ECE 497 YM - ADVANCED GEOMETRIC APPROACH TO COMPUTER VISION AND VISION BASED CONTROL Spring 2001, ECE, University of Illinois at Urbana-Champaign

"The real voyage of discovering consists not only 
   in seeking new lands, but in seeing with new eyes." 
                                        
                                  ---- Marcel Proust

Grades

• Semester is over. This homepage is now officially closed - links to handouts and homeworks are no longer accessible.
  
  
• Final Grades (Grades are followed by last four digits of your SSN's):
  A+: 2232, 3607 (excellent)
  A : 9586, 3818, 0745, 1604 (very good)
  A-: 2332, 0164 (good)
  If you have any questions regarding your final grade, please contact me through email. Have a happy summer vacation!
  
  

Prerequisites:
There is no a priori knowledge in computer vision required. This course may be taken independently of or together with the other Computer Vision course CS443/ECE449. The prerequisites are very much the same.

*This course does require a solid background in linear algebra (Math 318, Math381 or ECE415).

*Familiarity with MATLAB is recommended. If you have never used it before, it is never too late to start learning it now.

*Some familiarity with differential geometry (Math423 or Math424), control theory (ECE415), estimation theory(ECE461), or rigid body kinematics (ECE389/GE389) will certainly increase your appreciation but not crucial nor required.

*You may not need any of the above, as long as you are mathematically sophisticated enough. But you'd better talk to me first before you go ahead and register in this course.

Required Text:

*Lecture Notes (to be provided by the instructor), based on a working manuscript by Yi Ma, S. Soatto, J. Kosecka and S. Sastry.

Supplementary Text:

* Multiple View Geometry in Computer Vision , R. Hartley and A. Zisserman, Cambridge Press, 2000. (Available for purchase at the bookstores)

* Computer Vision - A Modern Approach , a book being written by David Forsyth and Jean Ponce (available online).

Reserved References (in the Engineering Library):

*A Mathematical Introduction to Robotic Manipulation, R. Murray, Z.-X. Li and S. Sastry, CRC Press Inc. 1994.

*Three-Dimensional Computer Vision: A Geometric Viewpoint, O. Faugeras, MIT Press, 1993.

*Robot Vision, B. Horn, MIT Press, 1986.

*Theory of Reconstruction from Image Motion, S. Maybank, Springer-Verlag, 1993.

*Motion and Structure From Image Sequences, J. Weng, N. Ahuja and T. Huang, Springer-Verlag, 1993.

*An Introduction to Differential Manifolds and Riemannian Geometry, W. Boothby, Academic Press, 1986.

Grading Policy: Homework (60%) and Final Project (40%).

*Homework: You are allowed to discuss on the homework in small groups, but you must write the solution independently to hand in. No late homework will be accepted (unless an extension is granted by the instructor to the whole class).

*Final Project: The final project can be done in a group of 2 or 3 students - depending on the final size of the class. The project can be theoretical, experimental or a mix of both. It consists of a midterm proposal, a final presentation (in class) and a report. With the instructor's approval, the final project can be related to the student's own graduate research.

Course Description and Outline ( postscript file or PDF file )

Topics and Schedule:

*Representation of a three-dimensional moving scene: Rigid motion, canonical exponential coordinates, Rodrigues formula, Euclidean, affine and projective transformations.

*Image formation basics: Mathematical model for ideal perspective projection and the pinhole camera, other geometric projection models.

*Image primitive and correspondence: Photometric features and geometric features, image correspondences and optical flows, feature selection, matching and tracking.

*Pose reconstruction from two views: Epipolar geometry, geometric characterization of the essential matrix and an eight-point linear algorithm.

*Velocity reconstruction from optical flow: Continuous epipolar geometry, geometric characterization of the continuous essential matrix and an eight-point linear algorithm.

*Uncalibrated camera: uncalibrated epipolar geometry, the fundamental matrix, Kruppa's equation and its degeneracy, camera self-calibration, projective, affine and Euclidean reconstruction, reconstruction up to ambiguous transformations.

*Project midterm proposal (7th week): A 1-2 page project proposal from each team.

