Model-based analytical FOE determination1

摘要

An analytical procedure for the estimation of the focus of expansion (FOE) location is introduced. The method is applied to a vector field which has been obtained from the analysis of the relative translational movement of a rigid body with respect to the acquiring camera (monocular system). A polynomial model is fitted to the vector field; the order and shape of the model are determined by the kinetic analysis of the Euclidean camera centered coordinate system in which the camera is moving, and some hypothesis concerning the approximation of the inverse of the depth function 1/Z(x,y). Two basic properties of complex differentiation theory are applied, assuming that each vector of the optic flow is a real-valued complex function of the form v(x,y)=vx(x,y)+ivy(x,y). These properties provide the set of points for which both components of the vector field vx(x,y) and vy(x,y) are harmonic and, as a subset, the set of points for which both components are zero. The use of perspective projection states that the FOE is the locus where vx(x,y)=0=vy(x,y) and, therefore, where the conditions stated by both properties meet.