Lightfield Coordinates Adapted to Asgeirsson's Theorem

TL;DR

This paper introduces a new coordinate system for lightfield imaging based on Asgeirsson's theorems, aiming to validate global constraints of lightfields through theoretical analysis and real image data.

Contribution

It proposes a novel lightfield coordinate system aligned with Asgeirsson's theorems, facilitating the validation of global lightfield properties.

Findings

New coordinate system better captures lightfield properties

Validation of Asgeirsson's theorems on real images

Enhanced understanding of lightfield constraints

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.