Question

Compute the epipoles e and e′ in homogeneous coordinates

Answer 1

To compute the epipoles e and e' in homogeneous coordinates, one must find the null spaces of the fundamental matrix F and its transpose, FT, which correspond to e and e', respectively. This is often done using singular value decomposition (SVD).

Step-by-step explanation:

To compute the epipoles e and e' in homogeneous coordinates, you first need to understand the fundamental matrix F which relates corresponding points in stereo images. The epipole e in the first image is the point such that Fe equals to the zero vector, meaning e is the null space of F. Similarly, the epipole e' in the second image is defined by the equation FTe' = 0, meaning e' is the null space of the transpose of F.

Step-by-step, if F is known, the epipoles can be computed as follows:

1. Compute the null space of F, which gives you the epipole e in the first image.
2. Compute the null space of FT (the transpose of F), which gives you the epipole e' in the second image.

These computations, typically performed using singular value decomposition (SVD), provide the epipoles in homogeneous coordinates. If F is a 3x3 matrix, then the epipoles will be 3x1 vectors in homogeneous coordinates.