Project 3: Fundamental Matrix
Algorithm Description
For part one I just followed the description in the lecture slides by setting up the regression problem and solving using matlab's built in regression.
Part two is literally two lines of code. I again just followed the lecture slides.
Ransac implementation: For part three I looped 2000 times forming a random sampling of the matched points, finding the fundamental matrix using part two, then counted the number of inliers below an image-dependent threshold. The distance metric used was abs(xFx') since for perfect matches/F matrix this goes to zero. I then returned the F matrix with the highest number of inliers as well as the inliers themselves.
Results
Shown below is the output from the first step and the results of running the algorithm on the three image pairs. Part one did fine resulting in a scaled fundamental matrix. (notice the scale is negative). Part two looks reasonable as well with the epipolar lines always touching the point if not passing directly through it. The error is from the fact that least squares regression is not exact. Even though I played with the parameters for part 3 all three (num iterations, and the threshold) I still got the best results with the threshold set at .02 and num_iterations at 2000 for all three pairs. Gaudi obviously looks the worse, but the other two look good with reasonable matches./p>
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