Texture Synthesis over Arbitrary Manifold Surfaces Li-Yi Wei Marc Levoy Computer Graphics Group Stanford University

Introduction + Synthesize a surface texture by coloring mesh vertices Input TextureInput MeshResult

Desirable Properties Share advantages of 2D algorithm [SIGGRAPH 2000] –Quality –Efficient –General –Easy to use Minimum distortion Minimum discontinuity

Previous Work Texture Mapping –Global [Catmull’74, Bier’86, Levy’98] –Local Triangle tiles [Neyret’99] Lapped textures [Praun’00]

Previous Work 3D Texture synthesis –procedural [Perlin’85, Turk’91, Witkin’91] –from example surface texture [Gagalowicz’86, Turk’01, Ying’01] volume texture [Heeger’95, Ghazanfarpour ’96]

Previous Work 2D Texture from Example –pyramid matching [Heeger’95, Simoncelli’98] –block shuffling [De Bonet’97, Xu’00] –Markov Random Field [Popat’93] –neighborhood search [Efros’99, Wei’00]

Texture Synthesis by Neighborhood Search noise Input pyramid noise Output pyramid Search Copy

Surface Texture Synthesis by Neighborhood Search Input pyramid Output pyramid Search

Differences between Images and Meshes Our Solution image mesh Synthesis Order Pixels/Vertices Local Orientation (Vector field) ? ? mesh re-tiling [Turk’92] user-specified relaxation random scanline u v grid Neighborhood flattening/resampling normal ? ? tangent bitangent

Process 1. Build image/mesh pyramids 2. Assign texture orientation 3. Generate texture

Image & Mesh Pyramids Mesh Retiling [Turk’92]

Retiling Density vertices73728 vertices

Texture Orientation Methods for orienting textures –user-specified –random (for isotropic textures) –smooth or symmetric (for anisotropic textures) by relaxation

4-way symmetric texture 4-way symmetric vector field Texture Orientation

Texture Orientation by Relaxation Minimize an error function –similar to [Hertzmann’00, Pedersen’95]

Synthesis

Synthesis : 2 Lowest Levels

Synthesis : Lowest Level Random copy

Synthesis Pass1 : Extrapolation Search Copy Shooting normal

Synthesis Pass2 : Full Neighborhood Search Copy

Neighborhood Comparison compare ?

Mesh Neighborhood Resample Compare Resampled Grid 2D Patch 3D Patch Flatten (Maillot’93)

Accelerating Neighborhood Search Tree-structured Vector Quantization [Wei’00]

Multiresolution Synthesis

Results: Random Orientation

Results: Other Orientations RandomUser-specified Relaxation 2-way symmetry 4-way symmetry

Results smooth4-way symmetryrandom

Results Surface displacement smooth2-way symmetry

Summary of Differences Turk’s approachOur approach Vector field Traversal order Neighborhood Mesh hierarchy smoothrandom, symmetric sweepingrandom surface marchingflattening/resampling explicit parent/childshooting normal

Future Work Texture transfer between models Texturing animated models Mesh signal processing

More Information

Texture Orientation Examples Random4-way symmetric2-way symmetric

Synthesis Order ScanlineRandom Input

Differences between Turk’01 and Our Approach Turk’s approach Our approach Vector field Traversal order Neighborhood Mesh hierarchy smooth random, symmetric sweepingrandom surface marchingflattening + resampling explicit parent/childshooting normal

Introduction Texture Synthesis Input Result

Introduction + Synthesize a surface texture by coloring mesh vertices Input TextureInput Mesh Result Synthesis

Previous Work Synthesis from Example General Applicable to surfaces Low distortion No discontinuity Texture mapping Lapped textures Efficient Procedural texturing

Image Texture Synthesis Exhaustively search neighborhoods

Image Texture Synthesis

Mesh Pyramid Mesh Retiling: Turk’92

Key Idea Reuse the neighborhood-search framework Output pyramid Input pyramid Search

Key Idea Reuse the neighborhood-matching framework

Synthesis Lowest Level Random copy

Synthesis : Pass1 Copy Search Shooting normal

Synthesis : Pass2 Search Copy

Neighborhood Comparison Compare ?

Mesh Neighborhood 3D Patch

Mesh Neighborhood Resample Compare 3D Patch 2D Patch Resampled Grid Flatten (Maillot’93)

Synthesis : Pass1 Random copy Copy Search Shooting normal

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