Bilateral Image Denoising 。non-linear 。edge-preserving noise-reducing smoothing Extended to mesh case!!!
Bilateral Image Denoising • non-linear • edge-preserving • noise-reducing smoothing • Extended to mesh case!!!
Bilateral Mesh Denoising Paper:Bilateral Mesh Denoising Vertex positions cannot simply be considered as the signal to be processed. Filtering a mesh using local neighborhoods. Main idea:local parameter space for every vertex using the tangent plane. The heights of vertices over the tangent plane gray-level values of an image. 。Update: vnew=v+d·n Once n is given,we need to compute the new d to update v
Bilateral Mesh Denoising Paper: Bilateral Mesh Denoising • Vertex positions cannot simply be considered as the signal to be processed. • Filtering a mesh using local neighborhoods. • Main idea: local parameter space for every vertex using the tangent plane. • The heights of vertices over the tangent plane ⟺ gray-level values of an image. • Update 𝒗: 𝒗 𝑛𝑒𝑤 = 𝒗 + 𝑑 ∙ 𝒏 Once 𝒏 is given, we need to compute the new 𝑑 to update 𝒗. 𝑑 𝒏 𝒗 𝑡 𝒒𝑖
Pseudo-code Denoise_Point(Vertex v,Normal n) {qi}=(v),N:number of neighbor vertices,dsum,K =0 for i=1 to N t=lv-qill d=(n,v-qi》 ws exp(-t2/(20s)) wr exp(-d2/(2o,)) dsum+=ws·wr·d 2 Kv+=Ws·Wn end return vnew =v+n.dsum/Kv
Pseudo-code Denoise_Point(Vertex 𝒗, Normal 𝒏) 𝑞𝑖 = Ω(𝒗), 𝑁: number of neighbor vertices, 𝑑sum, 𝐾𝒗 = 0 for 𝑖 ≔ 1 𝑡𝑜 𝑁 𝑡 = 𝒗 − 𝒒𝑖 𝑑 = 𝒏, 𝒗 − 𝒒𝑖 𝑤𝑆 = exp −𝑡 2/(2𝜎𝑠) 𝑤𝑟 = exp −𝑑 2/(2𝜎𝑟) 𝑑sum += 𝑤𝑆 ∙ 𝑤𝑟 ∙ 𝑑 𝐾𝒗 += 𝑤𝑆 ∙ 𝑤𝑟 end return 𝒗 𝑛𝑒𝑤 = 𝒗 + 𝒏 ∙ 𝑑sum/𝐾𝒗 𝑑 𝒏 𝒗 𝑡 𝒒𝑖
Detail Normal:weighted average of the normals 1-ring neighborhood of the vertex. k-ring neighborhood for extremely noisy data. weight:the area of the triangles. Mesh shrinkage:volume preservation technique. Scale the updated mesh to preserve the volume. How to compute the volume? ·Boundary. Parameters:os,o,,number of iterations
Detail • Normal: weighted average of the normals • 1-ring neighborhood of the vertex. • k-ring neighborhood for extremely noisy data. • weight: the area of the triangles. • Mesh shrinkage: volume preservation technique. • Scale the updated mesh to preserve the volume. • How to compute the volume? • Boundary. • Parameters: 𝜎𝑠 , 𝜎𝑟 , number of iterations
Figure 5:Results of denoising the Fandisk model.On the left is the input noisy model,in the middle is the results of [Jones et al.2003], and on the right is our result