Implicit Visibility and

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SIGGRAPH 07 Carsten Dachsbacher REVES/INRIA
Sophia-Antipolis Marc Stamminger University
of Erlangen George Drettakis REVES/INRIA
Sophia-Antipolis Fredo Durand MIT CSAIL

• Implicit Visibility and
• Antiradiance for
• Interactive Global Illumination

Presented by Yu-Ting Wu. 10/04/2007
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• Abstract

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Abstract
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Abstract

• Traditional rendering equation

Explicit Visibility Computation
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Abstract

• New rendering equation

Implicit Visibility !!
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Outline

• Introduction and Related Works
• Reformulating the Rendering Equation
• Discrete Finite Element Solution
• Implementation on Graphics Hardware
• Results
• Discussion
• Conclusion and Future Work

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• Introduction
• and
• Related Works

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Main Concept

• The main expense of global illumination is the
  cost of visibility
• Idea reformulate the rendering equation to
  treat the visibility implicitly
• Ignore the visibility problem first
• Then cancel out the extraneous light by
  introducing a new quantity antiradiance(negative
  light)

Facilitate the parallelization on graphics
hardware
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Related Works

• Negative light
• BACKALEW, C., and FUSSELL, D. SIGGRAPH 89
• PUECH, C., SILLION, F., and VEDEL, C. I3D 90
• Reformulation of rendering equation
• PELLEGRINI, M. SODA 99
• Dynamic global illumination
• TOLE, P., PELLACINI, F., WALTER, B., and
  GREENBERG, D. P. SIGGRAPH 02
• Precomputed radiance transfer (PRT)
• SLOAN, P.-P,. LUNA, B., and SNYDER, J.
  SIGGRAPH 05

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Overview

• System overview and techniques
• Propagate antiradiance to compensate the
  extraneous light and avoid explicit visibility
  computation
• Use spatial and directional finite elements to
  solve the new reformulated rendering equation

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Overview (cont.)

• Use pre-filtering in space and directions for
  form-factor computation
• Develop a hierarchical and clustering solution to
  deal with complexity

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Contributions

• A reformulation of the rendering equation
• Implicit visibility and the idea of antiradiance
• Two iterative solutions
• One provably converges but slower
• The other converges in practice and cheaper
• Hierarchical discretization
• Scalable for large scene
• Appropriate refinement and pre-filtering
• An efficient GPU implementation
• No visibility dependency, enhance parallelization

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• Reformulating the
• Rendering Equation

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Traditional Rendering Equation
Radiance
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Traditional Rendering Equation (cont.)
geometry operator
reflection operator
Rendering Equation
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Reformulation

• Replace the geometry operator G with an operator
  U which does not need explicit visibility
• Define the operator U

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Reformulation (cont.)
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Reformation (cont.)

• Introduce a new quantity, antiradiance, to cancel
  out the extraneous radiance
• Define a go-through operator J to let the
  incident light through opaque objects

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Reformulation (cont.)

• With the help of J, we can describe the relation
  between G and U

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Reformulation (cont.)
antiradiance, A
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Reformulation (cont.)

• Remove G to get rid of explicit visibility

Therefore, we can compute one iteration step of
classical light transport
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Reformulation (cont.)

• Finally we have reformulated the rendering
  equation by replacing G with U and A

New rendering equation
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Iterative Solution

• Two schemes to compute L and A
• Asymmetric Iteration corresponds to traditional
  global illumination and provably converges
• after one step of
• Iterate several steps of
• until convergence
• Symmetric Iteration iteratively propagate the
  above joint equation, cannot formally prove
  convergence but stable in practice

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Iterative Solution (cont.)

• Discussion
• Visually, convergence is achieved after less than
  10 iterations
• The output result doesnt make difference between
  these two solutions

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Iterative Solution (cont.)
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• Discrete Finite
• Element Solution

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Discretization

• Discretize the scene into a hierarchy of patches
  pi with centers xi
• Discretize the space of directions into m bins,
  each covers a solid angle ?bin 4p / m (620
  degrees in practice)

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Iterative Computation

• The iterative computation consists of two steps
• Global passsimilar to the link pass of
  traditional radiosity, generate operator U
• Local passtransfer incident radiance Lin to
  exitant intensity and antiradiance, thus, compute
  the operator K and J

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Iterative Computation (cont.)

