SemiGeneralizedHomography

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SemiGeneralizedHomography

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# 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](http://www2.macaulay2.com/Macaulay2/Downloads) 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.

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