A Frequency Analysis of Light Transport: from Theory to Implementation

Abstract

The simulation of complex light effects such as depth-of-field, motionblur or scattering in participating media requires a tremendous amountof computation. But the resulting pictures are often blurry. We claimthat those regions should be computed sparsely to reduce their cost. Todo so, we propose a method covariance tracing that estimates the localvariations of a signal. This method is based on a extended frequencyanalysis of light transport and permits to build efficient algorithms thatdistribute the cost of low frequency parts of the simulation of lighttransport.This thesis presents an improvement over the frequency analysis of locallight-fields introduced by Durand et al. [2005]. We add into thisanalysis of light transport operations such as rough refractions,motion and participating media effects. We further improve the analysisof previously defined operations to handle non-planar occlusions oflight, anisotropic BRDFs and multiple lenses.We present covariance tracing, a method to evaluate the covariancematrix of the local light-field spectrum on a per light-path basis. Weshow that covariance analysis is defined for all the defined Fourieroperators. Furthermore, covariance analysis is compatible with MonteCarlo integration making it practical to study distributed effects.We show the use of covariance tracing with various applications rangingfrom motion blur and depth-of-field adaptive sampling and filtering,photon mapping kernel size estimation and adaptive sampling ofvolumetric effects.