A possible method for computing both the epipolar geometry and the frontier points is to give an initial guess of the epipolar geometry and refine it gradually so that the epipolar tangency holds in both two views [4,1].
If the camera motions are pure translations (i.e. no rotation) and if the internal parameters of the camera do not change under the motions, then the epipolar lines and the epipoles in these two views coincide each other. Thus, in this case, the epipolar line is extracted as a bitangent line on apparent contours in two views, and the epipole is computed as an intersection point of two or more bitangent lines (see Fig. 3). These properties are called epipolar bitangency [12]. By using the epipolar bitangency, the epipolar geometry and frontier points are recovered in closed form avoiding the chicken and the egg problem.
Figure 3: Frontier points viewed from a translational camera.
Under pure translations, frontier points and the epipolar geometry
are computed from bitangency in images.