Multiple-View Geometry of Points and Lines

Abstract

In this chapter we study how the framework of epipolar geometry introduced in Part II generalizes to the case of multiple views. As we shall see, this entails studying constraints that corresponding points in different views must satisfy if they are the projection of the same point in space. Not only is this development crucial for understanding the geometry of multiple views but, as in the two-view case, these constraints may be used to derive algorithms for reconstructing camera configuration and, ultimately, the 3-D position of geometric primitives. The search for the m-view analogue of the epipolar constraint has been an active research area for almost two decades. It was realized early on in [Liu and Huang, 1986, Spetsakis and Aloimonos, 1987] that the relationship between three views of the same point or line can be characterized by the trilinear constraints. Consequently, the study of multiple-view geometry has involved multidimensional linear operators, also called tensors.

An idea which can be used once is a trick. If it can be used more than once it becomes a method.

— George Pólya and Gábor Szegö