An analytical procedure for the estimation of the focus of expansion (FOE) location is introduced. The method is applied to a vector field that has been obtained from the analysis of the relative translational movement of a rigid body with respect to the acquiring camera (monocular system). 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)=v/sub x/(x,y)+iv/sub y/,(x,y). These properties provide the set of points for which both components of the vector field v/sub x/(x,y) and v/sub y/(x,y) are harmonic and, as a subset, the set of points for which both components are null. The use of perspective projection states that the FOE is obtained as the locus where v/sup x/(x,y)=0=v/sub y/(x,y) and, therefore, where the conditions stated by both properties meet.
['José Manuel Menéndez', 'Narciso N. García', 'Luis Salgado', 'Enrique Rendón']
An algorithm for FOE localization