On the Spacetime Geometry of Galilean Cameras

Abstract

In this paper, a projection model is presented for cameras moving at constant velocity (which we refer to as Galilean cameras). To that end, we introduce the concept of spacetime projection and show that perspective imaging and linear pushbroom imaging are specializations of the proposed model. The epipolar geometry between two such cameras is developed and we derive the Galilean fundamental matrix. We show how six different "fundamental" matrices can be directly recovered from the Galilean fundamental matrix including the classic fundamental matrix, the linear pushbroom (LP) fundamental matrix and a fundamental matrix relating epipolar plane images (EPIs). To estimate the parameters of this fundamental matrix and the mapping between videos in the case of planar scenes we describe linear algorithms and report experimental performance of these algorithms.