EE 589/689 Foundations of computer vision (Fall quarter 2006): project 1

Study the file project1.m, which estimates the fundamental matrix (projective and affine, using different methods) and obtains affine structure from motion. What you have to do:

• Find 2 images of the same scene from quite different point of views and create a Matlab file containing the image file names and the corresponding points' coordinates (see ex_img.m for an example). Repeat for a stereo pair.
  One useful way to determine correspondences by hand with Matlab is to do:
  [I1,map1] = imread(file1); [I2,map2] = imread(file2);
  figure(1); image(I1); colormap(map1); title('image 1');
  figure(2); image(I2); colormap(map2); title('image 2');
  [u1,v1] = ginput; % Mark points in image 1
  [u2,v2] = ginput; % Mark corresponding points in image 2
  You can also use Matlab's data cursor and type the coordinates point by point (boring).
• Then, write the following functions called by project1.m (keep the input and output arguments strictly as indicated):
  • fmat8.m: fundamental matrix estimation
  • plotepip.m: plot images, correspondences and epipolar lines
  • fmat8aff.m: affine fundamental matrix estimation
  • affSfM.m: 2-view affine structure from motion (algorithm in 12.2.2 in the book)
  • affSfMtk.m: 2-view affine structure from motion (Tomasi-Kanade algorithm)
  • eucl_up.m: Euclidean upgrade assuming orthographic perspective
• Once your functions are working, use project1.m to explore the methods: try different image pairs, different correspondences, etc. Then, write a short report (1-2 pages) where you succintly comment on your results, in particular the following:
  • The quality of the fundamental matrix with the different methods: 8 points (try different subsets of 8 points), more than 8 points, and with/without preconditioning.
  • The location of the epipoles for each pair of images.
  • Affine reconstruction assumes weak (or orthographic) perspective. Comment on the results given the effect of perspective in the images.
  • The singular value curve of the measurement matrix in the Tomasi-Kanade algorithm.
• Email me:
  • A compressed file (gzip or zip) containing your two data files (each for a pair of images: very different views, and stereo pair), and your functions fmat8.m, etc.
  • A PDF file containing your evaluation & comments.

Deadline: Monday Nov. 20, 2006.

Suggested reading:

• Ch. 10-12 of the textbook (Forsyth and Ponce).
• Carlo Tomasi and Takeo Kanade: "Shape and motion from image streams under orthography: a factorization method". Int. J. Computer Vision 9(2):137-154 (Nov. 1992).

Auxiliary Matlab files:

• project1.m
• ex_img.m
• plot3D.m

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