computer graphics & visualization photon mapping

computer graphics & visualization

Image Synthesis

Photon Mapping


Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Motivation

“Today ray tracing is one of the most popular and powerful techniques in the image synthesis repertoire: it is simple, elegant, and easily implemented. [However] there are some aspects of the real world that ray tracing doesn’t handle very well (or at all!) as of this writing. Perhaps the most important omissions are diffuse inter-reflections (e.g. the ‘bleeding’ of colored light from a dull red file cabinet onto a white carpet, giving the carpet a pink tint), and caustics (focused light, like the shimmering waves at the bottom of a swimming pool).”

Andrew Glassner 1989



OverviewGenerating a Photon Mapped Image:

Two pass approach1. Generate Photon Map

“from the light source into the scene”

2. Render Image; e.g. with ray tracing“from the eye into the scene”



Ray tracing• The basic ray-tracing method– Recursive search for paths to the light source

• Interaction with matter• Point-wise evaluation of an illumination model• Shadows, reflection, transparency

ViewpointPoint light

source

R2

R1

R3

N2

N1

N3

T1

T2

L2 L1

L3

N: surface normals R: reflected rays L: shadow rays T: transmitted rays



Light sourcesTypes of light sources

Point Spherical Area General



From light source into the scene

Point light source

R2

R1

R3

N2

N1

N3

T1

T2

L3

Photon Map entries



Excursion: Path tracingSo far „recursive Raytracing“

Eye

Reflection

Reflection

Reflection

Refraction

Refraction

Reflection

Refraction

Refraction

Reflection

Reflection

Refraction

Refraction

Reflection

Refraction

“wastes most computationson little contribution”



New idea: „Path Tracing“Consider only a single path through the tree at a time

... and use Russian roulette to compute multiple paths

Eye

Reflection

Reflection

Reflection

Refraction

Refraction

Reflection

Refraction

Refraction

Reflection

Reflection

Refraction

Refraction

Reflection

Refraction



Back to Photons

[1,[[,[[,0[ absorbtionfor y Propabilit)(1 reflectionspecular for y Propabilit reflection diffusefor y Propabilitdsdsdddssd

N1

N1

N1



Why path-tracing for photons?

e

lightphoton n

PP

Constant photon energy

Well defined number of Photons in map

Problem: Aliasing



Aliasing/Noise



What to store in the photon map?

struct photon { float x,y,z; // position char phi, theta; // incident direction char p[4]; // color}

// phi = 255 * (atan2(dy,dx)+PI) / (2*PI);// theta = 255 * acos(dx) / PI;



How to store photons?• in a list / an array– simple– search operations O(n)

• in a grid– memory intense– search operations O(1)

• in a tree / kd-Tree– memory efficient– search operations O(log n)



A “balanced” kd-TreepointList = [(2,3), (5,4), (9,6), (4,7), (8,1), (7,2)] tree = kdtree(pointList)



KD-Tree Example



Pass 1 Shooting: Summary• For every light source– For a given number of photons• Choose random position (not for point lights)• Choose random direction• Start path tracing from light source• Stop in diffuse or absorbtion cases

– If diffuse: store position and direction in list

• Convert list to kd-tree



Pass 2 RenderingPhoton Map per se can not be rendered



Gathering

n

p

iirprrer

i

iirirrer

ii

iii

iirirrer

A

xxfxLxL

dA

xdxfxLxL

dAd

xdxL

dyLxfxLxL

1

2

2

),(),,(),(),(

),(),,(),(),(

)cos(

),(),(

)cos(),(),,(),(),(



Radiance Estimate

n

piirprrer

n

p

iirprrer

xxfr

xLxL

rA

A

xxfxLxL

1

1

),(),,(2

1),(),(

2

),(),,(),(),(



Splitting up the RE

iidridr

iicridr

iidicrisr

iirir

iirirr

dyLxf

dyLxf

dyLyLxf

dyLxf

dyLxfxL

)cos(),(),,(

)cos(),(),,(

)cos(),(),(),,(

)cos(),(),,(

)cos(),(),,(),(

,

,

,

Direct illumination from LS

Specular from caustics and diffuse illumination

Diffuse from caustics illumination

Diffuse from diffuse incoming illumination

indirectcausticsspeculardirectr LLLLL



Splitting up the RE

Raytracing: Shadow Caster

iidridr

iicridr

iidicrisr

iirir

iirirr

dyLxf

dyLxf

dyLyLxf

dyLxf

dyLxfxL

)cos(),(),,(

)cos(),(),,(

)cos(),(),(),,(

)cos(),(),,(

)cos(),(),,(),(

,

,

,







Splitting up the RE


Raytracing: Monte-Carlo Raytracing

iidridr

iicridr

iidicrisr

iirir

iirirr

dyLxf

dyLxf

dyLyLxf

dyLxf

dyLxfxL

)cos(),(),,(

)cos(),(),,(

)cos(),(),(),,(

)cos(),(),,(

)cos(),(),,(),(

,

,

,







Splitting up the RE



Photon Map: Direct Radiance Estimate

iidridr

iicridr

iidicrisr

iirir

iirirr

dyLxf

dyLxf

dyLyLxf

dyLxf

dyLxfxL

)cos(),(),,(

)cos(),(),,(

)cos(),(),(),,(

)cos(),(),,(

)cos(),(),,(),(

,

,

,







Splitting up the RE

iidridr

iicridr

iidicrisr

iirir

iirirr

dyLxf

dyLxf

dyLyLxf

dyLxf

dyLxfxL

)cos(),(),,(

)cos(),(),,(

)cos(),(),(),,(

)cos(),(),,(

)cos(),(),,(),(

,

,

,



Photon Map: Direct Radiance Estimate

Photon Map: Indirect Radiance Estimate







Irradiance CacheInstead of computing the Indirect Radiance Estimate, compute the irradiance ofa given pixel from the irradiance values of its neighbors; „if possible“.



Results



Problems



Disc Sampling



More Images

1 000 000 Photons, 100 Photons for radiance estimate, 11 Minutes



Realtime Photon tracing on GPUs0.05 Seconds

http://wwwcg.in.tum.de/Research/Publications/Photons/

http://wwwcg.in.tum.de/Research/Publications/Photons/

computer graphics & visualization photon mapping

Documents