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Merge pull request #29175 from asmorkalov:as/geometry2
Geometry module #29175 OpenCV Contrib: https://github.com/opencv/opencv_contrib/pull/4129 CI changes: https://github.com/opencv/ci-gha-workflow/pull/313 Continues - https://github.com/opencv/opencv/pull/28804 - https://github.com/opencv/opencv/pull/29101 - https://github.com/opencv/opencv/pull/29108 - https://github.com/opencv/opencv/pull/28810 Todo for followup PRs: - [x] Rename doxygen groups - [x] Fix JS modules layout and whitelists - [ ] Sort tutorials code/snippets ### 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 - [ ] 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
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@inproceedings{ding2023revisiting,
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title={Revisiting the P3P Problem},
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author={Ding, Yaqing and Yang, Jian and Larsson, Viktor and Olsson, Carl and {\AA}str{\"o}m, Kalle},
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booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
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pages={4872--4880},
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year={2023},
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url={https://openaccess.thecvf.com/content/CVPR2023/papers/Ding_Revisiting_the_P3P_Problem_CVPR_2023_paper.pdf}
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}
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@article{lepetit2009epnp,
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title={Epnp: An accurate o (n) solution to the pnp problem},
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author={Lepetit, Vincent and Moreno-Noguer, Francesc and Fua, Pascal},
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journal={International journal of computer vision},
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volume={81},
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number={2},
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pages={155--166},
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year={2009},
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publisher={Springer},
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url={https://www.tugraz.at/fileadmin/user_upload/Institute/ICG/Images/team_lepetit/publications/lepetit_ijcv08.pdf}
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}
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@inproceedings{strobl2011iccv,
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title={More accurate pinhole camera calibration with imperfect planar target},
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author={Strobl, Klaus H. and Hirzinger, Gerd},
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booktitle={2011 IEEE International Conference on Computer Vision (ICCV)},
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pages={1068-1075},
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month={Nov},
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year={2011},
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address={Barcelona, Spain},
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publisher={IEEE},
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url={https://elib.dlr.de/71888/1/strobl_2011iccv.pdf},
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doi={10.1109/ICCVW.2011.6130369}
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}
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@inproceedings{kinectfusion,
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author = {Izadi, Shahram and Kim, David and Hilliges, Otmar and Molyneaux, David and Newcombe, Richard and Kohli, Pushmeet and Shotton, Jamie and Hodges, Steve and Freeman, Dustin and Davison, Andrew and Fitzgibbon, Andrew},
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title = {KinectFusion: Real-time 3D Reconstruction and Interaction Using a Moving Depth Camera},
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booktitle = {},
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year = {2011},
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month = {October},
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abstract = {
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KinectFusion enables a user holding and moving a standard Kinect camera to rapidly create detailed 3D reconstructions of an indoor scene.
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Only the depth data from Kinect is used to track the 3D pose of the sensor and reconstruct, geometrically precise, 3D models of the physical scene in real-time.
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The capabilities of KinectFusion, as well as the novel GPU-based pipeline are described in full. We show uses of the core system for low-cost handheld scanning,
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and geometry-aware augmented reality and physics-based interactions. Novel extensions to the core GPU pipeline demonstrate object segmentation and user interaction directly
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in front of the sensor, without degrading camera tracking or reconstruction. These extensions are used to enable real-time multi-touch interactions anywhere,
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allowing any planar or non-planar reconstructed physical surface to be appropriated for touch.