*Multi-view reconstruction: Multi-linear constraints on images, algebraic and geometric dependency among multi-linear constraints.

*Batch reconstruction from multiple images: Estimation and optimization in presence of algebraic constraints, choice of objective functions, optimization on manifolds.

*Recursive estimation from image sequences: motion and structure as a filtering problem, observability, realization, stability, implicit extended Kalman filter (IEKF).

*Selected topics in vision based control: Vision based navigation (of mobile robot), vision based landing (of helicopter), kinematic chains and tracking of multi-body motion, three-dimensional map/model building from images.

*Final project presentation and report (last week): 20 minutes in class presentation for each project.

• Homework #1: homework1.ps.gz or homework1.pdf (due on February 14th).
• Homework #2: homework2.ps.gz or homework2.pdf (due on February 28th). Here is the image lena.gif .
• Homework #3: homework3.ps.gz or homework3.pdf (due on March 21st).
• Homework #4: homework4.ps.gz or homework4.pdf (due on April 6th).
• Homework #5: homework5.ps.gz or homework5.pdf (due on April 20th).

• Note: Homework #2 is now due on March 7th (upon popular demand).
  
  

• Graphical models for shape reconstruction from estimated surface normals, N. Petrovic and I. Cohen. (Presentation, May 2nd)
• "Visual control of a planar 3-degree-of-freedom manipulator", S. Bunchongchuitr.
• Visual servoing through affine transformation estimation, N. Gans.
• Shape by space carving, H. Wang and N. Xu.
• Multiple rigid body motion detection", K. Huang and J. Geis.
• Stereo vision system for hand gesture, K. Smith.
  
  
• Note: Project proposals from each team will be posted here soon. Each team will report their final project results (reports, codes, demos and systems) through a webpage. As soon a team thinks its webpage is in presentable shape, it may request to be linked here.
  

• Handout #1: notes1.ps.gz or notes1.pdf (out on January 18th). On "Rigid Body Transformation".
• Handout #2: notes2.ps.gz or notes2.pdf (out on January 26th). On "Rigid Body Transformation Continued".
• Supplementary Handout: SVD.ps.gz or SVD.pdf (out on January 31st). On "Singular Value Decomposition".
• Handout #3: notes3.ps.gz or notes3.pdf (out on January 31st). On "Image Formation Basics".
• Handout #4: notes4.ps.gz or notes4.pdf (out on February 2). On "Geometric Image Features".
• Handout #5: notes5.ps.gz or notes5.pdf (out on February 9). On "Pose Estimation from Two Views: A Linear Solution".
• Handout #6: notes6.ps.gz or notes6.pdf (out on February 16). On "Velocity Reconstruction from Optical Flows: A Linear Solution".
• Handout #7: notes7.ps.gz or notes7.pdf (out on February 26). On "Uncalibrated Camera: An Introduction".
• Handout #8: notes8.ps.gz or notes8.pdf (out on March 28). On "Preliminary Multiple View Reconstruction".
• Handout #9: notes9.ps.gz or notes9.pdf (out on April 6). On "Optimal Pose and Structure Reconstruction: Two Views".
• Supplementary Handout: LLSE.ps.gz or LLSE.pdf (out on April 13). On "Least-square Estimation and Filtering".
• Handout #10: notes10.ps.gz or notes10.pdf (out on April 16). On "Recursive Estimation".
• Handout #11: notes11.ps.gz or notes11.pdf (out on April 25). On "Vision Based Control".

• Note: There was a typo in Handout #5, page 5, equation (16). The above is now corrected version (02/28/01, 5:50pm).
  
  

* World computer vision homepage (where, with a little patience, you may find pretty much everything you need to know about vision).

* CVonline collection of computer vision materials (a good tutorial type of online resource for computer vision).

* Common image processing operators (some useful low level image processing routines).

* Basic Image Processing Demos (some old image processing demos that I did a long time ago when I was TAing at Berkeley - the MATLAB codes are already obsolete).

* UIUC robotics and computer vision group.

* UC Berkeley computer vision group.

* Stanford computer vision group.

* MIT AI Lab computer vision groups.

* UCLA computer vision group.

* My publication (which may be related to some of the subjects covered in class).