-
3D Modeling for EveryoneHsueh-Ti Derek Liu
University of Toronto
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3D modeling
Spectral geometry
SIGGRAPH Asia 2018 ICLR 2019 SIGGRAPH Asia 2019 SIGGRAPH 2020
SGP 2017 SIGGRAPH 2019 Eurographics 2019 SIGGRAPH Asia 2020
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Image Editing
-
3D scanning
medium.com
Macworld.com
OmniVirt.com
3D display
Advances in 3D Technology
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3D Modeling
-
3D Modeling is Hard
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2D Analogue
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Make 3D modeling available for everyone
-
3D modeling is a long-standing problem
blender cloud - springVaxman et al. 2018
wikimedia autodesk
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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
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Geometric filtering 3D Stylization Data-driven subdivision
appearancenormal
prior
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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]
?
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Appearance-driven Editing
Hsueh-Ti Derek Liu, Michael Tao, Alec Jacobson, “Paparazzi: Surface Editing by way of Multi-View Image Processing ”, SIGGRAPH Asia 2018
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Appearance-driven EditingV
R(V)
rendering
differentiable renderer ∂R∂V
image
filteri
ng
R′ (V)
-
Rendering Means to an End
… ?
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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
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Rendering as a tool for visualization Rendering as a tool for 3D modeling
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3D StylizationHsueh-Ti Derek Liu, Alec Jacobson, “Cubic Stylization”, SIGGRAPH Asia 2019
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Stylization3D 2D
non-photorealistic rendering [Hertzmann, Zorin 2000]
image stylization [Gatys et al. 2016]
2D 2D 3D 3D
3D stylization
?
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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
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How to characterize a cube?
-
How to characterize a cube? 266664001
377775
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266664010
377775
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
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
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[Loop 1987]
i
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
Subdivision Network
-
How to train subdivision networks
Loss function
� (
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
)
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
,
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
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