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},
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publisher = {ACM},
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url = {https://www.microsoft.com/en-us/research/publication/kinectfusion-real-time-3d-reconstruction-and-interaction-using-a-moving-depth-camera/},
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address = {},
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pages = {559-568},
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journal = {},
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volume = {},
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chapter = {},
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isbn = {978-1-4503-0716-1},
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}
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@article{fischler1981random,
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title={Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography},
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author={Fischler, Martin A and Bolles, Robert C},
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journal={Communications of the ACM},
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volume={24},
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number={6},
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pages={381--395},
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year={1981},
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publisher={ACM New York, NY, USA}
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}
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@inproceedings{Rabbani2006SegmentationOP,
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title={Segmentation of point clouds using smoothness constraints},
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keywords={ADLIB-ART-1373, EOS},
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author={Tahir Rabbani and Frank van den Heuvel and George Vosselman},
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year={2006},
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volume={35},
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pages={248--253},
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editor={H.G. Maas and D. Schneider},
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booktitle={ISPRS 2006 : Proceedings of the ISPRS commission V symposium Vol. 35, part 6 : image engineering and vision metrology, Dresden, Germany 25-27 September 2006}
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}
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@inproceedings{Terzakis2020SQPnP,
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title={A Consistently Fast and Globally Optimal Solution to the Perspective-n-Point Problem},
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author={George Terzakis and Manolis Lourakis},
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booktitle={European Conference on Computer Vision},
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pages={478--494},
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year={2020},
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publisher={Springer International Publishing},
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url={https://www.ecva.net/papers/eccv_2020/papers_ECCV/papers/123460460.pdf}
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}
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# Perspective-n-Point (PnP) pose computation {#calib3d_solvePnP}
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## Pose computation overview
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The pose computation problem @cite Marchand16 consists in solving for the rotation and translation that minimizes the reprojection error from 3D-2D point correspondences.
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The `solvePnP` and related functions estimate the object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients, see the figure below (more precisely, the convention in the computer vision field is to have the X-axis of the camera frame pointing to the right, the Y-axis downward and the Z-axis forward).
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Points expressed in the world frame \f$ \bf{X}_w \f$ are projected into the image plane \f$ \left[ u, v \right] \f$
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using the perspective projection model \f$ \Pi \f$ and the camera intrinsic parameters matrix \f$ \bf{A} \f$ (also denoted \f$ \bf{K} \f$ in the literature):
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\f[
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\begin{align*}
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\begin{bmatrix}
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u \\
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v \\
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1
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\end{bmatrix} &=
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\bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w
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\begin{bmatrix}
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X_{w} \\
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Y_{w} \\
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Z_{w} \\
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1
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\end{bmatrix} \\
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\begin{bmatrix}
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u \\
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v \\
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1
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\end{bmatrix} &=
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\begin{bmatrix}
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f_x & 0 & c_x \\
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0 & f_y & c_y \\
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0 & 0 & 1
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\end{bmatrix}
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\begin{bmatrix}
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1 & 0 & 0 & 0 \\
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0 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0
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\end{bmatrix}
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\begin{bmatrix}
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r_{11} & r_{12} & r_{13} & t_x \\
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r_{21} & r_{22} & r_{23} & t_y \\
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r_{31} & r_{32} & r_{33} & t_z \\
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0 & 0 & 0 & 1
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\end{bmatrix}
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\begin{bmatrix}
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X_{w} \\
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Y_{w} \\
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Z_{w} \\
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1
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\end{bmatrix}
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\end{align*}
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\f]
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The estimated pose is thus the rotation (`rvec`) and the translation (`tvec`) vectors that allow transforming
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a 3D point expressed in the world frame into the camera frame:
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\f[
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\begin{align*}
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\begin{bmatrix}
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X_c \\
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Y_c \\
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Z_c \\
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1
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\end{bmatrix} &=
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\hspace{0.2em} ^{c}\bf{T}_w
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\begin{bmatrix}
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X_{w} \\
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Y_{w} \\
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Z_{w} \\
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1
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\end{bmatrix} \\
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\begin{bmatrix}
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X_c \\
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Y_c \\
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Z_c \\
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1
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\end{bmatrix} &=
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\begin{bmatrix}
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r_{11} & r_{12} & r_{13} & t_x \\
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r_{21} & r_{22} & r_{23} & t_y \\
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r_{31} & r_{32} & r_{33} & t_z \\
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0 & 0 & 0 & 1
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\end{bmatrix}
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\begin{bmatrix}
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X_{w} \\
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Y_{w} \\
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Z_{w} \\
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1
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\end{bmatrix}
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\end{align*}
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\f]
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## Pose computation methods
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@anchor calib3d_solvePnP_flags
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Refer to the cv::SolvePnPMethod enum documentation for the list of possible values. Some details about each method are described below:
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- cv::SOLVEPNP_ITERATIVE Iterative method is based on a Levenberg-Marquardt optimization. In
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this case the function finds such a pose that minimizes reprojection error, that is the sum
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of squared distances between the observed projections "imagePoints" and the projected (using
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cv::projectPoints ) "objectPoints". Initial solution for non-planar "objectPoints" needs at least 6 points and uses the DLT algorithm.
