On computing a 'fuzzy' focus of expansion for autonomous navigation

The Focus of Expansion (FOE) is an important concept in dynamic scene analysis, particularly where translational motion is dominant, such as in mobile robot applications. In practice, it is difficult to determine the exact location of the FOE from a given set of displacement vectors due to the effects of camera rotation, digitization, and noise. Instead of a single image location, we propose to compute a connected region, termed 'Fuzzy' FOE, that marks the approximate direction of camera heading. The 'Fuzzy' FOE provides numerous clues about the 3-D scene structure and independent object motion. In this paper we discuss the main problems of the classic FOE approach and concentrate on the details of computing the 'Fuzzy' FOE for a camera undergoing translation and rotation in 3-D space. We present results on real outdoor images. 1. Introduction The FOE approach relies upon the well-known fact that, under forward camera translation, all image features seem to diverge radially from a particular image location, called the focus of expansion (FOE), which marks the direction of vehicle heading [7, 11, 141. The 3-D distance of stationary environmental features can subsequently be obtained by measuring how fast their images diverge away from the FOE. Thus the computation of camera motion is achieved in a purely two-dimensional step which is completely separated from reconstructing the scene's 3-D structure. In practice, locating the FOE accurately is not a trivial task for arbitrary camera motion and especially difficult under noisy conditions. Some researchers have therefore assumed planar