Lapped Textures Emil Praun Adam Finkelstein Hugues Hoppe Emil Praun Adam Finkelstein Hugues Hoppe...

Lapped TexturesLapped Textures

Emil PraunEmil Praun

Adam FinkelsteinAdam Finkelstein

Hugues HoppeHugues Hoppe

Emil PraunEmil Praun

Adam FinkelsteinAdam Finkelstein

Hugues HoppeHugues Hoppe

Princeton UniversityPrinceton University


Microsoft ResearchMicrosoft Research



Microsoft ResearchMicrosoft Research

GoalGoal

“example” image“example” image

textured surfacetextured surface

mesh geometrymesh geometry

?

GoalGoal

Little user effortLittle user effort

No apparent seamsNo apparent seams

No obvious periodicityNo obvious periodicity

Low distortionLow distortion

Local texture controlLocal texture control

AnisotropyAnisotropy

Little user effortLittle user effort

No apparent seamsNo apparent seams

No obvious periodicityNo obvious periodicity

Low distortionLow distortion

Local texture controlLocal texture control

AnisotropyAnisotropy

Previous 2D Texture SynthesisPrevious 2D Texture Synthesis

Histogram equalization [Heeger ’96]Histogram equalization [Heeger ’96]

Laplacian block shuffling [de Bonet ’97]Laplacian block shuffling [de Bonet ’97]

Pixel template matching [Efros ’99] [Wei ’00]Pixel template matching [Efros ’99] [Wei ’00]



Pixel template matching [Efros ’99] [Wei ’00]Pixel template matching [Efros ’99] [Wei ’00]



Pixel template matching [Efros ’99] [Wei Pixel template matching [Efros ’99] [Wei ’00’00]]

Random pasting of image blocks [Xu ’00]Random pasting of image blocks [Xu ’00]



Pixel template matching [Efros ’99] [Wei Pixel template matching [Efros ’99] [Wei ’00’00]]

Random pasting of image blocks [Xu ’00]Random pasting of image blocks [Xu ’00]

Previous 2D Texture SynthesisPrevious 2D Texture Synthesis

Previous 3D TexturingPrevious 3D Texturing

Volumetric textures:Volumetric textures:

• Noise functions [Perlin ’85, Worley ’96]Noise functions [Perlin ’85, Worley ’96]

• Solid textures by example [Ghazanfarpour ’96]Solid textures by example [Ghazanfarpour ’96]

Synthesizing texture on a surface:Synthesizing texture on a surface:

• Reaction-diffusion [Turk ’91, Witkin ’91] Reaction-diffusion [Turk ’91, Witkin ’91]

• Cellular textures [Fleischer ’95]Cellular textures [Fleischer ’95]

• Covering surface with triangular tiles [Neyret ’99] Covering surface with triangular tiles [Neyret ’99]

Volumetric textures:Volumetric textures:

• Noise functions [Perlin ’85, Worley ’96]Noise functions [Perlin ’85, Worley ’96]

• Solid textures by example [Ghazanfarpour ’96]Solid textures by example [Ghazanfarpour ’96]

Synthesizing texture on a surface:Synthesizing texture on a surface:

• Reaction-diffusion [Turk ’91, Witkin ’91] Reaction-diffusion [Turk ’91, Witkin ’91]

• Cellular textures [Fleischer ’95]Cellular textures [Fleischer ’95]

• Covering surface with triangular tiles [Neyret ’99] Covering surface with triangular tiles [Neyret ’99]

ApproachApproach

texture patchtexture patch

surfacesurface

Key Idea: Patch PastingKey Idea: Patch Pasting

texture patchtexture patchtexture patchtexture patch

surfacesurfacesurfacesurface““lapped textures”lapped textures”

Anisotropic vs. Isotropic imagesAnisotropic vs. Isotropic images

PROCESSPROCESS

AlgorithmAlgorithm

Cut texture patches from input textureCut texture patches from input texture

[Specify texture direction & scale on mesh][Specify texture direction & scale on mesh]

REPEATREPEAT

Pick texture patch T, mesh point PPick texture patch T, mesh point P

Grow surface patch S around P to size(T)Grow surface patch S around P to size(T)

