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Update Gao P3P with Ding P3P #27736 ### Pull Request Readiness Checklist 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 --- The current Gao P3P implementation does not cover all the degenerate cases, **see last line** in: https://github.com/opencv/opencv/blob/6d889ee74c94124f6492eb8f0d50946d9c31d8e9/modules/calib3d/src/p3p.cpp#L211-L221 See also: - https://github.com/opencv/opencv/issues/4854 --- <details> <summary>OBSOLETE</summary> To fix this, the USAC P3P from OpenCV 5 is used instead: https://github.com/opencv/opencv/blob/7e6da007cddcf83a527dfda95d57228fa5a535d3/modules/3d/src/usac/pnp_solver.cpp#L282 --- ## Some results ### Old P3P vs new In the following video, I have tried to highlight the viewpoints which cause issues: https://github.com/user-attachments/assets/97bec6a6-4043-4509-b50e-a9856d6423bd | | Old P3P | New P3P | | -------- | ------- | ------- | | Mean (ms) | 0.045701 | 0.024816 | | Median (ms) | 0.025146 | 0.023193 | | Std (ms) | 0.028953 | 0.006124 | ### New P3P vs AP3P https://github.com/user-attachments/assets/eaeb21dc-3ffd-4b6c-9902-4352f824aa45 The AP3 method is superior both in term of accuracy and computation time: | | New P3P | AP3P | | -------- | ------- | ------- | | Mean (ms) | 0.043750 | 0.023442 | | Median (ms) | 0.023193 | 0.021484 | | Std (ms) | 0.039920 | 0.005265 | ### New P3P vs AP3P (range test) https://github.com/user-attachments/assets/572e7b7a-2966-4bed-8e0c-b93d863987dc The implemented P3P method does not work well when the tag is small, at long range. | | New P3P | AP3P | | -------- | ------- | ------- | | Mean (ms) | 0.031351 | 0.025189 | | Median (ms) | 0.022217 | 0.020996 | | Std (ms) | 0.024920 | 0.009633 | --- - I have tried to simplify the P3P code, hope I did not break the implementation code - calculations are performed using double type for simplicity. - code such as the following are redundant and no more needed and should be replaced by `cv::Rodrigues`: https://github.com/opencv/opencv/blob/6d889ee74c94124f6492eb8f0d50946d9c31d8e9/modules/calib3d/src/usac/pnp_solver.cpp#L395 </details>