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)

Heres 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)

(Lets 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