Flatten S over T; paste T on meshFlatten S over T; paste T on mesh

Update mesh coverage infoUpdate mesh coverage info

UNTIL mesh is coveredUNTIL mesh is covered

Cut texture patches from input textureCut texture patches from input texture

[Specify texture direction & scale on mesh][Specify texture direction & scale on mesh]

REPEATREPEAT

Pick texture patch T, mesh point PPick texture patch T, mesh point P

Grow surface patch S around P to size(T)Grow surface patch S around P to size(T)

Flatten S over T; paste T on meshFlatten S over T; paste T on mesh

Update mesh coverage infoUpdate mesh coverage info

UNTIL mesh is coveredUNTIL mesh is covered

AlgorithmAlgorithm


surfacesurface

AlgorithmAlgorithm


surfacesurface

AlgorithmAlgorithm


surfacesurface

AlgorithmAlgorithm


surfacesurface

IssuesIssues

1.1. Texture patch creationTexture patch creation

2.2. Specifying direction fieldSpecifying direction field

3.3. Surface patch growthSurface patch growth

4.4. Patch parametrizationPatch parametrization

5.5. Face coverage estimationFace coverage estimation

6.6. Texture storage and renderingTexture storage and rendering







IssuesIssues













Texture Patch CreationTexture Patch Creation

Less Structure SplotchLess Structure Splotch

IssuesIssues













Direction Field: User-specifiedDirection Field: User-specified

Direction Field: User-specifiedDirection Field: User-specified

• Angle - Only for anisotropic patches.Angle - Only for anisotropic patches.

• Can be set for only small number of Can be set for only small number of faces – Gaussian radial basis function faces – Gaussian radial basis function is used for interpolation.is used for interpolation.

• Since the normal lies within the plane of Since the normal lies within the plane of the face we get an orthogonal basis :the face we get an orthogonal basis :

S = T x N. (N – normal to the plane).S = T x N. (N – normal to the plane).

• Angle - Only for anisotropic patches.Angle - Only for anisotropic patches.

• Can be set for only small number of Can be set for only small number of faces – Gaussian radial basis function faces – Gaussian radial basis function is used for interpolation.is used for interpolation.

• Since the normal lies within the plane of Since the normal lies within the plane of the face we get an orthogonal basis :the face we get an orthogonal basis :

S = T x N. (N – normal to the plane).S = T x N. (N – normal to the plane).

Direction Field: Local to PatchDirection Field: Local to Patch

IssuesIssues













Patch GrowthPatch Growth

1. 1. Choose a random point on a non fully covered triangle.Choose a random point on a non fully covered triangle.

2. Add triangles in a BFS order to cover the texture patch.2. Add triangles in a BFS order to cover the texture patch.

3. Stop when the patch is fully coverd. 3. Stop when the patch is fully coverd.

Condintions:Condintions:

a.a. The surface patch homeomorphic to a disk.The surface patch homeomorphic to a disk.

b.b. The distortion should not exceed a given limit.The distortion should not exceed a given limit.

c.c. We add edge only if it is within the texture patch.We add edge only if it is within the texture patch.

1. 1. Choose a random point on a non fully covered triangle.Choose a random point on a non fully covered triangle.

2. Add triangles in a BFS order to cover the texture patch.2. Add triangles in a BFS order to cover the texture patch.

3. Stop when the patch is fully coverd. 3. Stop when the patch is fully coverd.

Condintions:Condintions:

a.a. The surface patch homeomorphic to a disk.The surface patch homeomorphic to a disk.

b.b. The distortion should not exceed a given limit.The distortion should not exceed a given limit.

c.c. We add edge only if it is within the texture patch.We add edge only if it is within the texture patch.









