Representation of a Three-Dimensional Moving Scene

Abstract

The study of the geometric relationship between a three-dimensional (3-D) scene and its two-dimensional (2-D) images taken from a moving camera is at heart the interplay between two fundamental sets of transformations: Euclidean motion, also called rigid-body motion,which models how the camera moves, and perspective projection,which describes the image formation process. Long before these two transformations were brought together in computer vision, their theory had been developed independently. The study of the principles of motion of a material body has a long history belonging to the foundations of mechanics. For our purpose, more recent noteworthy insights to the understanding of the motion of rigid objects came from Chasles and Poinsot in the early 1800s. Their findings led to the current treatment of this subject, which has since been widely adopted.

I will not define time, space, place and motion, as being well known to all.

— Isaac Newton, Principia Mathematica,1687