Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane

Abstract

This paper presents a linear algorithm for simultaneous computation of 3D points and camera positions from multiple perspective views based on having a reference plane visible in all views. The reconstruction and camera recovery is achieved in a single step by finding the null-space of a matrix built from image data using Singular Value Decomposition. Contrary to factorization algorithms this approach does not need to have all points visible in all views. This paper investigates two reference plane configurations: Finite reference planes defined by four coplanar points and infinite reference planes defined by vanishing points. A further contribution of this paper is the study of critical configurations for configurations with four coplanar points. By simultaneously reconstructing points and views we can exploit the numerical stabilizing effect of having wide spread cameras with large mutual baselines. This is demonstrated by reconstructing the outside and inside (courtyard) of a building on the basis of 35 views in one single Singular Value Decomposition.