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.

本文介绍了两种快速且可解释的2D单应性分解方法：相似核相似（SKS）和仿射核仿射（ACA）。SKS和ACA可以通过输入坐标的多项式（从7阶到9阶）来表示单应性的每个元素，提供了几何参数化和计算效率的优势，并以统一的方式计算2D仿射变换。

快速且可解释的2D单应矩阵分解：相似-内核-相似与仿射-核心-仿射转换