Description
Camera Calibration:
1) Load the 100 pairs of corresponding 2-D and 3-D points in the files 2Dpoints.txt and
3Dpoints.txt (the i
th row of both files corresponds to the i
th point). Use these point
correspondences to solve (using Eigen-analysis) for the camera matrix P (whose
rasterized vector p has a unit L2 norm). [5 pts]
2) Given the computed matrix P (from Problem 1), project the 3-D homogeneous points
(Xi,Yi,Zi,1) to 2-D. Compute the sum-of-squared error (sum-of-squared distances)
between the resulting 3-D-to-2-D projected points and the given 2-D points (ensure
all 2-D points are inhomogeneous). [3 pts]
Homography:
3) The file homography.txt contains 15 corresponding 2-D points from two different
images, where the first and second columns correspond to the x and y coordinates of
the points in the first image and the third and fourth columns correspond to the x and
y coordinates of the points in the second image. Load the 2-D point sets and use the
Normalized Direct Linear Transformation algorithm to compute the final
homography H that maps the original points from image 1 to image 2 (i.e., make sure
P2 = HP1). [5 pts]
4) Plot the points from image 2 and the projected points from image 1 on the same plot.
Make sure the projected points are converted into inhomogeneous form. [1 pt]
5) Compute the sum-of-squared error (squared Euclidean distance) between the actual
points from image 2 and the projected points from image 1. [2 pts]
6) As usual, turn in and upload your material.
