Triangulation without Correspondences

This paper presents two di erent algorithms for reconstructing 3D points from two sets of noisy 2D image points without knowing point correspondences given the corresponding poses from the two images. We rst present a new way to form a 2D similarity function between two points from two images via 3D pseudo-intersection. Based on principles of proximity and exclusion, the rst algorithm uses a new a nity measure between 2D image points from two di erent images and a competition scheme to establish image point correspondences and recover their corresponding 3D points simultaneously. Based on an optimal graph theoretic approach, the second algorithmuses the similarity function to construct a bipartite graph, builds a corresponding ow network, and nally nds a maximum network ow that determines the correspondences between two images. The two proposed algorithms have been applied to aerial images from the ARPA RADIUS project. Experimental results have shown that the proposed algorithms are robust.