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Initial solution for planar "objectPoints" needs at least 4 points and uses pose from homography decomposition.
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- cv::SOLVEPNP_P3P Method is based on the paper of Ding, Y., Yang, J., Larsson, V., Olsson, C., & Åstrom, K.
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"Revisiting the P3P Problem" (@cite ding2023revisiting).
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In this case the function requires exactly four object and image points.
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- cv::SOLVEPNP_AP3P Method is based on the paper of T. Ke, S. Roumeliotis
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"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
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In this case the function requires exactly four object and image points.
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- cv::SOLVEPNP_EPNP Method has been introduced by F. Moreno-Noguer, V. Lepetit and P. Fua in the
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paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" (@cite lepetit2009epnp).
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- cv::SOLVEPNP_IPPE Method is based on the paper of T. Collins and A. Bartoli.
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"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method requires coplanar object points.
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- cv::SOLVEPNP_IPPE_SQUARE Method is based on the paper of Toby Collins and Adrien Bartoli.
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"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method is suitable for marker pose estimation.
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It requires 4 coplanar object points defined in the following order:
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- point 0: [-squareLength / 2, squareLength / 2, 0]
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- point 1: [ squareLength / 2, squareLength / 2, 0]
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- point 2: [ squareLength / 2, -squareLength / 2, 0]
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- point 3: [-squareLength / 2, -squareLength / 2, 0]
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- cv::SOLVEPNP_SQPNP Method is based on the paper "A Consistently Fast and Globally Optimal Solution to the
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Perspective-n-Point Problem" by G. Terzakis and M.Lourakis (@cite Terzakis2020SQPnP). It requires 3 or more points.
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## P3P
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The cv::solveP3P() computes an object pose from exactly 3 3D-2D point correspondences. A P3P problem has up to 4 solutions.
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@note The solutions are sorted by reprojection errors (lowest to highest).
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## PnP
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The cv::solvePnP() returns the rotation and the translation vectors that transform a 3D point expressed in the object
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coordinate frame to the camera coordinate frame, using different methods:
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- P3P methods (cv::SOLVEPNP_P3P, cv::SOLVEPNP_AP3P): need 4 input points to return a unique solution.
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- cv::SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
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- cv::SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
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Number of input points must be 4. Object points must be defined in the following order:
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- point 0: [-squareLength / 2, squareLength / 2, 0]
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- point 1: [ squareLength / 2, squareLength / 2, 0]
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- point 2: [ squareLength / 2, -squareLength / 2, 0]
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- point 3: [-squareLength / 2, -squareLength / 2, 0]
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- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
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## Generic PnP
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The cv::solvePnPGeneric() allows retrieving all the possible solutions.
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Currently, only cv::SOLVEPNP_P3P, cv::SOLVEPNP_AP3P, cv::SOLVEPNP_IPPE, cv::SOLVEPNP_IPPE_SQUARE, cv::SOLVEPNP_SQPNP can return multiple solutions.
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## RANSAC PnP
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The cv::solvePnPRansac() computes the object pose wrt. the camera frame using a RANSAC scheme to deal with outliers.
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More information can be found in @cite Zuliani2014RANSACFD
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## Pose refinement
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Pose refinement consists in estimating the rotation and translation that minimizes the reprojection error using a non-linear minimization method and starting from an initial estimate of the solution. OpenCV proposes cv::solvePnPRefineLM() and cv::solvePnPRefineVVS() for this problem.
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cv::solvePnPRefineLM() uses a non-linear Levenberg-Marquardt minimization scheme @cite Madsen04 @cite Eade13 and the current implementation computes the rotation update as a perturbation and not on SO(3).
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cv::solvePnPRefineVVS() uses a Gauss-Newton non-linear minimization scheme @cite Marchand16 and with an update of the rotation part computed using the exponential map.
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@note at least three 3D-2D point correspondences are necessary.
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