3D Modeling for EveryoneHsueh-Ti Derek Liu

University of Toronto

3D modeling

Spectral geometry

SIGGRAPH Asia 2018 ICLR 2019 SIGGRAPH Asia 2019 SIGGRAPH 2020

SGP 2017 SIGGRAPH 2019 Eurographics 2019 SIGGRAPH Asia 2020

Image Editing

3D scanning

medium.com

Macworld.com

OmniVirt.com

3D display

Advances in 3D Technology

3D Modeling

3D Modeling is Hard

2D Analogue

Make 3D modeling available for everyone

3D modeling is a long-standing problem

blender cloud - springVaxman et al. 2018

wikimedia autodesk

Classic 3D Modeling

primitive shape Today

?

Acquiring 3D data is easy nowadays

3D scanning

medium.com

3D datasets

Thingi10K

Future 3D Modeling

primitive shape complex shape

?novelperspectives

Geometric filtering 3D Stylization Data-driven subdivision

appearancenormal

prior

Geometric FilteringHsueh-Ti Derek Liu, Michael Tao, Alec Jacobson, “Paparazzi: Surface Editing by way of Multi-View Image Processing ”, SIGGRAPH Asia 2018

Image Filters

Geometric Filters

Complex Filters?

[Gatys et al. 2016]

?

Appearance-driven Editing

Hsueh-Ti Derek Liu, Michael Tao, Alec Jacobson, “Paparazzi: Surface Editing by way of Multi-View Image Processing ”, SIGGRAPH Asia 2018

Appearance-driven EditingV

R(V)

rendering

differentiable renderer ∂R∂V

image

filteri

ng

R′ (V)

Rendering Means to an End

… ?

A Simple Differentiable Renderer

Lambertian material

Flat shading orthographic camera

directional lights

orthographic projection

A Simple Differentiable Renderer

Lambertian material

Flat shading

directional lights DifferentiableSimple

Fast

Rendering as a tool for visualization Rendering as a tool for 3D modeling

3D StylizationHsueh-Ti Derek Liu, Alec Jacobson, “Cubic Stylization”, SIGGRAPH Asia 2019

Stylization3D 2D

non-photorealistic rendering [Hertzmann, Zorin 2000]

image stylization [Gatys et al. 2016]

2D 2D 3D 3D

3D stylization

?

Cubic Stylization

Chichén Itzá

source: wikimedia.org Feathered Serpent

source: wikimedia.org Block Statue

Egypt

United Kingdom

Draped Seated Woman by Henry Moore

© puffin11k

Taiwan

Taichi by Ju Ming source: wikimedia.org

© Art Poskanzer

!e Kiss by Constantin Brâncus

Romania

Chichén Itzá

source: wikimedia.org Feathered Serpent

source: wikimedia.org Block Statue

Egypt

United Kingdom

Draped Seated Woman by Henry Moore

© puffin11k

Taiwan

Taichi by Ju Ming source: wikimedia.org

© Art Poskanzer

!e Kiss by Constantin Brâncus

Romania

Chichén Itzá

source: wikimedia.org Feathered Serpent

source: wikimedia.org Block Statue

Egypt

United Kingdom

Taiwan

Taichi by Ju Ming source: wikimedia.org

© Art Poskanzer

!e Kiss by Constantin Brâncus

Romania

Draped Seated Woman by Henry Moore

© puffin11k

How to characterize a cube?

How to characterize a cube? 266664001

377775

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266664010

377775

AAAJXnicfdbdbts2FABgtdu62FvXdLsZMAwQFgTYBiOQsjRdLga0TpqkrfPn2olbywgomZZZi5JKUo4dQs+wp9nt9hy726OMUmyfE2+pABkH3zmiSOrIkJ9GTCrH+fve/U8+/ezB5yuV6hdfPvzq0erjr89lkomAtoMkSkTHJ5JGLKZtxVREO6mghPsRvfBHu0X+YkyFZEncUtOU9jgJYzZgAVGGLld/8nwaslj7nCjBJnnVsT3Pdosfp+rRuL/IXK6uORvOjuPubNv/DdwNpzzWrNlxevl45XuvnwQZp7EKIiJl13VS1dNEKBZENK96maQpCUYkpF0TxoRT2dPlmnJ73UjfHiTCnLGyS8VXaMKlnHLfVJoJDuVyrsC7csWIMrdvMY0zzhTlt6cVMZ+a6ca0p2N6pSblqNV1fGE5WEqDfPkuvpwu3aOczHJpl5MRFUnCzdJJHNDIZCVVnLC4GLrbYCFRmaDytxbt9HSDxdnErrPEPPGMz2vVsKidJRvzSS9tsRr82tMsTjNF4+BmhwdZZKvELjrD7jNBAxVNTUACwcxDsoMhESRQpn+qXp8OzJDlc9B9KuioHmU0182Deq7dra3apuvUNn/ZzpcqicCFm7Un2zXXebpUFQoynQ/1xKnNzrxaVnlNrb1iib6vm3ludN3mU7sQu+iAJDKz26OmxQQ9MniSUkGUGdVriVyb83+zP2uPiJCTSW4aMvRqRfSxQhbPC010V6HJMc6uzWoXUTHbsdnXpNhD00NBwjkxr5VncN88s7zr9m6WJwd6zc1vdsYbE70o0SRfsI/YBw4QB8B9xH1gipgCDxAPgEPEIfAQ8RCYIWbA7xG/Bx4hHgFHiCNgjpgDx4hj4ARxApwiToE/IP4ALBALYIlYAivECjhDnAGPEY+BrxBfAU8QT4CniKfA14iv5y9N8UceUGnCo/I//XZDmvRHGpI/14sS/XxxI15HXAfeRbwLvId4D/gF4hfA+4j3gQ8QHwAfIj4Efon4JfArxK+AXyN+DdxA3AA+QnwEfIz4GPgE8QnwKeJT4DPEZ8BNxE3gN4jfALcQt4DbiNvA54jPgS8QXwB3EHeA3yJ+C/wO8buyIc0Hxfyrwb47ON/ccLc2ds621p4dzz4tVqzvrB+sHy3Xemo9sw6tU6ttBdbv1h/Wn9ZfK/9UHlQeVh7dlN6/N7vmG+vWUfn2X0n0dzE=

