Unifying Two-View and Three-View Geometry

The core of multiple-view geometry is governed by the fundamental matrix and the trilinear tensor. In this paper we unify both representations by rst deriving the fundamental matrix as a rank-2 trivalent tensor, and secondly by deriving a uniied set of operators that are transparent to the number of views. As a result, we show that the basic building block of the geometry of multiple views is a trivalent tensor that specializes to the fundamental matrix in the case of two views, and is the trilinear tensor (rank-4 triva-lent tensor) in case of three views. The properties of the tensor (geometric interpretation, contraction properties , etc.) are independent of the number of views (two or three). As a byproduct, every two-view algorithm can be considered as a degenerate three-view algorithm and three-view algorithms can work with either two or three images, all using one standard set of tensor operations. To highlight the usefulness of this paradigm we provide two practical applications. First we present a novel view synthesis algorithm that starts with the rank-2 tensor and seamlessly move to the general rank-4 trilinear tensor, all using one set of tensor operations. The second application is a camera stabilization algorithm, originally introduced for three views, now working with two views without any modi-cation.