Homography Decomposition Revisited

Homography refers to a specific type of transformation that relates two images of the same planar surface taken from different perspectives. Recovering motion parameters from a homography matrix is a classic problem in computer vision. It is important to derive a fast and stable solution to homography decomposition, since it forms a critical component of many vision systems, e . g ., in Structure-from-Motion and visual localization. The current state-of-the-art solvers can be categorized into two types of methods, the numerical procedures based on singular value decomposition (SVD), and the closed-form solution. The SVD-based methods are stable but time-consuming, while the existing closed-form solution is faster but less stable. In this paper, we discuss the homography decomposition problem from a different viewpoint. In contrast to the existing methods which focus on the properties of the homography matrix, we propose a new method that uses three random point correspondences to obtain the motion parameters in closed form. The proposed method is conceptually simple, easy to understand and implement, and has a good geometrical interpretation. This solution can be seen as an alternative to the existing closed-form solution. We also discuss the configurations where the closed-form solutions might be unstable and present a framework for homography decomposition taking into account both the efficiency and stability.