Laplacian smoothing Diffusion flow:a mathematically well-understood model for the time- dependent process of smoothing a given signal f(x,t). Heat diffusion,Brownian motion 。Diffusion equation: afx,边=a△fx,t Ot 1.A second-order linear partial differential equation; 2.Smooth an arbitrary function f on a manifold surface by using Laplace-Beltrami Operator. 3. Discretize the equation both in space and time.Laplacian smoothing • Diffusion flow: a mathematically well-understood model for the time￾dependent process of smoothing a given signal 𝑓(𝒙,𝑡). • Heat diffusion, Brownian motion • Diffusion equation: 𝜕𝑓 𝒙,𝑡 𝜕𝑡 = 𝜆∆𝑓(𝒙,𝑡) 1. A second-order linear partial differential equation; 2. Smooth an arbitrary function 𝑓 on a manifold surface by using Laplace-Beltrami Operator. 3. Discretize the equation both in space and time