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 Computing 2 180 – 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.