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The fixed viewpoint constraint is a requirement that a catadioptric
sensor only measure the intensity of light passing through a single
point in 3-D space. The direction of the light passing through this
point may vary, but that is all. In other words, the catadioptric
sensor can only sample the 5-D plenoptic function [Adelson and Bergen, 1991]
[Gortler et al., 1996] at a single point in 3-D space. The fixed 3-D
point at which a catadioptric sensor samples the plenoptic function is
known as the effective viewpoint.
Suppose we use a single conventional camera as the only sensing
element and a single mirror as the only reflecting surface. If the
camera is an ideal perspective camera and we ignore defocus blur, it
can be modeled by the point through which the perspective projection is
performed; i.e. the effective pinhole. Then, the fixed
viewpoint constraint requires that each ray of light passing through
the effective pinhole of the camera (which was reflected by the mirror)
would have passed through the effective viewpoint if it had not been
reflected by the mirror.
Simon Baker
1/22/1998