Generalised epipolar constraints

Abstract

The frontier of a curved surface is the envelope of contour generators showing the boundary, at least locally, of the visible region swept out under viewer motion. In general, the outlines of curved surfaces (apparent contours) from different viewpoints are generated by different contour generators on the surface and hence do not provide a constraint on viewer motion. Frontier points, however, have projections which correspond to a real point on the surface and can be used to constrain viewer motion by the epipolar constraint.We show how to recover viewer motion from frontier points and generalise the ordinary epipolar constraint to deal with points, curves and apparent contours of surfaces. This is done for both continuous and discrete motion, known or unknown orientation, calibrated and uncalibrated, perspective, weak perspective and orthographic cameras. Results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces, is presented. A statistical evaluation is performed to estimate the stability of the solution. It is also shown how the full motion of the camera from a sequence of images can be obtained from the relative motion between image pairs.