Calculate epipolar line from essential matrix

Question

I have a question concerning a problem that was given in my Image Processing and Computer Vision Class:

Given: ->The intrinsic parameters of both cameras K=K'=1 [3x3 identity matrix] ->The fundamental matrix

Calculate i) the epipolar points of both cameras ii) the epipolar lines associated to point x=(2,2) (this is the point in the image plane of camera 1, i.e. the projection of a unknown 3D point seen by camera 1.

Solution: i) is easy. just solve the equations for F*e=0 and e'F=0 (i did that already) ii) i dont know for sure. I just know that i can calculate the epipolar line vector l by l=F*p (or Ftransposed for the other camera respectively, where p is a 3D point). is there a way to get the transformation matrix between the two cameras (i.e. the camera matrix of camera 2 if i assume camera 1 is alignet at the origin)

any help appreciated, Thanks in advance!

Answer 1

there is a point line correspondence, so for any given point in image 1 your can compute the epipolar line corresponding to that point by the equation you have mentioned. I am not sure what do you mean by transformation between two cameras, but if you know the fundamental matrix, you don't need any information about the intrinsic parameters of the cameras for a point line corerspondence.

you cannot compute the camera matrix for the second camera with just the fundamental matrix