Semi-analytic method for estimating stereo camera geometry from matched points

摘要

A novel semi-analytic algorithm to determine the parameters of stereo camera geometry from pairs of matched points is presented. It requires the restriction R = Ry (i.e. rotation about the vertical (or Y-) axis only), but admits any arbitrary translation t. A careful choice of representation for the three parameters (one for the rotational and two for the translational degrees of freedom) ensures that two parameters are expressible as rational functions of the third parameter at the minimum of the squared error function. This transforms the problem of locating the global minimum of a function in three parameters to one of finding the zeros of a thirteenth degree polynomial in a single parameter. This provides the exact numerical answer to the least squares problem. As each solution is known and the number of possible solutions (13) is also known, finding the global minimum becomes a trivial task. Moreover, the algorithm does not break down if the translation vanishes. For exact data, a fourth degree polynomial equation similar to Ullman's1 is obtained. Since we solve for an independent set of parameters, the so-called ‘degenerate cases’ (planes, etc.) pose no difficulty. On the contrary, all solutions are found.