Fast and Interpretable 2D Homography Decomposition:
  Similarity-Kernel-Similarity and Affine-Core-Affine Transformations
Shen Cai Zhanhao Wu Lingxi Guo Jiachun Wang Siyu Zhang Junchi Yan Shuhan Shen
In this paper, we present two fast and interpretable decomposition methods
for 2D homography, which are named Similarity-Kernel-Similarity (SKS) and
Affine-Core-Affine (ACA) transformations respectively. Under the minimal
$4$-point configuration, the first and the last similarity transformations in
SKS are computed by two anchor points on target and source planes,
respectively. Then, the other two point correspondences can be exploited to
compute the middle kernel transformation with only four parameters.
Furthermore, ACA uses three anchor points to compute the first and the last
affine transformations, followed by computation of the middle core
transformation utilizing the other one point correspondence. ACA can compute a
homography up to a scale with only $85$ floating-point operations (FLOPs),
without even any division operations. Therefore, as a plug-in module, ACA
facilitates the traditional feature-based Random Sample Consensus (RANSAC)
pipeline, as well as deep homography pipelines estimating $4$-point offsets. In
addition to the advantages of geometric parameterization and computational
efficiency, SKS and ACA can express each element of homography by a polynomial
of input coordinates ($7$th degree to $9$th degree), extend the existing
essential Similarity-Affine-Projective (SAP) decomposition and calculate 2D
affine transformations in a unified way. Source codes are released in
https://github.com/cscvlab/SKS-Homography.