GPU-accelerated surface denoising and morphing with lattice Boltzmann scheme

In this paper, we introduce a parallel numerical scheme, the Lattice Boltzmann method, to shape modeling applications. The motivation of using this originally-designed fluid dynamics solver in surface modeling is its simplicity, locality, parallelism from the cellular-automata-originated updating rules, which can directly be mapped onto modern graphics hardware. A surface is implicitly represented by the signed distance field. The distances are then used in a modified LBM scheme as its computing primitive, instead of the densities in traditional LBM. The scheme can simulate curvature motions to smooth the surface with a diffusion process. Furthermore, an initial value level set method can be implemented for surface morphing. The distance difference between a morphing surface and a target surface defines the speed function of the evolving level sets, and is used as the driving force in the LBM. Our GPU-accelerated LBM algorithm has achieved outstanding performance for the denoising and morphing examples. It has the great potential to be further applied as a general GPU computing framework to many other solid and shape modeling applications.