A Quick 3D-to-2D Points Matching Based on the Perspective Projection

This paper describes a quick 3D-to-2D point matching algorithm. Our major contribution is to substitute a new O(2n) algorithm for the traditional N ! method by introducing a convex hull based enumerator. Projecting a 3D point set into a 2D plane yields a corresponding 2D point set. In some cases, matching information is lost. Therefore, we wish to recover the 3D-to-2D correspondence in order to compute projection parameters. Traditionally, an exhaustive enumerator permutes all the potential matching sets, which is N ! for N points, and a projection parameter computation is used to choose the correct one. We define ”correct” as the points match whose computed parameters result in the lowest residual error. After computing the convex hull for both 2D and 3D points set, we show that the 2D convex hull must match a circuit of the 3D convex hull having the same length. Additionally a novel validation method is proposed to further reduce the number of potential matching cases. Finally, our matching algorithm is applied recursively to further reduce the search space. 1 keywords: Convex Hull, Residual Error, Horizon, Calibration