Chapter 17 - Tackling the perspective n-point problem

Abstract

This chapter introduces the perspective n-point problem, i.e., the problem of determining the pose of a known 3-D object appearing in a 2-D image when n points on it have been identified. The chapter starts by considering weak perspective projection: it shows that flat objects are subject to an ambiguity known as perspective inversion and describes a method for solving the three-point problem in that instance. After distinguishing full and weak perspective projection, the chapter goes on to analyze the numbers of points that are needed to disambiguate object pose for these projections and shows how they vary for coplanar and noncoplanar features. It is demonstrated how interpretive help can be obtained from symmetry—as in the case of symmetric trapezia—and from convexity, as convex polygons remain convex under perspective projection.