Summary:

Plenoptic Video Geometry is the study of the space of light rays as observed by a moving imaging sensor. The space of light rays is the most complete representation of visual information possible. All the information about the world that can be captured using visual sensors is encoded in the intensity function defined on the space of rays in 3D. This function is called the plenoptic function. Thus, if we understand the intrinsic structure of the plenoptic function, we can design optimal image acquisition devices and image processing algorithms to recover the information about the world that we seek.

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The plenoptic function.

At each location x in free space, the radiance, that is the light intensity or color observed at x from a given direction r at time t, can be measured by the plenoptic function:

where d=1 for intensity, d=3 for color images, and is the unit sphere of directions in (Adelson and Bergen 91).
Since the image irradiance that is recorded by an imaging device is proportional to the scene radiance, we assume that the intensity recorded by an imaging sensor at position x and time t pointing in direction r is equal to the plenoptic function L(x;r,t). A transparent medium such as air does not change the color of the light, therefore, we have a constant radiance along the view direction r:

Therefore, the plenoptic function in free space reduces to five dimensions -- the time-varying space of directed lines for which many representations have been presented (for an overview see Camahort and Fussel).