• Global pass
• Receiving patch pi (centered at xi)
• Sending patch pk(centered at xk)
• Interaction bin ?j lt-gt ?l

?l
?j
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Iterative Computation (cont.)

• Global pass (cont.)
• The flux from xk emitted toward dA is
• Distribute the incident flux uniformly over the
  receiving bin to get the incident radiance at xi

form-factor
Compare to traditional form-factor
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Iterative Computation (cont.)

• Global pass (cont.)
• Link creation

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Iterative Computation (cont.)

• Hierarchy and Refinement
• To make the computation tractable, solve the
  finite element problem hierarchically
• The method is similar to Hierarchical Radiosity
  with Clustering Smits et al. 1994 Sillion 1995

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Iterative Computation (cont.)

• Link refinement

Condition1 The solid angle of the sender with
respect to the receiver is larger than a bin ?
Subdivide the link
A
B

• Condition2
• The solid angle of the sender with respect to the
  receiver is smaller than a bin
• Compute form-factor and
• establish the link

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Hierarchy and Refinement (cont.)

• Interaction bin refinement
• The sender patch may cover a large solid angle so
  that spread over several bins, thus lead to
  artifacts
• Select a circular neighborhood of size of s to
  pre-filter the form-factor with Gaussian blur

Refinement using pre-filtering
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Iterative Computation (cont.)

• Local pass
• Transform incident radiance Lin to reflected
  intensity(IL) and antiradiance itensity(IA)

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Direct light and Dynamic Scenes

• Direct light initialization
• This approach is geared towards indirect
  illumination
• For direct illumination, using one of existed
  method to initialize the incident radiance of the
  samples in the scene
• Environment map
• Shadow map (for direct shadow)
• During rendering, sum direct and indirect
  lighting computation in screen-space

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Direct light and Dynamic Scenes(cont.)

• Moving objects and lights
• Moving or deforming objects are handled naturally
  with this approach because there is no need to
  consider visibility
• If the position of moving objects can be
  reasonably bound, the hierarchy doesnt need to
  be updated and only the form-factor need to be
  recomputed
• The moving light can be handled in the same way

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• Implementation on
• Graphics Hardware

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Data Structures

• Three tables with n rows(number of elements) each
  with m columns(number of bins), storing
• Exitant intensity Iex
• Incident radiance Lin
• Total intensity Itotal

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Data Structures
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Operations
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Operations (cont.)

• Global pass
• Energy is transferred from one outgoing bin of a
  sender to the bins of a receiver

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Operations (cont.)

• Push operation
• Push the energy down the hierarchy
• Local pass
• Iterate over all bins of every element
• Convolve the incident radiance with BRDF to
  obtain the reflected energy and antiradiance
• Accumulate the energy to Itotal table
• Pull operation
• Pull energy from the leaves to their parents

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• Results

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Implement Environment

• All the tests were run on
• Xeon processor (3Ghz)
• NVIDIA GeForce 8800 GTX
• The reference solutions are computed with
  PBRTPharr and Humphreys 2004, which using a
  path-tracer module
• Film

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Comparison
Path tracing 12K rays / pixel 350 x 330
pixels 13hr 39min
This paper 1024bins / 6088 elements 8
iterations 3min 45s on CPU
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Comparison (cont.)
512 bins
128 bins
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Comparison (cont.)
This paper 480K links / 12.5K elements 8
iterations 1.1 fps on GPU
Path tracing 8K rays / pixel 40hr
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Comparison (cont.)
GPU 9 fps
CPU Imin 45s
PBRT 8hr 25min
Form-factor with Visibility 80min
Instant Radiosity 9 fps
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Comparison (cont.)
Triangles / Elements / Links / Iterations / FPS /
FPS(anti-aliasing)
Initial linking / Local pass / Global pass / Push
pull / Texture memory / Link memory
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• Discussion

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Discussion and Limitation

• Limitation
• Increased memory usage
• The convergence of symmetric scheme can not be
  ensured

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• Conclusion
• and
• Future Work

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Conclusion

• A reformulation of the rendering equation using
  implicit visibility
• A GPU friendly method which enhances
  parallelization
• Interactive updates of global illumination for
  complex scene
• With moving objects and lights, and glossy
  reflectors

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Future Work

• Apply the different way of thinking visibility
  problem to other applications
• Occlusion culling
• More theoretical analysis of the system for
  efficiency and high-quality solutions
• Sampling
• Filtering