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Zhao Dong¹, Jan Kautz², Christian Theobalt³�Hans-Peter Seidel¹

Interactive Global Illumination Using Implicit Visibility

¹MPI Informatik

Germany

²University College London

UK

³Stanford University

US

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Motivation

Global Illumination (GI) Effects

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Title

Hard Shadow

Soft Shadow

[HLHS03]

Direct Lighting

Direct +Indirect Lighting

[Fantasylab]

Arbitrary BRDF

[KSS02]

Ok, let’s firstly talk a little bit about motivation

What’s global illunination effects?

The first 2 images show the most important Gi effect –soft shadow

On the left image, it is the hard shadow, which we can always see when rendering the scene with a point light

However, if we render our scene with area light or environmental lighting

The shadow should be soft shadow, which have umbra and penumbra area

The following 2 images show another GI effect – indirect lighting

Which means the light will be shot out again after bouncing with scene element.

Indirect lighting can greatly increase the realistic feeling of image,

You see, the left is without indirect lighting, the right is with it.

Usually the reflectance properties (BRDF) of scene element decide the detailful

Rendering effect, the final 2 images are the model with the same BRDF

Model rendered under different environmental lighting. It looks quite promising.

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Motivation

GI effects is important for realistic image synthesis.

Real-time GI rendering is an open problems, especially for dynamic scene.

Visibility update is always the key bottleneck.🡪 Implicitly evaluate visibility info.

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Related Works

Hierarchical Radiosity

Explicit visibility evaluation is expensive.
Dynamic scene 🡪 global update “links” per frame.

Interactive Ray Tracing

Difficult to interactively handle indirect lighting

or environmental (area) light sources.

Dynamic Ambient Occlusion

Multiplying incident lighting with a precomputed

factor that represents the visible hemispherical

area at a point. Just a ratio number, directional

info is incorrect.

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Title

[Hanrahan91]

[Wald07]

[Bunnell05]

Firstly let’s summary the most related existing works

The first one is hierarchical radiosity, which is proposed by Hanrahan.et al in 1991.

This is a great paper, which elegantly decrease the complexity of radiosity from O(N^2)

To O(NlogN). However, the method use ray casting to explicitly do the visibility evaluation.

If for a dynamic scene, globally update scene links for each frame is necessary. So it is

Difficult to get high performance.

Recently the interactive ray tracing is a quite hot area. Just like wald et al’s works

In 2007. Which can handle the direct lighting of fully dynamic scene with point light..

However, for enviromental or area light source, ray tracing usually need to do

Random sampling, so it is difficult to get good FPS. Also because the same reason

, the indirect lighting is also problemtic for ray tracing.

Dynamic AO is another GI approximation method, like the image shown here is the work

From Bunnell et al. this method can handle deformable scene in RT. However, from

The theory of AO, it is just Multiplying incident lighting with a precomputed

factor that represents the visible hemispherical

area at a point. Just a ratio number, directional

info is incorrect.

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Related Works

Precomputed Radiance Transfer

Dynamic Scene make the precomputation difficult
SH Exponentiation 🡪 Direct lighting only.

Implicit Visibility and antiradiance

Many similarities with our method
Our implicit visibility handling is slightly more

flexible, as we impose no restrictions on the

dynamics of the scene, but is also slightly more

expensive.

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Title

[Ren06]

[Dachsbacher07]

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Light Transport

Rendering Equation [Kajiya86]

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Title

Let’s firstly review Kajiyá’s rendering eq

Imagine we have a point x in the scene, omega x is its hemisphere, the view point is on the left.

There is another point y in the scene, which has some energy shooting to x, the incident direction

Is womega i, From the view point we can see point x, the direction is womega o;

In the rendering eq, the first term is bidirectional reflectance distribution function(brdf), it is quite

Related with omega I and omega o. The second term is the incident lighting from direction womega i.

The third term called visibility function, if there is no any occluder between y and x, the visibility term

Equal to 1, if there is some occluder, the visibility term will equal to 0

The final term we usually call it geometry term, which is related with the distance, normal and size of x and y.

If we want to render the scene , we need to solve the rendering equation. The first step, we need to discretize it.

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Light Transport

Approximate Render Equation

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Title

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Basic Implicit Visibility Concept

ShadowMap concept:

Keep the link with the shortest

distance in each bin.

Assumptions:

Each element is small.
Constant energy across each

element’s extent.

A surface element covers the

extent of the spherical bin.

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Title

Nearest Element

Let ‘s currently only consider one bin in the hemisphere.

There are 2 elements locates in this bin. Y3 and y4

Based on the visibility function , the y3 is occluded by y4.

Its visibility term should equal to 0.

Usually we need to make use of ray casting to check the

Y4’s Visibility for point x.

Here we want to introduce some kind of shadow map concept for the

Element in 1 bin. We want to keep the link with the shortest distance in each

Bin. If we compared the distance of y3tox and y4to x

We just keep the nearest element for point x in each bin! And that is the basic

Motivation of our implicit visibility method.

Of course, if we do this, we need several assumptions

Each element is small.

Constant energy across each

element’s extent.

A surface element covers the

extent of the spherical bin.

