Gradient-Domain Volumetric Photon Density Estimation

Supplemental material


1. Introduction

In this supplemental document, we demonstrate more results of the scenes in the main paper: "Gradient-Domain Volumetric Photon Density Estimation". The primal- and gradient-domain techniques included are:

By default, we employ 3D kernels in photon or beam gathering unless otherwise mentioned.

2. Code and scenes

The source code (Mistuba implementation) with instruction can be found at the following address: Github repo

Scenes (Mitsuba format) and the reference: You can download each scene individually by clicking on the scene's name below. Please note that some scenes have a Copyright. Refer to the acknowledgment section inside the paper.

3. Comparison

Equal-time comparisons are shown for the below scenes. We first show interactive 4-way comparisons between our method and other methods. Each visual comparison includes:

After the rendering in each result page, we show the convergence plot with the relative MSE metric. You can click on the technique name to show or hide a curve in the plot.

2. Experiments

a. Convergence

Scene Equal-time comparison Reference Comments
Kitchen 5 min
30 min

A complex scene with diffuse and specular light transport in homogeneous media with anisotropic phase function (g = 0.3).

Staircase 2 min
30 min

A scene with only diffuse light transport and isotropic phase function.

Bathroom 5 min
30 min

A complex scene with diffuse and specular light transport in homogeneous media with anisotropic phase function.

Spotlight 10 min
30 min

An even more challenging scene with dominant specular light transport and anisotropic phase function (g = 0.3).

b. Anisotropic Phase Function

g = 0.0 g = 0.225 g = 0.45 g = 0.675 g = 0.9
10 min 10 min 10 min 10 min 10 min

c. Dense Participating Media

Scene Equal-time comparison Reference Comments
Glass 5 min

A complex scene with a glass of milk and a glass of orange juice. Manifold exploration is used to handle the dielectric interfaces.

d. Bias vs. variance trade-off

Scene Equal-time comparison Reference Comments
Kitchen 5 min (VPM)
5 min (BRE)
5 min (Beam)

This presents the experiments with various kernel sizes in our technique. In general, our technique is not quite sensitive with kernel radius size unless it is set too large which causes too strong bias. Gradient-domain techniques take more time per iteration for estimate gradients to reduce variance, and so it is generally slower in reducing bias in progressive rendering.