GEOMETRY AND ALGEBRA IN COMPUTER VISION Research Among Peers (RAP), Fall 2002 Mathematics & ECE, University of Illinois at Urbana-Champaign

"Algebra is but written geometry; 
 geometry is but drawn algebra." 
               ---Sophie Germain

Program mission

• Meeting schedule and place: Friday 3pm - 4pm, 3169 Beckman Institute.
  
  
• Agenda of the week (Nov. 15): Kun Huang (student of Professor Ma) will speak about multiple-view 3-D reconstruction.
• Agenda of the week (Nov. 8): Professor Jean Ponce from CS speaks on Object Recognition (survey like).
• Agenda of the week (Nov. 1): Professor Fossum speaks on Hyperbolic Geometry and its relations to omnidirectional camera.
• Agenda of the week (Oct. 25): Professor Ma speaks on geometry of catadioptric camera, fundamental matrix and lorenz group.
• Agenda of the week (Oct. 11): Group Discussion. Bring you favorite problems, topics, or subjects for open discussion.
• Agenda of the week (Oct. 4): Professor Fossum speaks on real algebraic geometry and semi-algebraic sets.
• Agenda of the week (Oct. 3): A special vision seminar by Rene Vidal (a graduating PhD student of Professor Shankar Sastry, EECS UC Berkeley). The talk will present some fantastic results on Segmentation of Dynamical Scenes.
• Agenda of the week (Sept. 27): Svetlana Lazebnik (a PhD student of Professor Ponce) speaks on perspective visual hull and related research topics.
• Agenda of the week (Sept. 20): Cancelled.
• Agenda of the week (Sept. 13): Professor Ma speaks on group symmetry and multiple view geometry.
• Agenda of the week (Sept. 6): Professor Daniilidis from Upenn speaks on omnidiretional camera related research topics. Open discussions.

Professor Robert Fossum
Office: 2025 Beckman, Phone: 244-3572
Email: r-fossum@uiuc.edu

Students:
Ashutosh Garg (ashutosh@ifp.uiuc.edu),
John Lin (jy-lin@ifp.uiuc.edu),
Wei Hong (weihong@control.csl.uiuc.edu),
Yang Yang (yangyang@control.csl.uiuc.edu),
Jie Lai (jielai@uiuc.edu),
Kun Huang (kunh@control.csl.uiuc.edu),
Shankar Ramamohan (srrao@uiuc.edu),
Yu Huang (yuhuang@uiuc.edu),
Han Xu (xuhan@ifp.uiuc.edu)

Faculties:
Yoshi Shinagawa (sinagawa@uiuc.edu),
Volodymyr Kindratenko (kindr@ncsa.uiuc.edu),
Minh N. Do (minhdo@uiuc.edu),
John Sullivan (jms@math.uiuc.edu),
Sheldon Katz (katz@math.uiuc.edu),
Mathew Ando (mando@math.uiuc.edu),
Jeff Erickson (jeffe@uiuc.edu),
Sariel Har-Peled (sariel@cs.uiuc.edu),
Jean Ponce (ponce@cs.uiuc.edu)

If you would like to participate or be informed, simply send an email to yima@uiuc.edu

• Extension of Kruppa and Demazure's theorem: multiple views or high dimensions.
• Human motion: tracking, estimation, and animation
  • Too many references to list here (more than a hundred).
• Statistics, recognition, and classification in geometric spaces (manifolds)

Other related topics

• Multiple view geometry: classic and generalized
  • Rank conditions on the multiple view matrix. Yi Ma, Kun Huang, Rene Vidal, Jana Kosecka and Shankar S. Sastry, submitted to International Journal of Computer Vision, October 8, 2001.
  • Generalized rank condition in multiple view geometry with applications to dynamical scenes, K. Huang, Y. Ma and R. Fossum, submitted to ECCV, 2002.
  • General rank condition in multiple view geometry, R. Fossum, K. Huang and Y. Ma, submitted to Discrete and Computational Geometry, 2001.
  • On projection matrices P^k --> P^2, k = 3,..., 6, and their applications in computer vision, L. Wolf and A. Shashua. Proceedings of the international conference on computer vision, pages 412-419, Vancouver, Canada, 2001.
• Computer vision and graphics
• Vision based control and robotics

• Books on multiple view geometry
  • An Invitation to 3-D Vision, Yi Ma, J. Kosecka, S. Soatto and S. Sastry, Springer (expected 2002).
  • The Geometry of Multiple Images, O. Faugeras and Q.-T. Luong, MIT press, 2001.
  • Multiple View Geometry in Computer Vision, R. Hartley and A. Zisserman, Cambridge University press, 2000.