On the correspondence problem for wide angular separation of non-coplanar points

We describe a solution to the problem of stereo matching for non-coplanar points and wide angular separation of uncalibrated cameras. The image projections of four corresponding coplanar points, with no three collinear, are assumed to be known. The 'virtual image' that results by 2D warping of the first image towards the second one according to the homography of a known plane in 3D is used. Then, instead of trying to match points between the two images, we exploit the fact that all corresponding points between the virtual and the second image are in alignment. It is shown how the matching problem can be cast into an optimisation one, and a cost function for evaluating each possible solution is derived. For increased robustness to outliers a Hough-Transform-like algorithm is suggested for obtaining the optimal solution, and a randomised scheme is shown to be efficient for practical applications. Experimental results on both synthetic and real data are also included. (C) 1998 Elsevier Science B.V.