Labs for a University Course
To run computer these vision applications you need to have Python3.10.
- Clone repo:
git clone https://github.com/maksymshylo/computational_geometry.git
- Create virtual environment.
python3.10 -m venv .venv
- Activate it
source .venv/bin/activate
- Install requirements:
pip install -r requirements.txt
The application calculates disparity map for x and y axes with Semi-Global Matching algorithm.
$ python3 lab2/sgm_stereo.py --help
usage: sgm_stereo.py [-h] left_image right_image smoothing_coef min_dx max_dx min_dy max_dy
positional arguments:
left_image Path to left image
right_image Path to right image
smoothing_coef Smoothing coefficient for binary penalties
min_dx Min value for horizontal disparity
max_dx Max value for horizontal disparity
min_dy Min value for vertical disparity
max_dy Max value for vertical disparity
python3 labs/lab2/sgm_stereo.py \
--right_image test_images/teddy_right.png \
--left_image test_images/teddy_left.png \
--smoothing_coef 5 \
--min_dx 0 \
--max_dx 50 \
--min_dy 0 \
--max_dy 0
Left image | Right image | Disparity map |
---|---|---|
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python3 labs/lab2/sgm_stereo.py \
--right_image test_images/sofa_right.png \
--left_image test_images/sofa_left.png \
--smoothing_coef 5 \
--min_dx 0 \
--max_dx 20 \
--min_dy 0 \
--max_dy 20
Left image | Right image | Disparity map |
---|---|---|
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The application creates a panorama by applying homography transformation matrix.
$ python3 labs/lab3/homography.py --help
usage: homography.py [-h] --img1 IMG1 --img2 IMG2 --ransac_iter RANSAC_ITER --out_img OUT_IMG
options:
-h, --help show this help message and exit
--img1 IMG1 path to img1
--img2 IMG2 path to img2
--ransac_iter RANSAC_ITER max iteration for ransac algorithm
--out_img OUT_IMG path to output image
python3 labs/lab3/homography.py \
--img1 test_images/computer_1.png \
--img2 test_images/computer_2.png \
--ransac_iter 2000 \
--out_img computer_stitched.png
Left image | Right image | Stitched image |
---|---|---|
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The application creates a panorama by applying homography transformation matrix and Tree Reweighted Message Passing (TRW-S) as a stitching method.
Note: The first image for input is the base image for applying homography.
$ python3 labs/lab4/trws_stitch.py --help
usage: trws_stitch.py [-h] --images-list IMAGES_LIST [IMAGES_LIST ...]
--n-iter-trws N_ITER_TRWS --out-img OUT_IMG
options:
-h, --help show this help message and exit
--images-list IMAGES_LIST [IMAGES_LIST ...] Image paths. First image is the Source image.
--n-iter-trws N_ITER_TRWS Max iteration for TRWS algorithm
--out-img OUT_IMG Path to stitched image.
python3 labs/lab4/trws_stitch.py \
--images-list test_images/book2.jpg test_images/book1.jpg test_images/book3.jpg \
--n-iter-trws 5 \
--out-img book_stitched_trws.png
The first image | The second image | The third image | Stitched image |
---|---|---|---|
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python3 labs/lab4/trws_stitch.py \
--images-list test_images/ball2.jpg test_images/ball3.jpg test_images/ball1.jpg \
--n-iter-trws 5 \
--out-img ball_stitched_trws.png
The first image | The second image | The third image | Stitched image |
---|---|---|---|
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The application calculates the best fundamental matrix with 7-point Algorithm.
Note: The first image for input is the base image for applying homography.
$ python3 labs/lab5/fundamental_matrix.py --help
usage: fundamental_matrix.py [-h] left_image right_image epsilon n_iter
positional arguments:
left_image Left image
right_image Right image
epsilon Threshold parameter in PIXELS
n_iter Number of iterations
python3 labs/lab5/fundamental_matrix.py \
--left_image test_images/bike1.jpeg \
--right_image test_images/bike2.jpeg \
--epsilon 1 \
--n_iter 1000
The first image | The second image |
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python3 labs/lab5/fundamental_matrix.py \
--left_image test_images/mount1.jpeg \
--right_image test_images/mount2.jpeg \
--epsilon 1 \
--n_iter 1000
The first image | The second image |
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python3 labs/lab5/fundamental_matrix.py \
--left_image test_images/messL.png \
--right_image test_images/messR.png \
--epsilon 1 \
--n_iter 1000
The first image | The second image |
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The application calculates essential matrix for 2 images.
