Can multiple views make up for lack of camera registration?

摘要

It is known that the epipolar lines in stereo images can be determined from images themselves even when neither the camera registration nor the camera geometry is known; also that given relative orientation, relative translation can be obtained (and vice versa). In the process three equations are obtained for the four parameters of the (image) origin shifts, leaving at least one degree of freedom undetermined. If the origin shifts could be computed, however, then one could obtain the relative orientation and translation, whence depth. It could be argued that taking a third image into consideration would add at least three more equations while introducing only two more unknowns (the origin shift in the third image), thus making a total of six equations in the six unknowns and possibly yielding a unique solution. (More images could be added to overconstrain the problem and to compensate for measurement errors.) We show that this scheme would not work. The three equations in four parameters turn out to be equivalent to two equations and an identity. Thus each new image would add two more equations and as many unknowns and the shortfall could never be made up. The considerations involved here also have a bearing on direct calculations of rotation, translation and origin shifts as, for example, when only degenerate data (e.g. all points lying on a plane etc.) are available.