Lightfield Coordinates Adapted to Asgeirsson's Theorem

Abstract

John's differential equation and its canonical form, the ultrahyperbolic equation, plays important role in lightfield imaging. The equation describes a local constraint on the lightfield, that was first observed as a "dimensionality gap" in the frequency representation. Related to the ultrahyperbolic equation, Asgeirsson's theorems describe global properties. These indicate new, global, constraints on the lightfield. In order to help validate those theorems on real captured images, we introduce a coordinate system for the lightfield, which suits better the Asgeirsson theorems, and analyze behaviour in terms of the new coordinates.