Surfaces How to carry to surface? Texture Synthesis: Surfaces and - PDF document

Surfaces How to carry to surface? Texture Synthesis: Surfaces and RD from Wei & Levoy = + Textures Textures Images  surface given as mesh  synthesis into textures  synthesis onto vertices (fine enough) CS 176 Winter 2011 CS 176 Winter 2011 1 2 Direct Synthesis Orientation Field Color vertices  issues:  local orientation  synthesis order… th i d 2-way symmetry  flattening/resampling  hierarchy? Images from Wei & Levoy  notion of scale (Jacobian…) 4-way symmetry CS 176 Winter 2011 CS 176 Winter 2011 3 4 Orientation Field Synthesis Order Construction choices No obvious ordering on surface Images from Turk  interpolation  punt: random (Wei&Levoy)  push/pull with interpolation (Turk)  geodesics from seed point (Turk)  project to tangent plane  project to tangent plane  integral lines of orientation field i l li f i i fi ld  use symmetry (Wei&Levoy)  fast marching methods  incorporate geometry?  priority queue on vertices  user painted  arrival time CS 176 Winter 2011 CS 176 Winter 2011 5 6

Local Neighborhood Hierarchy Not a pixel grid when on surface… How to build pyramid? Images from Turk  use local tangent frame  retiling (Turk)  walking on surface ges from Ying et al.  upsampling with fixed vertices  rectangular (Turk)  rectangular (Turk)  mesh simplification h i lifi ti Imag  radial (Ying et al.)  edge collapse  local flattening Application by Jeff Somers  modern approaches (Wei&Levoy) Images from Wei&Levoy  resampling CS 176 Winter 2011 CS 176 Winter 2011 7 8 Scale Texture Map Directly Explicit control desirable Avoid needing zillions of vertices…  Progressively Variant Textures  Ying et al.: keep texture maps (Zhang et al.)  mapping  Textons, expl. scale  Textons expl scale Images from Zhang et al. Images from Ying et al. CS 176 Winter 2011 CS 176 Winter 2011 9 10 Comparison Algorithmic Generation Hierarchical or coherent? Reaction diffusion textures  biological pattern formation Diffusion Dissipation ss pat o Concentration Images from Turk Reaction CS 176 Winter 2011 CS 176 Winter 2011 11 12

On the Surface Details Examples Implementation  discretize equations  regular grid: finite differences  time discretization  forward Euler  backward Euler CS 176 Winter 2011 CS 176 Winter 2011 13 14 Anisotropy Numerical Solution rates along Account for distortion Iterative methods very slow coordinate directions  explicit Euler requires tiny time Hessian step  implicit Euler requires solution of  implicit Euler requires solution of linear system  new variables Rotation  ill-conditioned… Image from Witkin&Kass  Jacobian has to enter  multigrid (use libraries for this…) CS 176 Winter 2011 CS 176 Winter 2011 15 16 RD Systems Examples Need multiple species Witkin&Kass  two concentration arrays  two diffusion arrays  reaction function  initialize with random values  lots of ideas in Witkin & Kass CS 176 Winter 2011 CS 176 Winter 2011 17 18

Learning More Papers Appearance-Space Texture Synthesis, Lefebvre&Hoppe   Texture Synthesis over Abitrary Manifold Surfaces, Wei&Levoy  Texture Synthesis on Surfaces, Turk Synthesis of Progressively Variant Textures on Arbitrary Surfaces, Zhang  et al et al.  Texture and Shape Synthesis on Surfaces, Ying et al. Reaction-Diffusion Textures, Witkin&Kass  Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion, Turk  Tons more…  try google for these terms… CS 176 Winter 2011 19