This package implements relative pose estimation for multi-camera systems from two affine correspondences, including two multi-camera system solvers (solver_depth_inter_2ac, solver_depth_intra_2ac) and a single camera solver (solver_depth_mono_2ac).

Source codes and Matlab mex files with demo code are provided in the package. The core solvers are written by C++. Matlab mex files are compiled using Ubuntu 16.04 + Matlab R2019a. Run test_solver_AC.m in folder "test".

Reference

[1] Banglei Guan, and Ji Zhao. Affine Correspondences between Multi-Camera Systems for 6DOF Relative Pose Estimation. European Conference on Computer Vision, 2022. (Oral)

If you use this package in an academic work, please cite:

@inproceedings{guan2022affine,
  title={Affine Correspondences between Multi-Camera Systems for 6DOF Relative Pose Estimation},
  author={Guan, Banglei and Zhao, Ji},
  booktitle={European Conference on Computer Vision},
  year={2022}
 }

solver_depth_inter_2ac

A minimal solver for the relative pose estimation of multi-camera systems using two inter-camera affine correspondences. Returns a maximum of 48 solutions or 56 solutions.

• Solver: solver_depth_inter_2ac.mexa64

• API: [cay_sols, t_sols, R_sols, cay_sols_all] = solver_depth_inter_2ac(Image1(1:2,:), Image2(1:2,:), At, R_cam, t_cam, 0); [cay_sols, t_sols, R_sols, cay_sols_all] = solver_depth_inter_2ac(Image1(1:2,:), Image2(1:2,:), At, R_cam, t_cam, 1);

• Input data for Demo:

  Image1 (3*2 matrix): normalized homogeneous image coordinates of two inter-camera feature points expressed in view 1.

  Image2 (3*2 matrix): normalized homogeneous image coordinates of two inter-camera feature points expressed in view 2.

  At (2*2*2 matrix): At(:,:,1) = At1, At(:,:,2) = At2, where At1 and At2 are the corresponding 2*2 local affine transformations of two inter-camera feature points.

  R_cam (3*3*2 matrix): extrinsic rotation of two cameras expressed in the reference of the multi-camera system.

  t_cam (3*2 matrix): extrinsic translation of two cameras expressed in the reference of the multi-camera system.

  Option: 0 refers the 2AC-inter-48 solver, 1 refers the 2AC-inter-56 solver.

• Output data for Demo:

  cay_sols (3*N matrix): real number solutions of Cayley rotation parameter, N is the number of real number solutions.

  t_sols (3*N matrix): real number solutions of translation.

  R_sols (3*3*N matrix): real number solutions of rotation matrix.

  cay_sols_all (3*M matrix): all solutions of Cayley rotation parameter, including real number solutions and complex number solutions. M is the number of all the solutions.

solver_depth_intra_2ac

A minimal solver for the relative pose estimation of multi-camera systems using two intra-camera affine correspondences. Returns a maximum of 48 solutions.

• Solver: solver_depth_intra_2ac.mexa64

• API: [cay_sols, t_sols, R_sols, cay_sols_all] = solver_depth_intra_2ac(Image1(1:2,:), Image2(1:2,:), At, R_cam, t_cam);

• Input data for Demo:

  Image1 (3*2 matrix): normalized homogeneous image coordinates of two intra-camera feature points expressed in view 1.

  Image2 (3*2 matrix): normalized homogeneous image coordinates of two intra-camera feature points expressed in view 2.

  At (2*2*2 matrix): At(:,:,1) = At1, At(:,:,2) = At2, where At1 and At2 are the corresponding 2*2 local affine transformations of two intra-camera feature points.

  R_cam (3*3*2 matrix): extrinsic rotation of two cameras expressed in the reference of the multi-camera system.

  t_cam (3*2 matrix): extrinsic translation of two cameras expressed in the reference of the multi-camera system.

• Output data for Demo:

  cay_sols (3*N matrix): real number solutions of Cayley rotation parameter, N is the number of real number solutions.

  t_sols (3*N matrix): real number solutions of translation.

  R_sols (3*3*N matrix): real number solutions of rotation matrix.

  cay_sols_all (3*M matrix): all solutions of Cayley rotation parameter, including real number solutions and complex number solutions. M is the number of all the solutions.

solver_depth_mono_2ac

A minimal solver for the relative pose estimation of a single camera using two affine correspondences. Returns a maximum of 20 solutions.

• Solver: solver_depth_mono_2ac.mexa64

• API: [cay_sols, t_sols, R_sols, cay_sols_all] = solver_depth_mono_2ac(Image1(1:2,:), Image2(1:2,:), At);

• Input data for Demo:

  Image1 (3*2 matrix): normalized homogeneous image coordinates of two feature points expressed in view 1.

  Image2 (3*2 matrix): normalized homogeneous image coordinates of two feature points expressed in view 2.

  At (2*2*2 matrix): At(:,:,1) = At1, At(:,:,2) = At2, where At1 and At2 are the corresponding 2*2 local affine transformations of two feature points.

• Output data for Demo:

  cay_sols (3*N matrix): real number solutions of Cayley rotation parameter, N is the number of real number solutions.

  t_sols (3*N matrix): real number solutions of translation.

  R_sols (3*3*N matrix): real number solutions of rotation matrix.

  cay_sols_all (3*M matrix): all solutions of Cayley rotation parameter, including real number solutions and complex number solutions. M is the number of all the solutions.

Run

Compiled files using Ubuntu 16.04 + Matlab R2019a are provided. You can run the package in Matlab.

test_solver_AC.m is the demo which shows how to call the APIs.