266664100

377775

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

“cubic geometry has axis-aligned surface normals”Hsueh-Ti Derek Liu, Alec Jacobson, “Cubic Stylization”, SIGGRAPH Asia 2019

k k1 = | x | + | � |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

axis-aligned unit vector

non axis-aligned unit vectork

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

“surface normals of the output mesh”

L1-norm on Surface Normals

Earap + ∥n( )∥1?“as-rigid-as-possible”

“surface normals of the output mesh”

L1-norm on Surface Normals

Earap + ∥n( )∥1?Non-line

ar“as-rigid-as-possible”

“rotated surface normals of the input mesh”

Rotated Input Normals

Earap + ∥R × n( )∥1

“rotated surface normals of the input mesh”

Rotated Input Normals

Earap + ∥R × n( )∥1Linear

Different “Cubeness”

Orientation Dependent

Polygonal Boxes Stylization

Characterizing a shape using surface vertices Characterizing a shape using surface normals

Data-Driven SubdivisionHsueh-Ti Derek Liu, Vladimir G. Kim, Siddhartha Chaudhuri, Noam Aigerman, Alec Jacobson, “Neural Subdivision”, SIGGRAPH 2020

Subdivision Surfaces

Classic Subdivision[Loop 1987] ’

wi i

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i

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

Classic Subdivision[Loop 1987] ’

wi i

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

i

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

……

Smoothness prior

Kovacs et al. 2010

Neural Subdivisionsmoothness

priordata-driven prior

Hsueh-Ti Derek Liu, Vladimir G. Kim, Siddhartha Chaudhuri, Noam Aigerman, Alec Jacobson, “Neural Subdivision”, SIGGRAPH 2020

[Loop 1987]

i

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

Subdivision Network

How to train subdivision networks

Loss function

� (

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

)

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

,

AAACrnicdVFLSysxFE7Hx9X61qWbYBFcSJmRonZxQXTjogsFWwt1KJn0tA0mmSE5c69l6C9wq/jb/Ddmpi3YigcCh+9xcjhflEhh0fc/S97S8srqn7X18sbm1vbO7t5+y8ap4dDksYxNO2IWpNDQRIES2okBpiIJj9HzTc4//gNjRawfcJRAqNhAi77gDB10f9rdrfhVv+4H9XP6swmqflEVMq277l7p46kX81SBRi6ZtZ3ATzDMmEHBJYzLT6mFhPFnNoCOazVTYMOs2HRMjx3So/3YuKeRFuh3R8aUtSMVOaViOLSLXA7+xuUT7ZjOLSBFBG4xDWGm4T++FP7y8XdnYUuAjxfnRXY0Py0rvp1ILaBiQufmTkMMGKYG7N8HaIdZQ+j0hV6L2GWSqpkWh7l2SjZmay2cC/uXYSZ0kiJoPrlWP5UUY5pnR3vCAEc5cg3jRriDUz5khnF0CZddlLO86O9N66wa1Kr1+1rlSkxDXSOH5IickIBckCtyS+5Ik3AC5JW8kXfP91pe6HUnUq809RyQufKGXyf32Zs=

Training data

Network design

Machine Learning on Regular Grid

…

flaps of undirected edges [Hanocka et al. 2019]

fixed input dim. no ordering

flaps of half-edges

fixed input dim. canonical ordering

1

2

3

4

vertex rings

no fixed input dim. no ordering

Handling Irregular Mesh

rigid mo

tion

Rigid Motion Invariant

rigid mo

tion

rigid motioninvariant

Rigid Motion Invariant

Generalize when trained on single shape

training data

Generalize when trained on single shape

training data

Stylized Subdivision

Data-Driven prior

Smoothness prior Data-driven prior

Different Perspectives appearancenormal

data-driven priorPossibilities

3D Modeling for EveryoneHsueh-Ti Derek Liu

hsuehtil@cs.toronto.edu