Camera Resectioning from Image Edges with the $L_\infty$-Norm Using Linear Programming

This paper discusses how to resection camera using image edges extracted from projected polyhedron, with noise caused by shadows and occlusions etc. First, we propose a definition of the distance between two line segments in a 2D plane, which is an essential concept in computer vision. Based on it, the problem can be recast as a quasi-convex optimization problem in a famous and successful framewrok. Different from [8], our solution uses linear programming (LP) with the residual error defined by Euclidean distance, instead of using Second Order Cone Programming (SOCP) often utilized by most previous problems. Most related work makes use of the point to point correspondences. Intuitively, people may consider line segment correspondences should be more complex to handle than those of points. In fact, this paper shows that the problem can be simplified on the contrary.