Abstract

The motion field for an observer moving through a static environment depends on the observer's translational and rotational velocities along with the distances to surface points. We show how the equations describing the motion field can be split by an exact algebraic manipulation to form three sets of equations, the first of which relates properties of the motion field to the observer's direction of translational motion alone. Therefore, to solve for the direction of translation, the depths and rotational velocity need not be known or estimated. Unlike previous surface-based techniques, we require no assumptions about the smoothness of the surface from which the optic flow measurements are taken, or that the measurements come from the same surface. Instead, we show that this procedure can provide a robust estimate for the direction of translation, given simply a sparse sampling of the optic flow from scenes that contain a significant variation in depth. Moreover, given this estimate we show how two linear equations can be found, one of which provides an overdetermined system of the rotational velocity alone, and the other contains only the relative depths. Again we show that the rotational velocity can be computed robustly, given a sparse sampling of velocities.

© 1989 Optical Society of America