<title>Simple iterative method for finding the foe using depth-is-positive constraint</title>

Abstract

Abstract This short paper reexamines a direct-methods algorithm suggested by Negahdahripour and Horn[5]{3])that finds the focus of expansion (FOE) from translational motion imagery. We propose an practical extension of the algorithm, characterize it specifically for a VLSI implementation, discuss when it will converge to the correct solution, and demonstrate it on realimages (both synthetic and natural).The method does not require a solution to the correspondence problem or involve estimationof optical flow. 1 Introduction Negadahripour and Horn [5] proposed an algorithm that uses depth is positive as a constraint tofind the focus of expansion (FOE). They found that negative depth values obtained by solvingthe brightness change constraint equation in the case of incorrect FOE estimates imply constraintlines along which a true FOE must lie. They then estimated the position of the FOE from a leastsquares intersection of these constraint lines, each from a different incorrect FOE estimate.They tried the algorithm on synthetic derivative data (spatial derivatives are generated ran-donily; time derivatives are computed from the brightness change constraint equation; randomnoise is added) and to a limited extent on real data.In addition, Negadahripour and Horn [3][6]