ICVSS 2014

3D Reconstruction with Priors
Yasutaka Furukawa
Washington University in St. Louis
What are priors?
Outline
• Why priors?
• Prior enforcement through MRF
• Prior enforcement through primitives
• Prior enforcement through shortest-path
Brief Introduction of
Multi-View Stereo (MVS)
Camera pose 3d reconstruction
Input: Calibrated
photographs
Output: 3D geometry
MVS Principle
Feature matching
1995 1999 1998 1998
2004 2005 2005 2007
Computer Vision: Algorithms and Applications [Richard Szeliski]
A decade ago...
A Theory of Space by Space Carving

[ Kutulakos and Seitz, 1999 ]
Reconstructions w/ and w/o color
Volumetric graph cuts

by Vogiatzis, Torr, and Cipolla
CVPR 2005
1. This is called Haniwa.
2. This is Roberto Cipolla’s Haniwa.
This will be a final quiz!
Results
[ CVPR 2007 ]
Visual Effects
Digital mapping
Apple Maps
ComputerVision in Industry
• Amazon	

• Apple	

• Facebook	

• Google	

• Microsoft	

• Nokia
ComputerVision in Industry
• Amazon	

• Apple	

• Facebook	

• Google	

• Microsoft	

• Nokia
Mountain View
Seattle
Zurich
NYC
LA
…
ComputerVision in Industry
• Amazon	

• Apple	

• Facebook	

• Google	

• Microsoft	

• Nokia
Mountain View
Seattle
Zurich
NYC
LA
…
Google Seattle - 3DVision Team
• Bundling streetview data (by Sameer Agarwal)	

• Photo Tours (by the team) 	

• Picasa face movie (by Ira Kemelmacher-
Shlizerman and Rahul Garg)	

• Lens Blur (by Carlos Hernandez)
Steve Seitz, Sameer Agarwal, Carlos Hernandez,
David Gallup, Changchang Wu, Li Zhang
Face Movie

[Ira Kemelmacher-Shlizerman, Eli Shechtman,

Rahul Garg, Steve Seitz]
Lens Blur

[Carlos Hernandez]
Lens Blur

[Carlos Hernandez]
Why am I here?
What if no texture?
Noise suppression
[reatedigitalmotion.com]
Compression
[bitewallpapers.com]
Why priors?
• Fails in some important cases
• Noise suppression
• Compression
Why priors?
• Fails in some important cases
• Noise suppression
• Compression
• Uncanny valley for 3D reconstruction
Uncanny valley
[www.cubo.cc/creepygirl]
Uncanny valley for 3D
reconstruction
More accurate, but	

looks worse
Less accurate, but	

looks better
People like everything	

about this picture
3D photography hates everything

about this picture
Uncanny Valley for 3D
Reconstruction
Ten Things You Should Know About

Large Scale 3D Reconstruction

(3DV 2013)

Martin Byröd
Apple Maps
Why priors?
• Fails in some important cases
• Noise suppression
• Compression
• Uncanny valley for 3D reconstruction
Outline
• Why priors?
• Prior enforcement through MRF
• Prior enforcement through primitives
• Prior enforcement through shortest-path
Prior enforcement through MRF
Piecewise planar enforcement
through MRF
Motivations
[Furukawa	
  and	
  Ponce,	
  2007]
Enforce Prior in MVS
• Manhattan-world assumption	

• Planarity	

• Orthogonality
8.0
8.2
8.5
8.9
9.3
camera	

center image	

screen
Depthmap Problem
8.0
8.2
8.5
8.9
9.3
camera	

center image	

screen
Depthmap Problem
Discretized depth values

{ 0.1, 0.2, …, 8.0, 8.1, … 9.8, 9.9}
Standard Depthmap

Markov Random Field (MRF)
A Comparative Study of Energy Minimization Methods for Markov Random Fields with
Smoothness-Based Priors [Szeliski et al., PAMI 2008]
A Comparative Study of Energy Minimization Methods for Markov Random Fields with
Smoothness-Based Priors [Szeliski et al., PAMI 2008]
Markov Random Field (MRF)
Markov Random Field (MRF)
Markov Random Field (MRF)
7 7 6 0 6 7
p
q
Markov Random Field (MRF)
p
q
Markov Random Field (MRF)
0
p
q
Markov Random Field (MRF)
1
p
q
Markov Random Field (MRF)
2
p
q
Markov Random Field (MRF)
4
p
q
Markov Random Field (MRF)
0
p
q
Markov Random Field (MRF)
Markov Random Field (MRF)
Graph-cuts (alpha-expansion)

