PoseLib

This library provides a collection of minimal solvers for camera pose estimation. The focus is on calibrated absolute pose estimation problems from different types of correspondences (e.g. point-point, point-line, line-point, line-line).

The goals of this project are to provide

• Fast and robust implementation of the current state-of-the-art solvers.
• Consistent calling interface between different solvers.
• Minimize dependencies, both external (currently only Eigen) and internal. Each solver is (mostly) stand-alone, making it easy to extract only a specific solver to integrate into other frameworks.
• Robust estimators (based on LO-RANSAC) that just works out-of-the-box for most cases.

Robust Estimation and Non-linear Refinement

We provide robust estimators for the most common problems

• Absolute pose from points (and lines)
• Essential / Fundamental matrix
• Homography
• Generalized relative pose

It is fairly straight-forward to implement robust estimators for other problems. See for example absolute_pose.h. If you implement estimators for other problems, please consider submitting a pull-request.

In robust.h we provide interfaces which normalizes the data, calls the RANSAC and runs a post-RANSAC non-linear refinement. It is also possible to directly call the individual components as well (see e.g. ransac.h, bundle.h, etc.). The RANSAC is straight-forward implementation of LO-RANSAC which generate hypothesis with minimal solvers and relies on non-linear refinement for refitting.

The robust estimator takes the following options

struct RansacOptions {
    size_t max_iterations = 100000;
    size_t min_iterations = 1000;
    double dyn_num_trials_mult = 3.0;
    double success_prob = 0.9999;
    double max_reproj_error = 12.0;  // used for 2D-3D matches
    double max_epipolar_error = 1.0; // used for 2D-2D matches
    unsigned long seed = 0;
    // If we should use PROSAC sampling. Assumes data is sorted
    bool progressive_sampling = false;
    size_t max_prosac_iterations = 100000;
};

and the non-linear refinement

struct BundleOptions {
    size_t max_iterations = 100;
    enum LossType {
        TRIVIAL, TRUNCATED, HUBER, CAUCHY, TRUNCATED_LE_ZACH
    } loss_type = LossType::CAUCHY;
    double loss_scale = 1.0;
    double gradient_tol = 1e-8;
    double step_tol = 1e-8;
    double initial_lambda = 1e-3;
    double min_lambda = 1e-10;
    double max_lambda = 1e10;
    bool verbose = false;
};

Note that in robust.h this is only used for the post-RANSAC refinement.

In bundle.h we provide non-linear refinement for different problems. Mainly minimizing reprojection error and Sampson error as these performed best in our internal evaluations. These are used in the LO-RANSAC to perform non-linear refitting. Most estimators directly minimize the MSAC score (using loss_type = TRUNCATED and loss_scale = threshold) over all input correspondences. In practice we found that this works quite well and avoids recursive LO where inliers are added in steps.

Camera models

PoseLib use COLMAP-compatible camera models. These are defined in colmap_models.h. Currently we only support

• SIMPLE_PINHOLE
• PINHOLE
• SIMPLE_RADIAL
• RADIAL
• OPENCV

but it is relatively straight-forward to add other models. If you do so please consider opening a pull-request. In contrast to COLMAP, we require analytical jacobians for the distortion mappings which make it a bit more work to port them.

The Camera struct currently contains width/height fields, however these are not used anywhere in the code-base and are provided simply to be consistent with COLMAP. The Camera class also provides the helper function initialize_from_txt(str) which initializes the camera from a line given by the cameras.txt file of a COLMAP reconstruction.

Python bindings

See pybind/README.md for details on how to compile the python bindings. The python bindings expose all minimal solvers, e.g. poselib.p3p(x,X), as well as all robust estimators from robust.h.

Examples of how the robust estimators can be called are

camera = {'model': 'SIMPLE_PINHOLE', 'width': 1200, 'height': 800, 'params': [960, 600, 400]}

pose, info = poselib.estimate_absolute_pose(p2d, p3d, camera, {'max_reproj_error': 16.0}, {})

or

F, info = poselib.estimate_fundamental_matrix(p2d_1, p2d_2, {'max_epipolar_error': 0.75, 'progressive_sampling': True}, {})

The return value info is a dict containing information about the robust estimation (inliers, iterations, etc). The last two options are dicts which describe the RansacOptions and BundleOptions. Ommited values are set to their default (see above), except for the loss_scale used for the Cauchy loss which is set to half of the threshold used in RANSAC (which seems to be a good heuristic). Dicts with the default options can be obtained as opt = poselib.RansacOptions() or poselib.BundleOptions().

Some of the available estimators are listed below, check pyposelib.cpp and robust.h for more details. The table also shows which error threshold is used in the estimation (RansacOptions.max_reproj_error or RansacOptions.max_epipolar_error). All thresholds are given in pixels.

poselib.CameraPose

The python bindings expose a poselib.CameraPose class which is the return type for most methods. While the class internally represent the pose with q and t, it also exposes R (3x3) and Rt (3x4) which are read/write, i.e. you can do pose.R = Rnew and it will update the underlying quaternion q.

Benchmarking the robust estimators

To sanity-check the robust estimators we benchmark against the LO-RANSAC implementation from pycolmap.

For all of the metrics higher is better (except for runtime).