Polygonal HullsPolygonal Hulls

Start w/ boundary pixels, edges between Start w/ boundary pixels, edges between neighborsneighbors

Conservatively simplify polygonsConservatively simplify polygons

Start w/ boundary pixels, edges between Start w/ boundary pixels, edges between neighborsneighbors

Conservatively simplify polygonsConservatively simplify polygons

IssuesIssues













Align Patch to Direction FieldAlign Patch to Direction Field


surfacesurface

Tangential Vector FieldTangential Vector Field

Optimizing the ParametrizationOptimizing the Parametrization

Least squares best match to unit axesLeast squares best match to unit axesSparse linear system. No explicit fairness functionalSparse linear system. No explicit fairness functional

Least squares best match to unit axesLeast squares best match to unit axesSparse linear system. No explicit fairness functionalSparse linear system. No explicit fairness functional


TTTTSSSS

BBBB

CCCC

AAAA

((TT))((TT))

((SS))((SS))

((AA))((AA))

((BB))((BB))

((CC))((CC))

tttt

ssss

face in 3Dface in 3Dface in 3Dface in 3D 2D texture space2D texture space2D texture space2D texture space


For each mesh face For each mesh face f f ={A,B,C} the vector T ={A,B,C} the vector T lies within the face plain.lies within the face plain.

Barycentric coordinates:Barycentric coordinates:

T = T = A + A + B + B + C and C and + + + + = 0. = 0.

For each mesh face For each mesh face f f ={A,B,C} the vector T ={A,B,C} the vector T lies within the face plain.lies within the face plain.

Barycentric coordinates:Barycentric coordinates:

T = T = A + A + B + B + C and C and + + + + = 0. = 0.


TTTTSSSS

BBBB

CCCC

AAAA

((TT))((TT))

((SS))((SS))

((AA))((AA))

((BB))((BB))

((CC))((CC))

tttt

ssss

face in 3Dface in 3Dface in 3Dface in 3D 2D texture space2D texture space2D texture space2D texture space

ddTT = = (A) + (A) + (B) + (B) + (C) - (C) -

tt

^

We wish to minimize :We wish to minimize : f

ts dd22

Result of OptimizationResult of Optimization

IssuesIssues













Coverage estimationCoverage estimation

off-screen bufferoff-screen bufferoff-screen bufferoff-screen buffer

Render patch trianglesRender patch triangles

Flag covered trianglesFlag covered triangles

Remember 1 pixel Remember 1 pixel

per uncovered triangle per uncovered triangle

























IssuesIssues













Texture Storage and RenderingTexture Storage and Rendering

Method 1: Method 1: Texture AtlasTexture Atlas

• Pre-composite into a global texture map.Pre-composite into a global texture map.

-- OR ---- OR --

Method 2: Method 2: Runtime pastingRuntime pasting

• Composite at run-time using hardwareComposite at run-time using hardware

Method 1: Method 1: Texture AtlasTexture Atlas

• Pre-composite into a global texture map.Pre-composite into a global texture map.

-- OR ---- OR --

Method 2: Method 2: Runtime pastingRuntime pasting

• Composite at run-time using hardwareComposite at run-time using hardware

Texture AtlasTexture Atlas

Texture Atlas is a set of charts {Texture Atlas is a set of charts {11,…, ,…, kk}.}.

Each chart Each chart j j is a mapping from a subset U is a mapping from a subset U

j j of the mesh to the Euclidean plane (the of the mesh to the Euclidean plane (the

texture plane).texture plane).

{U{U11,…, U,…, Ukk} is a cover of the surface.} is a cover of the surface.

If i If i j then j then j j and and i i don’t overlap except on don’t overlap except on

the edges.the edges.

Texture Atlas is a set of charts {Texture Atlas is a set of charts {11,…, ,…, kk}.}.

Each chart Each chart j j is a mapping from a subset U is a mapping from a subset U

j j of the mesh to the Euclidean plane (the of the mesh to the Euclidean plane (the

texture plane).texture plane).

{U{U11,…, U,…, Ukk} is a cover of the surface.} is a cover of the surface.

If i If i j then j then j j and and i i don’t overlap except on don’t overlap except on

the edges.the edges.

