Panoramic Imaging: Sensor-Line Cameras and Laser Range-Finders

4

Epipolar Geometry

Epipolar geometry characterizes the geometric relationships between projection centers of two cameras, a point in 3D space, and its potential position in both images. A benefit of knowing the epipolar geometry is that, given any point in either image (showing the projection of a point in 3D space), epipolar geometry defines a parameterized (i.e., Jordan) curve (the epipolar curve) of possible locations of the corresponding point (if visible) in the other image. The parameter t of the curve (t) then allows in computational stereo to move along the curve when testing image points for actual correspondence. Interest in epipolar geometry is also motivated by stereo viewing.¹ There is a “preferred” epipolar geometry which supports depth perception, and this is defined by parallel epipolar lines; these lines are a special case of epipolar curves.

4.1 General Epipolar Curve Equation

The epipolar geometry of two sensor-matrix cameras defines epipolar lines, but these are in general not all parallel in each of the two image planes. The epipolar geometry of two rotating sensor-line cameras defines Jordan curves on cylinders, and we will also identify the case where two panoramic images support depth perception.

Computational stereo with large panoramic images (of the order ...