Polynomial point matching algorithm based on epipolar geometry

Point correspondence problem is one of the key problems in computer vision. There are several approaches for solving this problem, such as descriptor-based approach, an approach that is based on epipolar geometry, as well as hybrid methods. This article reviews point matching by the means of epipolar geometry. These methods are intended to be used with a photogrammetric system that is currently under development. The system uses artificial circular retroreflective targets. We propose to use multipartite weighted undirected graph as a mathematical model of the point correspondence problem. Its vertices represent images of the circle targets in the photos, while its edges define the set of images that satisfy mutual epipolar constraint. We show the exact solution of the point correspondence problem via superclique, and show that the exact solution has exponential time complexity. We also review various heuristic approaches to point matching. Heuristic algorithms do not always provide an exact solution of the problem, but they have much lower time complexity. The architecture of our photogrammetric systems makes it possible to use such fast heuristic point matching algorithms: all the discrepancies will be automatically determined and filtered out in the further stages of photogrammetric reconstruction. This allows to iteratively find an exact reconstruction of the scene in reasonable time. We propose a new polynomial point matching algorithm, and estimate its time complexity as O($n^4$). We also estimate its efficiency and performance in comparison to other in-house algorithms, as well as in comparison to H.-G. Maas’s algorithms. Our new algorithm outperforms all competitors.