Question

Assume the stereo geometry described in class with the 3 -D origin at (0,0,0), a baseline of b=3 cm separating the two lens centers, and a distance between each lens and corresponding image plane of f=0.5 cm. The optical axis of each camera is parallel to the z-axis of the 3-D coordinate system. The left and right image planes each have their own local coordinate systems and a point P at (x,y,z) in the 3 - D scene appears at location (x l′,yl′)=(0.5,1.0) in the left image and at (xr′,yr' )=(2.0,1.0) in the right image where all values are in cm.

a) For the point P what is the epipolar line?
b) Why are epipolar lines important?
c) Find the location (x,y,z) of the point P in the 3 -D scene.

Answer 1

a) The epipolar line for point P is the line connecting the left and right image points corresponding to P. b) Epipolar lines are important for determining correspondences between points in stereo images. c) To find the location of point P in the 3D scene, use triangulation.

Step-by-step explanation:

a) The epipolar line for point P is the line connecting the left and right image points corresponding to P. In this case, the epipolar line passes through the left image point (0.5, 1.0) and the right image point (2.0, 1.0).

b) Epipolar lines are important because they help us determine correspondences between points in stereo images. They allow us to find matching points in different camera views, which is necessary for tasks like 3D reconstruction and depth estimation.

c) To find the location (x,y,z) of point P in the 3D scene, we can use the concept of triangulation. By knowing the distance between the two lens centers (baseline) and the distance between each lens and the corresponding image plane (focal length), we can calculate the disparity between the left and right image points. Using the disparity and the known parameters, we can then find the 3D coordinates of point P.