cs775 course projecthitesh/photon_mappi… · cs775 course project gaurav bhagwat hitesh...

CS775 Course Project

Gaurav BhagwatHitesh Kewalramani

Background: GlobalIllumination

Known techniques

Photon Mapping

Upgrade: Progressive Algo

A New Approach

Error Estimates

Approaching Goal

Published Results

Our ImplementationRoadmap

References

CS775 Course ProjectProgressive Photon mapping: A Probabilistic

Approach


Indian Institute of Technology, Bombay

March 27, 2012




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Outline

Background: Global IlluminationKnown techniquesPhoton MappingUpgrade: Progressive Algo

A New ApproachError EstimatesApproaching GoalPublished Results

Our Implementation Roadmap

References




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

What we know ...

I Solutions to rendering equationI Ray Tracing (LDS*E)I Radiosity (LD*E)I Distributed Ray Tracing (Monte Carlo) and Path Tracing

(??)

I Limitations?

Figure: http://graphics.ucsd.edu/h̃enrik/images/cbox.html




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

A new method

I Goal: Reduce High freq error, same efficiency, decoupleillumination, capture all paths (Whats new??) .

I Photon Mapping is two-pass global illumination algorithm.

I Photon Tracing (1st pass): Construction of Photon MapsI Photons shoot from light source to hit surfaces of various

materials.I Russian roulette - Absorb, Reflect, Transmit (Error?).I Store the hit point in kd-tree (Hence a Map!!).I Three photon Maps - Global, Caustic, Direct.




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

A Photon Map

Figure:www.cs.utexas.edu/mechin/photonmapping/photonmapping.htm

Figure: Realistic Image Synthesis using Photon Mapping (Book)




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Rendering (2nd Pass)

c = L(x , ω) ≈ 1

∆A

M∑j=1

fr (x , ωp, ωj)∆φ(x , ωj) (1)

I Gather the M nearest photons using the nearest neighborsearch function on the photon map.

I For each photon, divide the amount of flux (real photons)that the photon represents by the area of ∆A (also calledkernel) and multiply by the BRDF applied to that photon.

I The sum of those results for each photon represents totalsurface radiance returned by the surface intersection in thedirection of the ray that struck it.




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Photon Mapping Process

Figure: http://www.spot3d.com/vray/help




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Limitations

I Variance due to Russian roulette, also slow convergence.

I Huge Memory.

I Sparse Scenes?




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

A better way...

I No need to do everything in one step. Also lets focus onlyon visible points ( A new 1st pass).

I Photon mapping generation remains the same.

I Photon tracing or radiance estimate done incrementally.

I Converges fast.

Figure: Progressive Photon Mapping [1]




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Limitations

I Still we need to store local charactericstics.

I Number of Photons? Number of Passes? (A tradeoff?)

I No reduction in Error :(

I Correctness?




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Scope for improvement

I Keep the approach same, progressive.

I Goal: Reduce Error and Variance.

I Do something about the memory.

I How?? ... we know that Photon mapping computes aMonte Carlo estimate of reflected radiance L(x , ω) as

L(x , ω) ≈ 1

M

M∑j=1

kr (xj − x)γj (2)




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Relationships

I The error ε(x , r) is given as difference between radiancecalculated at position x using a kernel kr and the truevalue L(x , ω).

ε(x , r) =1

M

M∑j=1

kr (xj − x)γj − L(x , ω) (3)

I The variance of the error ε(x , r) is given as

Var [ε(r , x)] ≈ (Var [γ] + E [γ]2)pl(x)

Mr2

∫k(ψ)2dψ (4)

where the p.d.f of a photon in support of kernel kr is givenas pl(x) and γj are the random values as samples ofrandom variable γ.

I Expected error is following

E [ε(x , r)] = r2E [γ]τ (5)




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

What those new values mean??

I Given the above values, equation 1 becomes

c̄N =1

N

N∑i=1

1

pe(xi , ωi )W (xi , ωi )(L(xi + ωi ) + εi ) (6)

I Giving the average error in radiance estimate as ε̄N , andvariance as Var [ε̄N ], it is stated that,

N →∞,Var [ε̄N ] = 0⇒ Var [c̄N ] = 0

N →∞,E [ε̄N ] = 0⇒ E [c̄N ] = c

I The Magic...let the variance of radiance estimate increaseby small factor in every time step i , such that the averageit still vanishes.

r2i+1

r2i=

Var [errori ]

Var [errori+1]=

i + α

i + 1(7)




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Results

I same as progressive mostly.

I well behave in edges and corners.

I Almost same time.

I Less memory :)




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

Steps

I Implement Photon mapping (1st pass)

I Make it progressive.

I Try Probabilistic.

I Result Comparison.




Known techniques

Photon Mapping


A New Approach

Error Estimates

Approaching Goal

Published Results


References

References

Claude Knaus and Mathhias Zwicker Progressive PhotonMapping. ACM Trans. Graph. 2011

Hachisuka, Toshiya and Ogaki, Shinji and Jensen, HenrikWann Progressive Photon Mapping. ACM Trans. Graph.Dec 2008

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