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

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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


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SLIDE 1

Texture Synthesis: Surfaces and RD Textures

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Textures Surfaces

How to carry to surface?

+ =

from Wei & Levoy

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 surface given as mesh

 synthesis into textures  synthesis onto vertices (fine enough)

Images

Direct Synthesis

Color vertices

 issues:

 local orientation

th i d

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 synthesis order…  flattening/resampling  hierarchy?  notion of scale (Jacobian…)

Orientation Field

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2-way symmetry 4-way symmetry

Images from Wei & Levoy

Orientation Field

Construction choices

 interpolation

 push/pull with interpolation (Turk)

 project to tangent plane

Images from Turk

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 project to tangent plane

 use symmetry (Wei&Levoy)  incorporate geometry?

 user painted

Synthesis Order

No obvious ordering on surface

 punt: random (Wei&Levoy)  geodesics from seed point (Turk)

i l li f i i fi ld

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 integral lines of orientation field  fast marching methods

 priority queue on vertices  arrival time

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SLIDE 2

Local Neighborhood

Not a pixel grid when on surface…

 use local tangent frame

 walking on surface

 rectangular (Turk)

ges from Ying et al.

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 rectangular (Turk)  radial (Ying et al.)

 local flattening

(Wei&Levoy)

Imag Images from Wei&Levoy

Hierarchy

How to build pyramid?

 retiling (Turk)

 upsampling with fixed vertices

h i lifi ti

Images from Turk

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 mesh simplification

 edge collapse

 modern approaches

 resampling

Application by Jeff Somers

Scale

Explicit control desirable

 Progressively Variant Textures

(Zhang et al.)

 Textons expl scale

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 Textons, expl. scale

Images from Zhang et al.

Texture Map Directly

Avoid needing zillions of vertices…

 Ying et al.: keep texture maps  mapping

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Images from Ying et al.

Comparison

Hierarchical or coherent?

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Algorithmic Generation

Reaction diffusion textures

 biological pattern formation

Diffusion Dissipation

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Concentration ss pat o Reaction

Images from Turk

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SLIDE 3

On the Surface

Examples

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Details

Implementation

 discretize equations  regular grid: finite differences

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 time discretization

 forward Euler  backward Euler

Anisotropy

Account for distortion

rates along coordinate directions

Hessian

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 new variables

 Jacobian has to enter

Rotation

Image from Witkin&Kass

Numerical Solution

Iterative methods very slow

 explicit Euler requires tiny time

step

 implicit Euler requires solution of

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 implicit Euler requires solution of

linear system

 ill-conditioned…  multigrid (use libraries for this…)

RD Systems

Need multiple species

 two concentration arrays  two diffusion arrays

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 reaction function  initialize with random values  lots of ideas in Witkin & Kass

Examples

Witkin&Kass

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SLIDE 4

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

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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…