Computation of Binocular Eye Position from Vertical Disparities with the use of Probabilistic Place Coding

Abstract

Stereoscopic vision exploits the fact that points in a 3-D scene will in general project to different locations in the images in the left and the right eye. The differences in retinal locations, measured horizontally and vertically, are called horizontal ( H) and vertical ( V) disparities respectively. Their size is affected by the positions of the eyes which determine the viewing geometry parameters, that is distance to the fixation point ( d) and the angle of gaze ( g). H is also affected by the depth of the scene point relative to fixation distance, which is why one can recover 3-D scene structure using binocular vision. Achieving metric reconstruction requires knowledge of d and g to allow for their influence on H. Computational analyses have shown that d and g can in principle be recovered from V because of its relative insensitivity to scene depth variations. As d and g are the only two unknowns in the equation for V, in theory only two measurements of V (at suitable retinal locations) are needed. A practical system, however, dealing with noisy images composed of many points, needs to pool information from measurements of V at numerous retinal locations. A place-coding algorithm of the Hough transform type is well suited to this purpose (S A Peek, J E W Mayhew, J P Frisby, 1984 Image and Vision Computing2 180 – 190), but it has not hitherto been used in a way which deals appropriately with measurement noise. We describe how this can be done and demonstrate with computer simulations greatly improved estimation of d and g as well as improved robustness to noise. The new method also permits the solution of an important aspect of the stereo correspondence problem—that of finding epipolar lines.