In perspective projections – lines project into lines, so lines in one image must project to lines in the other image.
In stereo images, any point on the epipolar line must be on the other epipolar line, this constraint allows us to reduce the search for a given point, to it’s epipolar line which is a 1D vector search.
Definitions for epipolar constraints:
Base line – the line that joins the two camera centers.
Epipolar plane for a given point – contains the baseline and a given point and forms the plan between them.
Epipolar lines are the intersection of the epipolar planes of the given point with the image planes.
Epipole – point of intersection of baseline with image plane.
Formula for the epipolar line in algebraic terms for calibrated cameras:
Let x’ be the point in world coordinate system on the first image, and x be the point in world coordinate system on the second image, let E be the essential matrix, so x’ * Ex = 0 , which is the formula of the epipolar line, on the second image.
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