Since we are doing an approximation global illumination method, based on our experiments.

These assumption are reasonable in most cases.

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Basic Implicit Visibility Concept

Naive Solution

O(N²), N is the

Number of scene

Element.

Hierarchical Solution

Similar with hierarchical

Radiosity[Hanrahan91]

O(NlogN)

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Title

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Algorithm Overview

Preprocess Geometry:

Create surface elements (surfels) based on input geometry
Create Hierarchical geometric structures (QuadTree)

For each frame Do:

Update the geometry information for initial geometric hierarchy.
Create hierarchical links between elements.
Refine hierarchical links, Top 🡪 Down, Remove unnecessary links.
Push down all the links to leaf node.
For each bounce Do:

Gathering incident energy from links and compute illumination in leaf nodes.
Pull up the indirect lighting energy from leaf to root.

End For
End For

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Preprocess Geometry

Create Surfels:

One vertex 🡨🡪 One Surfel
Surfel position = vertex position
Surfel normal = vertex normal
Surfel texture coords = vertex texture coords

Texture coords is for Parameterization.

Surfel area [Bunnell05]:

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Normal

Position

Area

Surface Elements

(Surfels)

Texture

Coords

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Preprocess Geometry

Create hierarchical geometric structures

Based on UV texture coords (One texture atlas 🡪 One QuadTree)
For deformable model, geometric hierarchy created once.
For parent node in hierarchy:

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Title

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Create Hierarchical Links

Similar with Hierarchical Radiosity [Hanrahan91]

Plus implicit visibility check: Shortest distance link

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Atlas0

Atlas1

Atlas2

Atlas3

BinArray of

Stored Link

Shortest Link

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Refine Hierarchical Links

Why?

Unnecessary links for the same bin appear in different tree levels

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Title

A

B

C

A

B

C

A

BinArray of

Shortest Link

BinArray of

Shortest Link

Same bin

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Refine Hierarchical Links

For the arrow in the figure:

Different Color 🡪 Different Bins
The length of arrow 🡪 distance of link

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Title

Level2

Level1

Level0

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Illumination Computation

Push down the links to leaf node

Leaf node is vertex, so we evaluate illumination for each vertex

(Leaf node level).

Illumination Computation

For each vertex, Gathering incident energy from hierarchical links.
For deformable model, each frame we can reuse the hierarchical links to compute N-bounces lighting.
Similar with Hierarchical Radiosity [Hanranhan91], each leaf node should Pull up its out shooting energy to it’s parent node! (multiply with its area ratio)

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Algorithm Implementation

Preprocess Geometry:

Create surface elements (surfels) based on input geometry
Create Hierarchical geometric structures (QuadTree)

For each frame Do:

Update the geometry information for initial geometric hierarchy.
Create hierarchical links between elements.
Refine hierarchical links, Top 🡪 Down, Remove unnecessary links.
Push down all the links to leaf node.
For each bounce Do:

Gathering incident energy from links and compute illumination in leaf nodes.
Pull up the indirect lighting energy from leaf to root.

End For
End For

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Title

Preprocess once, which depends

on the model’s Complexity, and

it is very fast on CPU side!

Execute for each frame. Create

And Refine hierarchical links is

the main Computation cost!

Currently implemented on

CPU!

Fully run on GPU side and it is

Quite fast!

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Results: Various Bin Numbers

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Title

Path Tracing

6x12x12, 6.23FPS

6x16x16, 4.42FPS

6x8x8, 7.89FPS

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Results: Efficiency Analysis

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Title

6x8x8

6x12x12

6x16x16

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Results: Indirect Lighting

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Direct, 6x16x16, 5.73FPS

One-bounce, 6x16x16, 4.95FPS

Two-bounces, 6x16x16, 4.43FPS

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Results: Non-hierarchical VS Hierarchical

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Path Tracing

Non-hierarchy, 6x16x16, 8.5s

6x16x16, 4.83FPS

6x16x16, coarse mesh

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Results: Area Light (One-bounce)

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Path Tracing

6x16x16, 5.12FPS

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Results: Glossy && Between objects

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Path Tracing

6x12x12, 8.02FPS

Direct Lighting,6x12x12,3.86FPS

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Result: Video

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Limitation && Problems

Limitations:

Parameterization based on the texture coords, so input model must be textured.
Our method is related with space distribution of vertex, so for too coarse input mesh, the light leaking will happen.
Create && Refine hierarchical links currently only implemented on CPU, and occupy most of the time 🡪 Moderately complex scenes.
Currently no explicit strategy for maintaining the temporal coherence of hierarchical links structure, so some flickering effects appear in animation.

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Conclusion && Future Works

Conclusion

A novel global illumination method that builds on and extends the traditional hierarchical radiosity approach by implicitly evaluating visibility.
Full global illumination solutions for moderately complex and arbitrarily deforming dynamic scenes at near-real-time frame rates on a single PC.

Future Works

Investigate explicit temporal coherence strategies 🡪 improve animation quality
Decoupling the tessellation of the mesh from shading computation.
Integration with NormalMap/DisplacementMap

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Questions and Thanks!

Questions and Thanks!

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