GPU-Accelerated Surface Denoising and Morphing with LBM Scheme Ye Zhao Kent State University, Ohio

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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)

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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)

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM LBM: Microscopic Dynamics Microscopic particles inside fluids Fictitious particles moving along lattice links

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Lattice Structure

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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM LBM Computation Collision: modeled as a relaxation process –τ represents the relaxation time –BGK model (1954) for equilibrium Streaming along a link to a neighbor

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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Diffusion PDE with LBM For fluid dynamics –BGK equilibrium model For diffusion only, we use

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

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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Previous Results: Image Pixel densities used as the computing primitive in the LBM scheme Image merging

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Previous Results: Volume Voxel density as the computing primitive in the LBM scheme

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Surface Denoising In smoothing, can be defined by the curvature for anisotropic denoising

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Surface Denoising

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Surface Denoising

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Surface Morphing

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Movie

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Surface Morphing

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Movie

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Computation on GPU Texture Images Fragment Processing Fragments Fragment w/ Colors Graphics: Data Numerical Calculation Fragments Results Computation:

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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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.

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM 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

Ye ZhaoGPU-Accelerated Surface Denoising and Morphing with LBM Thank You! Questions?