Math 199: Spring & Summer 2002

Special Studies in Mathematics

Topics: Image Analysis Research Projects for Undergraduates

Meeting Time: Thursday, 2-3pm
Location: MS 7629

Mentors: Luminita Vese & Stanley Osher
Office: MS 7620-D

E-mail: lvese@math.ucla.edu & sjo@math.ucla.edu

Description:
All enrolled students are meeting with the mentors once a week. During these meetings, each student presents a paper selected together with the mentors. Also, students in teams of two are working on projects, related with the presented papers. Additional meetings for each project are held every week. The students have to prepare a written repport in the end, describing their research project.

Participants
  • Faculty Members: Stanley Osher, Luminita Vese.
  • Undergraduate Students: Tony Kim, Grace Tsui, Avanti Paranjpye, Jarrick Lau, Arif Tirta, Edward Cheon.

    Material Covered:
  • Active contours without edges , Chan, T.F.; Vese, L.A., IEEE Transactions on Image Processing, Volume: 10, Issue: 2, Feb. 2001, Pages: 266 -277.
  • Nonlinear Total Variation Based Noise Removal Algorithms L. Rudin, S. Osher, E. Fatemi, Physica D 60 (1-4): 259-268 NOV 1 1992.
  • Geodesic active contours , Caselles V, Kimmel R, Sapiro G, IJCV, 22 (1): 61-79 FEB-MAR 1997.
  • What is in a pebble shape , D. Durian.
  • Scale-Space and Edge-Detection using Anisotropic Diffusion, P. Perona and J. Malik, IEEE Transactions on PAMI, 12 (7): 629-639 JUL 1990.
  • Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, G. Aubert and P. Kornprobst, Series: Applied Mathematical Sciences. Volume. 147, Springer 2002.

    Projects:
  • Linear active contours without edges : Jarrick Lau and Arif Tirta.
    This project was on the extension of the piecewise-constant active contours model without edges to the piecewise-linear case.

  • Image denoising with total variation minimization and different L^p norms for the fidelity term: Avanti Paranjpye and Edward Cheon
  • Project

    This project was devoted to comparisons using the total variation minimization model for image denoising, for various L^p norms of the fidelity term.

  • Geodesic active contours for contour detection of pebble shapes and computation of the cumulative curvature: Tony Kim and Grace Tsui.
    This project was on the applications of geodesic active contours to images of pebbles. The goal was to detect and extract the contour shape of the pebble, and compute the cumulative distribution of the curvature. This is useful in the study of erosion of pebbles, in physics. This project is in collaboration with Prof. Douglas Durian, from the Physics Dept., UCLA.



    REU Program Summer 2000

    Mentors: Luminita Vese and Tony Chan.
    Research project: Minimizing functionals using partial differential equations and applications to matching of objects in dimension one.
    Students: Roya Furmurly and Narineh Movsessian.



    Useful Links

  • Math 199 General Course Information
  • IPAM Research in Industrial Projects for (undergraduate) Students (RIPS)