1 NORMALIZED 8-POINT ALGORITHM (10 POINTS )
Implement the function “FM_by_normalized_8_point” in “FM.py”. You need to compute the Fundamental Matrix using the 8-point algorithm. To verify your implementation, you can compare your result with the following opencv function:
F, _= cv2.findFundamentalMat(pts1, pts2, cv2.FM_8POINT)
Here’s the general idea for normalizing the input points:
1. Find the centroid of the points (find the mean x and mean y value)
2. Compute the mean distance of all the points from this centroid
3. Construct a 3 by 3 matrix that would translate the points so that the mean distance would be sqrt(2)
(Let's say (x,y) is the centroid and m is the mean distance from centroid. This would be the matrix:
[[sqrt(2)/m, 0, -x(sqrt(2)/m)],
[0, sqrt(2)/m, -y(sqrt(2)/m)],
[0, 0, 1]]
Now you can use this matrix to normalize (and later de-normalize) the points.
You can find more information about this in the wikipedia page.
- normalize the input points
+ 2 pts
- construct the coefficient matrix of the linear system correctly
+ 2 pts
- solve the linear least square problem correctly
+ 2 pts
- get correct results
+ 2 pts
- comments that explain in details how your code works
+ 2 pts
2 R ANSAC (10 POINTS )
Implement the function “FM_by_RANSAC” in “FM.py”. You need to compute the Fundamental Matrix using RANSAC. Here is the pseudo code:
To verify your implementation, you can compare your result with the following opencv function:
F, mask = cv2.findFundamentalMat(pts1,pts2, cv2.FM_RANSAC)
- compute number of inliers correctly
+ 3 pts
- get correct results
+ 5 pts
- comments that explain in details how your code works
+ 2 pts