Minimal Solvers

Naming convention

For the solver names we use a slightly non-standard notation where we denote the solver as

pXpYplZlpWll

where the number of correspondences required is given by

• Xp - 2D point to 3D point,
• Ypl - 2D point to 3D line,
• Zlp - 2D line to 3D point,
• Wll - 2D line to 3D line.

The prefix with u is for upright solvers and g for generalized camera solvers. Solvers that estimate focal length have the postfix with f and similarly s for solvers that estimate scale.

Calling conventions

All solvers return their solutions as a vector of CameraPose structs, which defined as

struct CameraPose {
   Eigen::Vector4d q;
   Eigen::Vector3d t;
};

where the rotation is representation as a quaternion q and the convention is that [R t] maps from the world coordinate system into the camera coordinate system.

For 2D point to 3D point correspondences, the image points are represented as unit-length bearings vectors. The returned camera poses (R,t) then satisfies (for some lambda)

  lambda * x[i] = R * X[i] + t

where x[i] is the 2D point and X[i] is the 3D point. Note that only the P3P solver filters solutions with negative lambda.

Solvers that use point-to-point constraints take one vector with bearing vectors x and one vector with the corresponding 3D points X, e.g. for the P3P solver the function declaration is

int p3p(const std::vector<Eigen::Vector3d> &x,
        const std::vector<Eigen::Vector3d> &X,
        std::vector<CameraPose> *output);

Each solver returns the number of real solutions found.

For constraints with 2D lines, the lines are represented in homogeneous coordinates. In the case of 2D line to 3D point constraints, the returned camera poses then satisfies

  l[i].transpose() * (R * X[i] + t) = 0

where l[i] is the line and X[i] is the 3D point.

For constraints with 3D lines, the lines are represented by a 3D point X and a bearing vector V. In the case of 2D point to 3D point constraints

  lambda * x[i] = R * (X[i] + mu * V[i]) + t

for some values of lambda and mu. Similarly, for line to line constraints we have

  l[i].transpose() * (R * (X[i] + mu * V[i]) + t) = 0

Generalized Cameras

For generalized cameras we represent the image rays similarly to the 3D lines above, with an offset p and a bearing vector x. For example, in the case of point-to-point correspondences we have

p[i] + lambda * x[i] = R * X[i] + t

In the case of unknown scale we also estimate alpha such that

alpha * p[i] + lambda * x[i] = R * X[i] + t

For example, the generalized pose and scale solver (from four points) has the following signature

 int gp4ps(const std::vector<Eigen::Vector3d> &p, const std::vector<Eigen::Vector3d> &x,
              const std::vector<Eigen::Vector3d> &X, std::vector<CameraPose> *output);

Upright Solvers

For the upright solvers it assumed that the rotation is around the y-axis, i.e.

R = [a 0 -b; 0 1 0; b 0 a] 

To use these solvers it necessary to pre-rotate the input such that this is satisfied.

Implemented solvers

The following solvers are currently implemented.

Absolute Pose

Relative Pose

How to compile?

Getting the code:

> git clone https://github.com/vlarsson/PoseLib.git
> cd PoseLib

Example of a local installation:

> mkdir _build && cd _build
> cmake -DCMAKE_INSTALL_PREFIX=../_install ..
> cmake --build . --target install -j 8
  (equivalent to  'make install -j8' in linux)

Installed files:

> tree ../_install
  .
  ├── bin
  │   └── benchmark
  ├── include
  │   └── PoseLib
  │       ├── solvers/gp3p.h
  │       ├──  ...
  │       ├── poselib.h          <==  Library header (includes all the rest)
  │       ├──  ...
  │       └── version.h
  └── lib
      ├── cmake
      │   └── PoseLib
      │       ├── PoseLibConfig.cmake
      │       ├── PoseLibConfigVersion.cmake
      │       ├── PoseLibTargets.cmake
      │       └── PoseLibTargets-release.cmake
      └── libPoseLib.a

Uninstall library:

> make uninstall

Benchmark

Conditional compilation of benchmark binary is controlled by WITH_BENCHMARK option. Default if OFF (without benchmark).

Add -DWITH_BENCHMARK=ON to cmake to activate.

> cmake -DWITH_BENCHMARK=ON ..

Use library (as dependency) in an external project.

cmake_minimum_required(VERSION 3.13)
project(Foo)

find_package(PoseLib REQUIRED)

add_executable(foo foo.cpp)
target_link_libraries(foo PRIVATE PoseLib::PoseLib)

Citing

If you are using the library for (scientific) publications, please cite the following source:

@misc{PoseLib,
  title = {{PoseLib - Minimal Solvers for Camera Pose Estimation}},
  author = {Viktor Larsson},
  URL = {https://github.com/vlarsson/PoseLib},
  year = {2020}
}

Please cite also the original publications of the different methods (see table above).

Changelog

2.0 - Jan. 2022

• Added robust estimators (LO-RANSAC) and non-linear refinement
• Refactored CameraPose to use quaternion instead 3x3 matrix. Removed alpha.
• Implemented TR-IRLS method from Le and Zach (3DV 2021)
• Restructured pybind11 interface
• Added support for PROSAC sampling
• Many minor fixes and improvements....

1.0 - Jan. 2020

• Initial release

License

PoseLib is licensed under the BSD 3-Clause license. Please see License for details.

Acknowledgements

The RANSAC implementation is heavily inspired by RansacLib from Torsten Sattler.