The fix overrides user selection of solver and it's not obvious behaviour. Alternatives I see:

• Add recommendation to documentation how to check the function result (estimate error) and add recommendations.
• Change default method value to make the step-by-step approach more obvious.

Let me talk to colleagues and I'll return back.

The fix overrides user selection of solver and it's not obvious behaviour. Alternatives I see:

* Add recommendation to documentation how to check the function result (estimate error) and add recommendations.
* Change default method value to make the step-by-step approach more obvious.

Let me talk to colleagues and I'll return back.

@asmorkalov This isn't correct fix (because of that I moved PR to draft state). Problem isn't about solver. I guess, that it is a fundamental problem. In getPerspectiveTransform we search perspective transform only with h_33 != 0 (because use h_33 = 1 normalization), but for several cases (including issue case) solution should have h_33 = 0, because there is no proper solution with h_33 != 0. In issue reproducer correct inv_M* (obtained by inverse and findHomography) matrices have h_33 = 0.

I will try to prepare a correct fix in the near future

@asmorkalov In

A More General Approach
What might be wrong with setting h33 = 1?
If h33 actually = 0, we can’t get the right answer.

So, that's exactly the problem. We can't limit ourselves only with h33 = 1 normalization case where h33 != 0. In case of failure we must consider h11^2 + h12^2 + h13^2 + h21^2 + h22^2 + h23^2 + h31^2 + h32^2 + h33^2 = 1 normalization case where h33 can be zero.

For implementation of new normalization case I used last 3 slides of the same source

@asmorkalov Do you have any ideas why the error on macOS or ARM64 is significantly larger?

/Users/opencv-cn/GHA-OCV-2/_work/opencv/opencv/opencv/modules/imgproc/test/test_imgwarp.cpp:1796: Failure
Expected: (cvtest::ocl::TestUtils::checkNorm2(obtained_homogeneous_dst_points, expected_homogeneous_dst_points)) <= (1e-8), actual: 0.00404862 vs 1e-08
/home/ci/opencv/modules/imgproc/test/test_imgwarp.cpp:1796: Failure
Expected: (cvtest::ocl::TestUtils::checkNorm2(obtained_homogeneous_dst_points, expected_homogeneous_dst_points)) <= (1e-8), actual: 0.0620923 vs 1e-08

Tried to use double in test - to increase precision

@MaximSmolskiy Friendly reminder.

@asmorkalov Do you have any ideas why the error on macOS or ARM64 is significantly larger?

/Users/opencv-cn/GHA-OCV-2/_work/opencv/opencv/opencv/modules/imgproc/test/test_imgwarp.cpp:1796: Failure
Expected: (cvtest::ocl::TestUtils::checkNorm2(obtained_homogeneous_dst_points, expected_homogeneous_dst_points)) <= (1e-8), actual: 0.00404862 vs 1e-08
/home/ci/opencv/modules/imgproc/test/test_imgwarp.cpp:1796: Failure
Expected: (cvtest::ocl::TestUtils::checkNorm2(obtained_homogeneous_dst_points, expected_homogeneous_dst_points)) <= (1e-8), actual: 0.0620923 vs 1e-08

@asmorkalov I found that the significant difference in accuracy was due to the cv::eigen function (which depends on the Eigen library being included):

1. without Eigen - good accuracy
2. with Eigen - bad accuracy

I used cv::SVDecomp instead of cv::eigen to improve accuracy and get rid of this rather unexpected behavior