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Lattice Boltzmann Method in Graphics & Visualization

Explore the application of Lattice Boltzmann Method (LBM) beyond fluid dynamics in graphics and visualization. Learn how to utilize LBM for image processing, surface processing, volume graphics, and computer vision, unlocking its potential in non-fluid applications. Discover research topics, such as modifying LBM scheme for theoretical PDE recovery, enhancing hardware acceleration performance, optimizing memory use, and integrating with specific applications. Dive into advanced topics like Diffusion Equation recovery using BGK model for equilibrium and Volume Smoothing techniques. Delve into LBM applications for Poisson Image Editing, Level Set equations, and surface motion. Unleash the power of LBM in non-fluid domains for innovative solutions and cutting-edge advancements.

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Lattice Boltzmann Method in Graphics & Visualization

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  1. Introduction:Lattice Boltzmann Method for Non-fluid Applications Ye Zhao

  2. Lattice Boltzmann Method • Microscopic numerical solver initially desinged for fluid dynamics • Simple, explicit and parallel scheme • Parallel scheme for hardware acceleration • Graphics hardware: GPU, GPU cluster

  3. LBM in Computer Graphics • Natural phenomena with fluids • Fluid Flows • Smoke and fire • Ink dispersion • Snowing • Liquid mixture (Wang et al. 2006) • More … • Non-fluids • Lighting (Geist et al. 2004) • Image Processing

  4. Navier-Stokes Equation • Model the macroscopic behavior of fluid

  5. Fictitious particles moving along lattice links Microscopic particles inside fluids Microscopic Dynamics

  6. Lattice Boltzmann Equation • Discretize Boltzmann equation on discrete moving directions i(1988) • f : probability distribution function of particle populations on each link • Recover the Navier-Stokes equation • At the limit of low Mach number fluids

  7. Lattice Structure

  8. Collision • BGK model (1954) for equilibrium • Streaming along a link to a neighbor Single-relaxation-time LBM

  9. Macroscopic Properties • Density, velocity and viscosity

  10. Body Forces

  11. Graphics Hardware • Graphics processing units(GPU) • Low price • Inherently parallel • Programmable • Booming growth rate on speed • 3.0 GHz dual-core Pentium4: 24.6 GFLOPs • NVIDIA GeForce FX 7800: 165 GFLOPs • Ideal general-purpose applications • Large data sets • High parallelism • Minimal dependencies between data elements

  12. Graphics: Computation: Fragments Fragments Texture Images Data Fragment Processing Numerical Calculation Fragment w/ Colors Results Computation on GPU

  13. LBM Acceleration on GPU • Computation on cluster • Large-scale simulation • Domain decomposition • Simple addition, subtraction and multiplication

  14. LBM for Non-fluids Applications • Actually LBM is a special numerical solver for partial differential equations (PDE) • PDEs are widely used in graphics and visualization applications • Image processing • Surface processing • Volume graphics and visualization • Computer vision …

  15. Use LBM in these fields? • Pros: • LBM is simple to implement • both CPU and GPU • Flexible and easy to modify its scheme • Computational speed very fast with hardware acceleration • Cons: • Difficult understanding at the beginning • Memory usage • Worth a try!

  16. Research Topics • How to modify LBM scheme in order to theoretically recover the preferred PDEs • How to improve hardware acceleration performance • New-generation GPU architecture • Memory use optimization • How to incorporate with particular applications

  17. BGK model (1954) for equilibrium Modify LBM Equilibrium Equation for Diffusion • For fluid dynamics • For diffusion only

  18. Recover Diffusion Equation • Chapman-Enskog expansion, ε represents a small expansion parameter (Knudsen number) • Use this and Taylor expansion on LBM equation

  19. Recover Diffusion Equation (Continue) • We get expanded equation : • Constraints • Summation on expanded equation over i

  20. Recover Diffusion Equation (Continue) • Diffusion tensor defined by lattice structure • For a particular lattice structure we obtain • For D3Q19

  21. Applications • Volume Smoothing

  22. Volume Smoothing

  23. Volume Smoothing

  24. Surface Smoothing

  25. Surface Smoothing

  26. Image De-noising

  27. Poisson Image Editing • Poisson Equation with Dirichlet boundary • is a computed guidance field computed from origin image

  28. Performance • GPU NVidia 8800GTX with 768MB memory

  29. More Applications • Apply to others beyond diffusion • Use level set equation as a pivot example • It has many application fields • Combine several different types of PDEs

  30. Level Set • Propagation interface as zero level set • d is distance to interface • Surface motion F = Signed speed in direction of normal

  31. F Speed Function • Curvature flow  diffusion on distance field • Advected propagation by a external field • Constant speed expansion

  32. LBM for Level Set • Use distance field as the computational primitive in LBM • Play the role as density in fluids • Design appropriate equlibrium function for PDEs

  33. Thanks

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