Description

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​.

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)