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Texture Synthesis on [Arbitrary Manifold] Surfaces Presented by: Sam Z. Glassenberg* * Several slides borrowed from Wei/Levoy presentation

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Topics Investigated Thus Far 2D Texture Mapping (CS318) 3D Textures (Hypertexture) 2D Texture Synthesis

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+ Synthesize a texture on a surface by coloring mesh vertices Input TextureInput MeshResult Today’s Goal

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Vertex Painting Advantages –Speed No additional transformation required –Simplicity –Uniformly distributed across geometry Disadvantages –Texture resolution dependent on mesh complexity

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2 SIGGRAPH Papers: 1.Texture Synthesis on Surfaces, by Greg TurkTexture Synthesis on Surfaces 2.Texture Synthesis over Arbitrary Manifold Surfaces, by Li-Yi Wei and Marc LevoyTexture Synthesis over Arbitrary Manifold Surfaces

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

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Differences between Images and Meshes image mesh Synthesis Order Pixels/Vertices Local Orientation (Vector field) ? ? scanline u v grid Neighborhood normal ? ? tangent bitangent

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

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Turk Solution Turk repulsion [Turk’91] User specified/ interpolated sweeping Surface marching image mesh Synthesis Order Pixels/Vertices Local Orientation (Vector field) ? ? scanline u v grid Neighborhood normal ? ? tangent bitangent

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Both Papers Extend Fast Texture Synthesis using Tree-structured Vector Quantization Specifically by generalizing their definition of “search neighborhoods” to apply to meshes

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

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Surface Texture Synthesis by Neighborhood Search (Wei/Levoy) Input pyramid Output pyramid Search

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

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What aspects of image pyramids must we maintain in mesh pyramids? Uniform density Power-of-two complexity differences between levels

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Image & Mesh Pyramids Mesh Retiling [Turk’92]

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2 Turk-ish Methods for Mesh Retiling Turk ’92, used by Wei/Levoy –Uniformly distributes mesh vertices –Requires “shooting normals” to move between levels Turk ’91, used by Turk –Uniformly distributes mesh vertices –Maintains parent/child relationship between levels

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Retiling Density 24576 vertices73728 vertices

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Turk ‘91 Create a mesh hierarchy in which mesh M k = (V k, T k ) is defined by its Vertices and Triangles –For the lowest mesh in the hierarchy, place n points on the surface –Use repulsion to distribute points easily –Add 3n points to make the next level –Repeat Connect points by projecting nearby points onto a tangent plane Perform Delaunay triangulation to reduce triangles

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Now, we need to determine orientation… In Turk’s method, we use this orientation to determine the computation order (Surface Sweeping) In Wei/Levoy’s method, orientation is needed to “flatten” the neighborhoods.

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Texture Orientation Generate a coordinate frame Three orthogonal axes – s (texture right) – t (texture up) – n (surface normal)

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Texture Orientation Methods for orienting textures –user-specified (Turk) –random (Wei/Levoy) –smooth or symmetric (Wei/Levoy)

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Texture Orientation (User-specified)

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4-way symmetric texture 4-way symmetric vector field Texture Orientation (Symmetry)

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Texture Orientation random2-way symmetry4-way symmetry

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Texture Orientation (Relaxation) Minimize an error function

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Results (Wei/Levoy): Random Orientation

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Results (Wei/Levoy): Other Orientations RandomUser-specified Relaxation 2-way symmetry 4-way symmetry

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Texture Synthesis on Surfaces: Wei/Levoy Style

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Synthesis

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Synthesis : 2 Lowest Levels

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Synthesis : Lowest Level Random copy

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Synthesis Pass1 : Extrapolation Search Copy Shooting normal

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

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Neighborhood Flattening Project the triangles adjacent to p onto p’s local texture coordinate system Add triangles one-at-a-time until neighborhood template is covered

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Neighborhood Comparison compare ?

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Synthesis Pass 2 : Full Neighborhood Search Copy

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Multiresolution Synthesis

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Texture Synthesis on Surfaces: According to Turk

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Turk’s Surface Sweeping Select an anchor vertex A Assign s(v) = sweep distance to vertex v along the vector field from A (for all v) Consensus orientation b/w 2 vertices v and w: O vw = (O(v) + O(w))/2 Calculate a new s(v) as a weighted average that its neighboring values dictate it should have. Visit vertices in order by sweep distance

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Turk’s Texture Synthesis (Pseudocode) I = Input texture N(v) = Neighborhood around v M(a,b) = Neighborhood around (a,b) D(M,N) = Match Value (sum of squared differences)

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Turk’s Mesh Neighborhoods r = average distance between mesh vertices O(v) = Surface tangent vector P(v) = O(v) rotated 90 o about surface normal Together, O and P make a coordinate frame ! u v normal P O Now, we can traverse the surface by point repelling

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Point Repelling Use color interpolation to determine color at current surface point Move r in the direction of O or P When an edge is reached, fold the path over the next polygon

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Results smooth4-way symmetryrandom

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Results Surface displacement smooth2-way symmetry

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Results

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

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