GPU-Accelerated Surface Denoising and Morphing with LBM Scheme

1. GPU-Accelerated Surface Denoising and Morphingwith LBM Scheme Ye Zhao Kent State University, Ohio

2. Introduction • A parallel numerical scheme for shape modeling applications • Local and explicit computation • Easy for programming • Straightforward GPU acceleration • Modified from initially-designed fluid solver • Lattice Boltzmann method • Used in non-fluid applications • Smoothing and morphing examples GPU-Accelerated Surface Denoising and Morphing with LBM

3. Previous Work:LBM in Computer Graphics • Natural phenomena with fluids • Fluid Flows (Wei 04) • Smoke and fire (Wei03, Zhao03) • Ink dispersion (Chu 05) • Liquid mixture (Wang 06) • More … • Non-fluids • Lighting (Geist 04) • Diffusion phenomena (Zhao 07) GPU-Accelerated Surface Denoising and Morphing with LBM

4. Previous Work: Denoising and Morphing • Most smoothing techniques propose energy functions defined by the normal or curvature properties, and perform the constrained energy minimization • Explicit integration (Taubin 95) • Implicit fairing (Desbrun 99) • Shape interpolation • With distance field (Payne 92, Cohen-Or 98) • Level set scheme (Breen and Whitaker 01, Museth 02, Lefohn 04) • PDE surface (Du and Qin 05) • Laplacian and Poisson based methods (Lipman 04, Sorkine 04, Xu 05, Yu 04) GPU-Accelerated Surface Denoising and Morphing with LBM

5. Background:Lattice Boltzmann Method • A promising numerical scheme for simulating fluid dynamics • Microscopic operations with essential physics • Macroscopic averaged properties obey the Navier-Stokes equations • Clear statistical physics background • Easy implementation of complex boundaries • Fully parallel algorithm GPU-Accelerated Surface Denoising and Morphing with LBM

6. Fictitious particles moving along lattice links Microscopic particles inside fluids LBM: Microscopic Dynamics GPU-Accelerated Surface Denoising and Morphing with LBM

7. Lattice Structure GPU-Accelerated Surface Denoising and Morphing with LBM

8. Lattice Boltzmann Equation • Discretize Boltzmann equation on discrete moving directions i(1988) • f i: probability distribution function of particle populations on each link • ei: direction vector of each link • Ωi: Collision between particles • Recover the Navier-Stokes equation • At the limit of low Mach number flows GPU-Accelerated Surface Denoising and Morphing with LBM

9. LBM Computation • Collision: modeled as a relaxation process • τrepresents the relaxation time • BGK model (1954) for equilibrium • Streaming along a link to a neighbor GPU-Accelerated Surface Denoising and Morphing with LBM

10. Macroscopic Properties • Density, velocity and viscosity • Easily computed from packet distribution and link vectors • Add body force GPU-Accelerated Surface Denoising and Morphing with LBM

11. 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 • Pros: • LBM is easy to implement • both CPU and GPU • Flexible and easy to modify its scheme • Computational speed very fast with hardware acceleration GPU-Accelerated Surface Denoising and Morphing with LBM

12. Diffusion PDE with LBM • For fluid dynamics • BGK equilibrium model • For diffusion only, we use GPU-Accelerated Surface Denoising and Morphing with LBM

13. Recover Diffusion Equation • Chapman-Enskog expansion, ε represents a small expansion parameter (Knudsen number) • Use this and Taylor expansion on LBM equation GPU-Accelerated Surface Denoising and Morphing with LBM

14. Recover Diffusion Equation • We get expanded equation : • Summation on expanded equation over i • Diffusion tensor defined by lattice structure GPU-Accelerated Surface Denoising and Morphing with LBM

15. LBM for PDEs • For a particular 3D lattice structure we obtain • Model the Laplace equation • Model the Poisson equation with the similar procedure by using function h as the body force in the LBM scheme GPU-Accelerated Surface Denoising and Morphing with LBM

16. Previous Results: Image • Pixel densities used as the computing primitive in the LBM scheme • Image merging GPU-Accelerated Surface Denoising and Morphing with LBM

17. Previous Results: Volume • Voxel density as the computing primitive in the LBM scheme GPU-Accelerated Surface Denoising and Morphing with LBM

18. Process the Surface • Option 1: use voxelization algorithm to generate volume data from the surface, then apply volume processing with LBM • Implemented in our previous work • Not easy to apply shape interpolation • Option 2: implicitly represent the shape as distance field, then directly use the distance as the computing primitive in the LBM • We use the distance field LBM in this paper GPU-Accelerated Surface Denoising and Morphing with LBM

19. Distance Field LBM • Distance field • Using distance in the LBM, replacing with the curvature • The LBM computation with distance field simulates mean curvature flow for surface smoothing GPU-Accelerated Surface Denoising and Morphing with LBM

20. Surface Denoising • In smoothing, can be defined by the curvature for anisotropic denoising GPU-Accelerated Surface Denoising and Morphing with LBM

21. Surface Denoising GPU-Accelerated Surface Denoising and Morphing with LBM

22. Surface Denoising GPU-Accelerated Surface Denoising and Morphing with LBM

23. Surface Morphing • Extends our approach to the surface smoothing, we add the external expansion term to the level-set model • By define body force in the LBM scheme • For morphing, we define the force by the difference between the target shape and the morphing shape GPU-Accelerated Surface Denoising and Morphing with LBM

24. Surface Morphing GPU-Accelerated Surface Denoising and Morphing with LBM

25. Movie GPU-Accelerated Surface Denoising and Morphing with LBM

26. Surface Morphing GPU-Accelerated Surface Denoising and Morphing with LBM

27. Movie GPU-Accelerated Surface Denoising and Morphing with LBM

28. GPU Acceleration • Graphics processing units(GPU) • Low price • Powerful parallel machine • Booming growth rate on speed • Industry-supported continuing development • Ideal general-purpose applications • Large data sets • High parallelism • Minimal dependencies between data elements • The LBM algorithm is very amenable and easy to accelerate with simple and straightforward mapping GPU-Accelerated Surface Denoising and Morphing with LBM

29. Our Performance • We extend previous LBM fluid solver on GPU to this project • Modification overload is minimal • Performance measured on • CPU: Intel Core2 6300 with 3.25 GB RAM • GPU: Nvidia Geforce 8800GTX with 768MB texture memory GPU-Accelerated Surface Denoising and Morphing with LBM

30. Discussion • Easy solution to some PDEs in the cellular-automata originated updating rules • Nonlinear operations are implicitly implemented in its collision operation, avoiding complex numerical computations; • Good programmability in implementing the core LBM algorithm • With a few lines of codes and a short coding time • Straightforward mapping to GPUs for achieving great performance of simulation. GPU-Accelerated Surface Denoising and Morphing with LBM

31. Discussion • Distance field generation is a bottleneck in the preprocessing • Accuracy determined by the resolution of the lattice for the Eulerian approach • High accuracy increases memory consumption • Quality of the resulting surfaces also defined by • Simulation resolution • Rendering method from the implicit representation GPU-Accelerated Surface Denoising and Morphing with LBM

32. Discussion • GPU memory size is limited but improving very fast • Multiple GPUs may be used for extremely-large data • Adaptive and “Narrow-band” simulation may be used for the advanced LBM scheme GPU-Accelerated Surface Denoising and Morphing with LBM

33. Thank You! Questions? GPU-Accelerated Surface Denoising and Morphing with LBM