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epipolar geometry
Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model.
==Epipolar geometry==
The figure below depicts two pinhole cameras looking at point X. In real cameras, the image plane is actually behind the focal center, and produces an image that is the symmetry about the focal center of the lens. Here, however, the problem is simplified by placing a ''virtual image plane'' in front of the focal center i.e optical center of each camera lens to produce an image not transformed by the symmetry. OL and OR represent the centers of symmetry of the two cameras lenses. X represents the point of interest in both cameras. Points xL and xR are the projections of point X onto the image planes.
Each camera captures a 2D image of the 3D world. This conversion from 3D to 2D is referred to as a perspective projection and is described by the pinhole camera model. It is common to model this projection operation by rays that emanate from the camera, passing through its focal center. Note that each emanating ray corresponds to a single point in the image.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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