Catadioptric sensors that approximate wide-angle perspectiveprojections
Hicks, R.A.; Bajcsy, R.
Computer Vision and Pattern Recognition, 2000. Proceedings. IEEE Conference on
Volume 1, Issue , 2000 Page(s):545 - 551 vol.1
Digital Object Identifier 10.1109/CVPR.2000.855867
Summary:We present two families of reflective surfaces that are capable of
providing a wide field of view, and yet still approximate a perspective
projection to a high degree. These surfaces are derived by considering a
plane perpendicular to the axis of a surface of revolution and finding
the equations governing the distortion of the image of the plane in this
surface. We then view this relation as a differential equation and
prescribe the distortion term to be linear. By choosing appropriate
initial conditions for the differential equation and solving it
numerically, we derive the surface shape and obtain a precise estimate
as to what degree the resulting sensor can approximate a perspective
projection. Thus these surfaces act as computational sensors, allowing
for a wide-angle perspective view of a scene without processing the
image in software. The applications of such a sensor should be numerous,
including surveillance, robotics and tradition photography
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