Calibrated and Partially Calibrated Semi-generalized Homographies

This code library is an implementation of our proposed minimal solvers for computing semi-generalised homographies for calibrated and partially-calibrated cameras :

1. Calibrated case : sh5_2, sh5_3, sh5_4, sh4.5_2, sh4.5_3
2. Partially calibrated case : sh5f_2, sh5f_3

Additionally, we also have two absolute pose solvers designed for our homography setup :

1. Calibrated case : P3P+N
2. Partially calibrated case : P5Pf+N

We have also released the Macaulay2 scripts for computing the elimination ideals (Please refer to [1] for more details) :

1. Calibrated case : input_sh5.txt
2. Partially calibrated case : input_sh5f.txt

Executing Macaulay2 script :

1. Based on the operating system, please refer to Macaulay2 for instructions on how to setup.
2. Each of the two scripts compute the elimination ideals and write to .txt files.

Executing the Minimal Solvers

• Input : Each of our solvers require a tuple, (q, p, c), as the input where q <-> (p, c) denotes the 2D-2D point correspondences.

• q denotes an array of size 3x5, of 5 vectors, each denoting the viewing ray for the corresponding 2d image observation by the query pinhole camera.

• p denotes an array of size 3x5, of 5 vectors, each denoting the viewing ray for the corresponding 2d image observation in the coordinate system of the global generalized camera system.

• Each p ray is accompanied with camera center c, or the position of the center of the pinhole camera within the generalized camera system.

• Output : The output is the generalized semi-generalized homographies,Hs and the corresponding plane vectors, Nss.

• We have used the standard approaches for a homography decomposition to extract the relative pose and the scale.

• An example of this, and a sample test script on synthetic scenes can be found in the synthetic_scenes/* folder, for both calibrated as well partially calibrated cameras.

• The solvers for now are released in the MATLAB programming language while the C++ version will soon be released.

References

[1] Bhayani, S., Sattler, T., Baráth, D., Beliansky, P., Heikkila, J., & Kukelova, Z. (2021). Calibrated and Partially Calibrated Semi-Generalized Homographies. ArXiv, abs/2103.06535.