Merge pull request #25182 from MaximSmolskiy:increase-decomposeProjectionMatrix-precision-for-small-scales
Increase decomposeProjectionMatrix precision for small scales #25182
### Pull Request Readiness Checklist
Fix #23733
It is checked before that `|s| > DBL_EPSILON` (if not, then `s` will be equal to `0`, but `c` will be equal to `1`, then `z` will be equal to `1` and there will be no any problems with small values), so `sqrt(c^2 + s^2) >= |s| > DBL_EPSILON` and thus small values are already taken into account before and there is no need to add `DBL_EPSILON` to `c^2 + s^2` (and I think adding `DBL_EPSILON^2` instead of `DBL_EPSILON` would be more correct).
I ran `Python` script from issue.
`NumPy` and `SciPy` results
```
*Numpy*
P (case 1):
[[1. 0. 0. 0.]
[0. 1. 0. 0.]
[0. 0. 1. 0.]]
Numpy, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
Numpy scaled 1e-6, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
P (case 2):
[[52. -7. 4. 12.]
[-6. 49. 12. 8.]
[ 4. 17. 1. 0.]]
Numpy, R.T @ R - I:
[[-8.88178420e-16 -3.86302608e-16 -2.52050796e-17]
[-3.86302608e-16 -5.55111512e-16 7.11675423e-18]
[-2.52050796e-17 7.11675423e-18 -5.55111512e-16]]
Numpy scaled 1e-6, R.T @ R - I:
[[ 2.22044605e-16 -2.00683644e-16 -1.90063998e-17]
[-2.00683644e-16 0.00000000e+00 1.16926308e-17]
[-1.90063998e-17 1.16926308e-17 2.22044605e-16]]
*Scipy*
P (case 1):
[[1. 0. 0. 0.]
[0. 1. 0. 0.]
[0. 0. 1. 0.]]
Scipy, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
Scipy scaled 1e-6, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
P (case 2):
[[52. -7. 4. 12.]
[-6. 49. 12. 8.]
[ 4. 17. 1. 0.]]
Scipy, R.T @ R - I:
[[-1.11022302e-16 -8.74062812e-18 -1.26178867e-17]
[-8.74062812e-18 -1.11022302e-16 2.07820373e-17]
[-1.26178867e-17 2.07820373e-17 -1.11022302e-16]]
Scipy scaled 1e-6, R.T @ R - I:
[[0.00000000e+00 4.04691435e-17 1.12452918e-16]
[4.04691435e-17 4.44089210e-16 3.74164141e-16]
[1.12452918e-16 3.74164141e-16 4.44089210e-16]]
*Numpy*
Numpy, P' - P:
[[ 1.35525272e-20 -9.31736242e-21 8.47032947e-22 3.38813179e-21]
[-3.38813179e-21 6.77626358e-21 1.69406589e-21 0.00000000e+00]
[-1.69406589e-21 0.00000000e+00 0.00000000e+00 4.85524279e-22]]
*Scipy*
Scipy, P' - P:
[[0.00000000e+00 8.47032947e-22 3.38813179e-21 3.38813179e-21]
[3.38813179e-21 1.35525272e-20 1.52465931e-20 1.52465931e-20]
[8.47032947e-22 3.38813179e-21 2.54109884e-21 3.39866995e-21]]
```
`OpenCV` results before
```
*OpenCV*
P (case 1):
[[1. 0. 0. 0.]
[0. 1. 0. 0.]
[0. 0. 1. 0.]]
OpenCV, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
OpenCV scaled 1e-6, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
P (case 2):
[[52. -7. 4. 12.]
[-6. 49. 12. 8.]
[ 4. 17. 1. 0.]]
OpenCV, R.T @ R - I:
[[ 2.22044605e-16 -9.12253504e-17 -2.20527203e-19]
[-9.12253504e-17 0.00000000e+00 -9.12405093e-18]
[-2.20527203e-19 -9.12405093e-18 2.22044605e-16]]
OpenCV scaled 1e-6, R.T @ R - I:
[[-1.28197013e-06 1.30450769e-07 7.67357467e-09]
[ 1.30450769e-07 -1.52141637e-06 -9.92455574e-09]
[ 7.67357467e-09 -9.92455574e-09 -1.35328272e-06]]
*OpenCV*
OpenCV, P' - P:
[[-6.75449076e-11 1.73936564e-11 -4.94463312e-12 -1.61106020e-11]
[ 1.41759913e-11 -7.54512016e-11 -1.67717374e-11 -9.74644390e-12]
[-2.90254385e-12 -2.53521998e-11 -1.49130587e-12 4.00724440e-13]]
```
`OpenCV` results after
```
*OpenCV*
P (case 1):
[[1. 0. 0. 0.]
[0. 1. 0. 0.]
[0. 0. 1. 0.]]
OpenCV, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
OpenCV scaled 1e-6, R.T @ R - I:
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
P (case 2):
[[52. -7. 4. 12.]
[-6. 49. 12. 8.]
[ 4. 17. 1. 0.]]
OpenCV, R.T @ R - I:
[[ 2.22044605e-16 -9.12253504e-17 -2.20527203e-19]
[-9.12253504e-17 0.00000000e+00 -9.12405093e-18]
[-2.20527203e-19 -9.12405093e-18 2.22044605e-16]]
OpenCV scaled 1e-6, R.T @ R - I:
[[ 0.00000000e+00 4.36198333e-17 -2.66855078e-17]
[ 4.36198333e-17 2.22044605e-16 3.17216400e-17]
[-2.66855078e-17 3.17216400e-17 -2.22044605e-16]]
*OpenCV*
OpenCV, P' - P:
[[ 6.77626358e-21 0.00000000e+00 -8.47032947e-22 1.69406589e-21]
[-1.69406589e-21 6.77626358e-21 0.00000000e+00 3.38813179e-21]
[ 8.47032947e-22 3.38813179e-21 2.11758237e-22 1.45657284e-21]]
```
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
Maxim Smolskiy
e3ff6ce0cc