language: en

Unifying Two-View and Three-View Geometry

SHAI AVIDAN AMNON SHASHUA
Institute of Computer Science, The Hebrew University,
Jerusalem 91904, Israel
avidan@cs.huji.ac.il

Abstract. The core of multiple-view geometry is governed by the fundamental matrix and the trilinear tensor. In this paper we unify both representations by first re-deriving the fundamental matrix as a rank deficient tensor, and secondly by deriving a unified 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 the trilinear tensor of three views and that this tensor specializes to the fundamental matrix (in it's tensor form) in the case of two 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 fundamental matrix (in its tensor form) and seamlessly move to the general 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 modification.

1. Introduction