H = u2H( u, u0 )  H = hw05.u2H( u, u0 ) 
Create function u2H
computing homography from four image matches. Let u
be the image coordinates of points in the first image (2×4 matrix/np.array) and u0
(2×4) be the image coordinates of the corresponding points in the second image. Then H
is a 3×3 homography matrix (np.array), such that
$\lambda_i \left[\begin{array}{c}u_{0 i}\\1\end{array}\right] = H \left[\begin{array}{c}u_i\\1\end{array}\right]$
for all i
and some nonzero λ_i
. Matrix H
is regular. Return an empty array []
if there is no solution.
u2H
. Use the following test data:u
and u0
for your and the reference image, respectively.
H
) that maps your image to the reference image. Find it as the best homography by optimizing over all 210 quadruplets among the ten matches. Minimize the maximal transfer error (in the domain of points u0
) on all image matches. Create function u2h_optim
(with arbitrary inputs and outputs) solving this step. The function will be used in the one of the future homeworks.
u
, u0
, the array of indices of the four matches used to compute the homography as point_sel
and the homography matrix H
in 05_homography.mat
file.
H
. The pixels can be found e.g. by an image intensity thresholding, or coordinates C
of the square corners from Input Data can be used. Store the corrected bitmap image as 05_corrected.png
.
05_correctedn.png
.
H
. Export as 05_homography.pdf
.
The part of reference image is transferred to your image, so we need the transformation of coordinates in the opposite direction.
u
of all pixels in your image that are to be filled. These are typically integers.
u0
point to the reference image (typically not integers).
i
:
u0_{i}
. The easier way is to take the nearest pixel (rounding the coordinates). In general situations, the coordinates should be checked no to be outside the image.
u_{i}
).
Upload an archive consisting of:
matlab  python 

05_homography.mat 

05_homography.pdf 

05_corrected.png 

05_correctedn.png (optional) 

hw05.m  hw05.py containing required functions 
any other files required by your solution 
The input entry point script hw05
should make all work without manual intervention.