Q1: What problem does epipolar geometry want to solve
use more than one camera to find the depth information loosen by taking an image using a pin-hole camera
Q2: How to understand epipolar means
the prefix “epi” from Greek epi ‘upon, near to, in addition’. which denote the concept “space around”
“polar” from the word “pole”
“pole” means “a long, slender, rounded piece of wood or metal, typically used with one end placed in the ground as a support for something”
so the “polar” in geometry field is explained in “the straight line joining the two points at which tangents from a fixed point touch a conic section.”
the final explanation of “epipolar geometry” is the geometry use the thin line(polar) to find the space information(epi-)
Q3: What concepts in this algorithm
EPILINE:
document refers
1
"The projection of the different points on OX form a line on the right plane (line l′)."
the point is the projection on the right image, it is pixels on image coordinate epiline corresponding to the point x on the left image it can be described as “epipolar constraint”
EPIPOLAR CONSTRAINT:
from the document
1
"It means, to find the point x (correspond pixel location) on the right image,search along this epiline. It should be somewhere on this line"
the document adds
1
"Think of it this way, to find the matching point in other images, you need not to search the whole image, just search along the epiline.So it provides better performance and accuracy"
EPIPOLAR PLANE:
all points will have its corresponding epilines in the other image. look at the image on the document to understand
EPIPOLE:
right camera projection pixel location on left image called “epipole”
Q4: How to find epipolar lines and epipoles above?
to find them, we need two more ingredients, Fundamental Matrix (F) and Essential Matrix (E).
Q5: The difference between Fundamental & Essential
Essential Matrix :
contains information about translation and rotation, which describes the location of the second camera, relative to the first in global coordinates.
Fundamental Matrix :
contains the same information as Essential Matrix in addition to the information about the intricacies of both cameras, so that we can relate the two cameras in pixel coordinates.
(If we are using rectified images and normalize the point by dividing by the focal lengths, F=E).
because Essential is a subset of Fundamental, we can say Fundamental Matrix F maps a point in one image to a line (epiline) in the other image.
