Observability and Estimation of Rigid Motion under Perspective Projection

Stefano Soatto, CDS, Caltech

Consider a sequence of images produced by a camera moving through a static environment.

The "visual ego-motion" problem consists in reconstructing the motion of the observer (camera) and the structure of the ambient space (scene) from a sequence of monocular images representing perspective projections of the scene during motion.

This problem can be seen as estimation of the state of a stochastic system; however, the model which defines the visual motion problem in the euclidean space is not locally observable, and therefore the linearization- based estimation techniques are bound to fail.

We will describe a new formulation of motion estimation as identification of a system in exterior differential form. The parameters to be identified live in a topological space which we call the "essential manifold".

Using classical computer vision results we will show that the proposed model is nonlinearly globally observable under "general position" assumptions (the observer does not move on a quadric surface that contains all the visible points).

A recursive estimator for visual motion, called the "essential estimator", will be described (CDS memo CIT-CDS-93-021/022 and 94-001).