Constraints

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Constraints

Stereo matching is a difficult problem, especially when the images are noisy. But also with perfect images, ambiguities occur during the matching process, thus for one point in the one image there may be more points in the other image. In order to minimize false matches, matching constraints must be imposed. The following list shows some commonly used constraints.

Similarity, Photometric constraint

For an intensity-based approach (see Section 2.4.1 for more information), the matching pixels must have a similar intensity value. This constraint holds for an object with nearly lambertian surface and a parallel camera system. Also only an ambient light source should exist otherwise reflections and highlights would occur.

Epipolar constraint

Generally, the search for a corresponding point has to be made over the whole image. This is not true if the epipolar constraint is used. For a point in one image, the corresponding point in the other image must lie on the epipolar line. Thus the search is 1 only.

Uniqueness[MT79]

A given pixel or feature in one image can only correspond to at most one pixel or feature in the other image. This constraint does not hold for transparent or occluded areas.

Continuity[MT79]

The disparity should vary smoothly almost everywhere

Ordering[BB81]

If
and
and if is on the right of , then should also be on the right of and vice versa. The ordering fails at regions known as forbidden zone (Figure 2.10).

Figure 2.10:
The ordering constraint fails, if a given 3D point (N here) falls onto the forbidden zone of another 3D point (M). The ordering in the right image is the reversed version of the ordering in the left image.

Disparity limit

In most intensity-based approaches not the whole epipolar line is taken into account when searching for corresponding points, thus a limit for the disparity is set. For a point in the left image only points
in the right image are compared, where
.

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