Texture AtlasTexture Atlas

Patches of triangles with similar normalsPatches of triangles with similar normals

2D packing problem for arbitrary polygons2D packing problem for arbitrary polygons

Patches of triangles with similar normalsPatches of triangles with similar normals

2D packing problem for arbitrary polygons2D packing problem for arbitrary polygons

Runtime PastingRuntime Pasting

Store vertex coordinates for each patchStore vertex coordinates for each patch

Composite at run-time using hardwareComposite at run-time using hardware

May render triangles several timesMay render triangles several times

Store vertex coordinates for each patchStore vertex coordinates for each patch

Composite at run-time using hardwareComposite at run-time using hardware

May render triangles several timesMay render triangles several times

Atlas vs. Runtime PastingAtlas vs. Runtime Pasting

AtlasAtlas

+ Faster rendering, more portableFaster rendering, more portable

+ Easy to paint unique details (eyes, nose on bunny)Easy to paint unique details (eyes, nose on bunny)

– Sampling artifacts; user effortSampling artifacts; user effort

PastingPasting

– Increases model complexity (Increases model complexity ( 1.6 –3)1.6 –3)

+ Huge effective resolution Huge effective resolution

+ Reuse splotch parameterization for many texturesReuse splotch parameterization for many textures

AtlasAtlas

+ Faster rendering, more portableFaster rendering, more portable

+ Easy to paint unique details (eyes, nose on bunny)Easy to paint unique details (eyes, nose on bunny)

– Sampling artifacts; user effortSampling artifacts; user effort

PastingPasting

– Increases model complexity (Increases model complexity ( 1.6 –3)1.6 –3)

+ Huge effective resolution Huge effective resolution

+ Reuse splotch parameterization for many texturesReuse splotch parameterization for many textures

RESULTSRESULTS

Results: SplotchesResults: Splotches

(completely automatic: no direction field)(completely automatic: no direction field)

Results: AnisotropicResults: Anisotropic

Controlling Direction and ScaleControlling Direction and Scale

Usage of more than 1 patchUsage of more than 1 patch

25 frames25 framesper sec!per sec!

tiny texturetiny texturefootprintfootprint

tiny texturetiny texturefootprintfootprint

LimitationsLimitations

low-frequencylow-frequencycomponentscomponents

boundaryboundarymismatchesmismatches

direction field direction field singularitiessingularities

TimingsTimings

Texture patch creation: Texture patch creation: 1 min1 min

Specifying direction field: Specifying direction field: 15 min15 min

Surface patch growthSurface patch growth

Patch parameterizationPatch parameterization

Face coverage estimationFace coverage estimation

Rendering: Rendering: 25fps25fps @ 1024 @ 102422

Texture patch creation: Texture patch creation: 1 min1 min

Specifying direction field: Specifying direction field: 15 min15 min

Surface patch growthSurface patch growth

Patch parameterizationPatch parameterization

Face coverage estimationFace coverage estimation

Rendering: Rendering: 25fps25fps @ 1024 @ 102422

Preprocessing:Preprocessing:

20sec – 6 min20sec – 6 min

Preprocessing:Preprocessing:

20sec – 6 min20sec – 6 min

Pentium III 733MHz, GeForce graphicsPentium III 733MHz, GeForce graphicsPentium III 733MHz, GeForce graphicsPentium III 733MHz, GeForce graphics

Human Human efforteffortHuman Human efforteffort

ConclusionsConclusions

Effective texture-by-example through:Effective texture-by-example through:

Overlapping texture patches Overlapping texture patches

Minimal edge blending Minimal edge blending

Aligning to direction field Aligning to direction field fast optimization fast optimization

Runtime compositing Runtime compositing high effective resolution high effective resolution

Effective texture-by-example through:Effective texture-by-example through:

Overlapping texture patches Overlapping texture patches

Minimal edge blending Minimal edge blending

Aligning to direction field Aligning to direction field fast optimization fast optimization

Runtime compositing Runtime compositing high effective resolution high effective resolution

Future WorkFuture Work

Other texture types:Other texture types:

• AnimatedAnimated

• ““Thick” (volumetric) textures Thick” (volumetric) textures fur fur

• NPR renderingNPR rendering

Fine-tuning patch placementFine-tuning patch placement

Greater automationGreater automation

Other texture types:Other texture types:

• AnimatedAnimated

• ““Thick” (volumetric) textures Thick” (volumetric) textures fur fur

• NPR renderingNPR rendering

Fine-tuning patch placementFine-tuning patch placement

Greater automationGreater automation

Date post:	19-Dec-2015
Category:	Documents
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