$ python3 labs/lab6/essential_matrix.py --help
usage: essential_matrix.py [-h] [--left_image LEFT_IMAGE] [--right_image RIGHT_IMAGE] [--epsilon EPSILON] [--n_iter N_ITER]
[--pixel_size PIXEL_SIZE]
options:
-h, --help show this help message and exit
--left_image LEFT_IMAGE left input image
--right_image RIGHT_IMAGE right input image
--epsilon EPSILON threshold parameter in PIXELS
--n_iter N_ITER number of iterations for RANSAC fundamental matrix finding
--pixel_size PIXEL_SIZE size of pixel in microns
python3 labs/lab6/essential_matrix.py \
--left_image labs/lab6/test_images/left.jpeg \
--right_image labs/lab6/test_images/right.jpeg \
--epsilon 1 \
--n_iter 1000 \
--pixel_size 0.8
output
Finding Essential matrix.
Input
Fundamental matrix:
[[-6.91974362e-09 3.82229878e-07 -3.72199828e-04]
[ 3.40310473e-07 -4.92928196e-08 -2.91128152e-03]
[-3.43488734e-04 1.76278676e-03 1.00000387e+00]]
Intrinsic matrix:
[[5.75e+03 0.00e+00 1.50e+03]
[0.00e+00 5.75e+03 1.50e+03]
[0.00e+00 0.00e+00 1.00e+00]]
Step 1. Calculating essential matrix.
essential_matrix = intrinsic_matrix.T @ fundamental_matrix @ intrinsic_matrix =
[[ -0.22878402 12.63747533 1.09690089]
[ 11.25151503 -1.62974385 -14.2298415 ]
[ 0.90043483 13.00760602 -0.29703359]]
Step 2. Make singular value decomposition of the essential_matrix.
U, S, Vh = np.linalg.svd(essential_matrix)
U
[[-0.51093267 -0.46986081 -0.71984625]
[ 0.72682224 -0.68325893 -0.0699047 ]
[-0.4589959 -0.55891686 0.6906046 ]]
S
[1.90609931e+01 1.73054248e+01 1.36128410e-14]
Vh
[[ 0.41348573 -0.71412181 -0.5648536 ]
[-0.46710611 -0.69888418 0.54163898]
[ 0.78156345 -0.03988658 0.6225493 ]]
Step 3. Updating sigma to have sigma1=sigma2>0 and sigma3=0
S1 = (S[0] + S[1]) * 0.5 * np.identity(3); S1[-1, -1] = 0
np.diagonal(S1):
[18.18320898 18.18320898 0. ]
Step 4. Updating essential matrix
updated_essential_matrix = U @ S1 @ Vh.T =
[[ 2.2597089 10.31057155 -6.92025951]
[14.3367462 2.50956919 10.82465637]
[ 3.80659049 11.00116769 -6.11757954]]
Check rank of essential matrix: rank(updated_essential_matrix) = 2
Check essential matrix constraint:
0 = det(E) = 3.94798984843875e-13
0 = 2 * E @ E.T @ E - trace(E @ E.T ) * E =
[[ 4.09272616e-12 4.54747351e-12 -9.09494702e-13]
[-1.81898940e-12 3.63797881e-12 -4.54747351e-12]
[ 3.63797881e-12 4.54747351e-12 -4.54747351e-13]]
Calculating translation vector
translation_vector = ((S1[0, 0] + S1[1, 1]) * 0.5) * det(U) * Vh.T[2, :]
[-10.27085107 9.84873469 11.31994399]
Calculating rotation matrix
W = [[ 0 1 0]
[-1 0 0]
[ 0 0 1]]
rotation_matrix = det(U) * U @ W @ Vh.T * det(Vh.T) =
[[-0.96575665 0.25228888 0.06053438]
[ 0.19703588 0.8649821 -0.46150063]
[-0.16879264 -0.43376986 -0.88507217]]
The first image | The second image |
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