view dependent precomputed light transport using nonlinear gaussian function approximations l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations PowerPoint Presentation
Download Presentation
View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations

Loading in 2 Seconds...

play fullscreen
1 / 33

View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations - PowerPoint PPT Presentation


  • 106 Views
  • Uploaded on

View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations. View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations. View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations' - barny


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
view dependent precomputed light transport using nonlinear gaussian function approximations

View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations

View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations

View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations

View-Dependent Precomputed Light Transport Using Nonlinear Gaussian Function Approximations

Paul Green1 Jan Kautz1 Wojciech Matusik2 Frédo Durand1

MIT CSAIL1 MERL2

ACM Symposium in Interactive 3D Graphics 2006

slide2

Interactive 6D Relighting

Geometry & Viewpoint

Reflectance

All-Frequency Lighting

Rendered Frame

goal 6d relighting
Goal: 6D Relighting
  • High-quality view-dependent effects
    • Sharp highlights
  • Spatially varying BRDFs
  • Allow rendering w/ large environment maps (e.g. 6x256x256)
  • Without paying a prohibitive data storage price
applications
Applications
  • Games
  • Architectural Visualization
outline
Outline
  • Background / Previous Work
    • PRT
    • Nonlinear Approximation
  • Our Representation
    • Rendering
    • Fitting
    • Results
  • Conclusion
slide6

Shadowing

Inter-reflection

Incident Radiance

Precomputed Light Transport

Transport function maps distant light to incident light

Can Include BRDF if outgoing direction ωo is fixed

Distant Radiance

Exit Radiance

Courtesy of Sloan et al. 2003

slide7

Courtesy of Sloan et al. 2003

Light Transport

  • RadianceLoat pointpalong directionisweighted sum of distant radianceLi

Outgoing Radiance

Transport Vector

Distant Radiance (Environment Map)

example
Example

It’s a Dot Product Between Lighting and Transport Vectors!!

Transport Function

Environment Map

Exit Radiance (outgoing color)

BRDF Weighted Incident Radiance

light transport
Light Transport
  • Data Size Problem
    • Many GB’s of data
    • Rendering is slow
      • 6x64x64 cubemap ~24,000 mults/vert
  • Can reduce size in different basis:
    • Spherical Harmonics
    • Wavelets
    • Zonal Harmonics
prt with spherical harmonics
PRT with Spherical Harmonics
  • Precomputed Radiance Transfer [Sloan et al 02,03]
    • Low Order Spherical Harmonics
    • Soft Shadows and Low

Frequency Lighting

    • Not Suitable For Highly Glossy Materials
    • Not Practical For High Frequency Lighting

Image from slides by Ng et al.2003

nonlinear wavelet prt
Nonlinear Wavelet PRT
  • Nonlinear Wavelet Lighting Approximation [Ng et al 03]
    • Haar Wavelets
    • Nonlinear Approximation
    • All Frequency Lighting
    • Fixed View For Arbitrary BRDFs

Image from slides by Ng et al.2003

separable prt
Separable PRT
  • Factor BRDF into product of view-only and light-only functions [Liu et al 04, Wang et al 04]
  • Nonlinear Wavelet Approximation [Ng et al 03]
  • Need factorization per BRDF
  • Very specular materials still require many coefficients

Liu et al 04

our goal 6d relighting
Our Goal: 6D Relighting
  • High quality view-dependent effects
  • Representation of transport that enables
    • Spatially varying BRDFs
    • Arbitrary highlight scale
    • compact storage
    • High-res environment maps (e.g. 6x256x256)
  • Sparse view samplingRequires high-quality interpolation
    • Over view directions
    • Over mesh triangles
outline14
Outline
  • Background / Previous Work
    • PRT
    • Nonlinear Approximation
  • Our Representation
    • Rendering
    • Fitting
    • Results
  • Conclusion
factoring transport
Factoring Transport

Per view

View-dependent

?

Nonlinear Gaussian Function Approximation

Represent with SH or Wavelets

View-independent (diffuse)

our nonlinear representation

- mean

- std. deviation

Our Nonlinear Representation

Sum of N isotropic Gaussians

previous work nonlinear wavelet

Nonlinear: 8 Largest Coefficients

SSE = 25.1

Previous work: Nonlinear Wavelet
  • Nonlinear: Approximating basis set depends on input
  • Truncate small coefficients
  • Effect of coefficients is still linear

Linear: First 8 Coefficients

SSE = 140.2

our solution even more nonlinear

Nonlinear: 8 Largest Coefficients

Nonlinear sum of 2 Gaussians

SSE = 5.61

SSE = 25.1

Our solution: Even More Nonlinear
  • We don’t start from linear basis
  • No Truncation of coefficients
  • Nonlinear parameter estimation
  • Parameters have nonlinear effects
advantages of sum of gaussians

Haar 70 terms

original

N = 2

N = 1

Advantages of sum of Gaussians
  • Arbitrary freq bandwidth
  • Accurate approx w/small storage
  • Good interpolation
  • Good visual quality
rendering
Rendering

Lighting

Approximated Transport

?

gaussian pyramid
Gaussian Pyramid

Pre-convolve environment with Gaussians of varying sizes

Only done Once

Can start with large cubemap e.g. 6x256x256

Larger σ

rendering23
Rendering

Lighting

Approximated Transport

Exit Radiance (outgoing color)

Tri-linear lookup in Gaussian Pyramid

rendering novel views

?

p

Rendering Novel Views
  • Precomputed Transport Functions for sparse set of outgoing directions
  • Naïve solution: (Gouraud Shading) Interpolate Outgoing Radiance

Cross-fading artifacts

better interpolate parameters

?

p

Better: Interpolate Parameters
  • Interpolate Gaussian parameters
    • Mean, Std. Dev, Weights
  • Analogous to Phong vs Gouraud shading

t=0

t=0.5

t=1

interpolation drawbacks
Interpolation Drawbacks
  • Visibility may not interpolate correctly
    • But is usually plausible
  • Correspondences
    • Makes fitting more difficult

View-dependent

View-independent

data fitting

p

Data Fitting
  • Precompute Raw Transport Data
  • Solve large scale nonlinear optimization problem
    • For each vertex
      • For each view
        • Fit Gaussians to transport data
nonlinear optimization

-

N = 1

p

Nonlinear Optimization

original

N = 2

Objective has terms for

  • Fitting the Data
  • Regularization
    • Angular smoothness

and correspondences

    • Spatial smoothness

and correspondences

results
Results
  • 6x256x256 Environment Maps
  • Single Gaussian
  • 2.8 GHz P4
  • 1GB RAM
  • Nvidia 6800 Ultra
  • Software screen capture
contributions

original

N = 2

Haar

Contributions
  • New parametric representation of PLT
    • Compact Storage
    • High Quality
    • Interpolation of parameters
    • Sparse View Sampling
    • Efficient Rendering
    • Spatially varying BRDFs