Structure from translational observer motion

Abstract

This work presents a unified, globally based geometric framework, using congruence geometry, for the description and computation of structure from motion. It is based on projectively invariant tangent information in a sequence of monocular images, i.e. occluding contours under general perspective. The strength of the framework is demonstrated by applying it to the case of translational observer motion, a type of motion that is of great practical importance since it can be easily implemented with the help of various gyroscopic devices. Introducing a simple technique for the computation of the direction of motion (“Focus Of Expansion”) as a function of time, the recovery of translational observer motion is reduced to a problem of determining its speed. From such speed information, we show how to reconstruct the observer motion — as well as a set of silhouette curves on the observed target - and illustrate with a few simulated examples. The FOE-reconstruction method is then generalized from the real to the complex domain, showing how to combine conjugate complex geometric elements in order to obtain real geometric information concerning the direction of observer motion. We conclude by applying this method to real image data.