Behaviour of the epipolar map

In [Boy 96], we have shown that given two epipolar correspondents p₁ and p₂, there exist neighbourhoods of p₁ and p₂ where the epipolar map is smooth and has a smooth inverse, provided that p₁ and p₂ are not projections of a multiple point. In fact, in the neighbourhood of the projection of a multiple point, the epipolar map yields two correspondents, as shown in figure 5.

  

Figure 5: The epipolar correspondence is ambiguous in the proximity of a multiple point: p₁ has two close correspondents p₂.

The epipolar correspondence is thus ambiguous in the proximity of a multiple point. The criterion one can use to resolve this ambiguity is that the image of P₁, P₂ and the multiple point must appear in the same order along occluding contours (this assumes that occluding contours have the same orientation). Note that this criterion is similar to the ordering constraint in stereo-vision.