESRI or Google Earth – we can do image fusion of intensity and RGB images of the terrain; Pfizer – we will concentrate on how protein surface geometry and physico-chemical properties can be analyzed in the large scale with possible implications for the design of drugs with less side effects.

 

A more theoretically inclined student (with appropriate very strong math background) may spend her time to learn about how differential equations on manifolds can be used to extract meaningful information about the shape; boundary interpolation, and spectral/diffusion methods in machine learning.