gives you very good solutions
Prefers front-parallel surfaces
Markov Random Field (MRF)
We want piecewise planar
Piecewise planarity from MRF
1. Advanced MRF and optimization
• Global Stereo Reconstruction under Second Order Smoothness Priors [Woodford et al., CVPR
2008] Best Paper Award
2. Integrate with top-down (primitive) approach
• Manhattan World Stereo [Furukawa et al., CVPR 2009]
• Piecewise Planar Stereo for Image-based rendering [Sinha et al., ICCV 2009]
• Fusion of Feature- and Area-Based Information for Urban Buildings Modeling from Aerial
Imagery [Zebedin et al., ECCV 2008]
• Piecewise Planar and Non-Planar Stereo for urban Scene Reconstruction [Gallup et al., CVPR
2010]
Advanced MRF for
Depthmap Estimation
Global Stereo Reconstruction under Second Order Smoothness Priors

[Woodford et al., CVPR 2008] Best Paper Award
Reference image
Ground truth
Standard MRF
Standard MRF
p q
Standard MRF
p
q
Standard MRF
p q
Standard MRF
p q
MRF with a triple
clique
p q r
Standard MRF
p q
MRF with a triple
clique
p q r
Standard MRF
p q
MRF with a triple
clique
p q r
0 = |3 + 5 - 2 x 4|
Standard MRF
p q
MRF with a triple
clique
p q r
0 = |3 + 5 - 2 x 4|
Standard MRF
p q
MRF with a triple
clique
p
q
r
Standard MRF
p q
MRF with a triple
clique
p
q
r
MRF with a triple clique
Optimization becomes a
challenge
Standard MRF
(submodular)
MRF with a triple clique
(non-submodular)
• Graph-cuts

(alpha-expansion)
• Belief propagation

(TRW)
• QPBO
• Belief propagation

(TRW?)
Optimization becomes a
challenge
Standard MRF
(submodular)
MRF with a triple clique
(non-submodular)
• Graph-cuts

(alpha-expansion)
• Belief propagation

(TRW)
• QPBO
• Belief propagation

(TRW?)
Fusion moves…
Experimental results
Reference image Neighboring image
Output depthmap
[Woodford et al.]
Comparative experiment
Reference image Ground truth
Standard MRF MRF with a triple clique
[Woodford et al.]
How to enforce piecewise planar
1. Advanced MRF and optimization
• Global Stereo Reconstruction under Second Order Smoothness Priors [Woodford et al., CVPR
2008] Best Paper Award
2. Integrate with top-down (primitive) approach
• Manhattan World Stereo [Furukawa et al., CVPR 2009]
• Piecewise Planar Stereo for Image-based rendering [Sinha et al., ICCV 2009]
• Fusion of Feature- and Area-Based Information for Urban Buildings Modeling from Aerial
Imagery [Zebedin et al., ECCV 2008]
• Piecewise Planar and Non-Planar Stereo for urban Scene Reconstruction [Gallup et al., CVPR
2010]
Standard Depthmap
8.0
8.2
8.5
8.9
9.3
camera	

center image	

screen
Planemap
[Furukawa	
  and	
  Ponce,	
  2007]
1. Extract Manhattan

directions
2. Extract planes
Planemap
Possible planes a
b
c
d
e f
g h
1. Extract Manhattan

directions
2. Extract planes
Planemap
Possible plane ids a
b
c
d
e f
g h
e
e
e
e
e
1. Extract Manhattan

directions
2. Extract planes
Depthmap to Planemap
Depthmap ( )
Planemap ( )
Planemap MRF
Planemap MRF
p
Planemap MRF
p
7 6 0 6 7
Planemap MRF
p
10 3 10
Planemap MRF
0
p
q
Planemap MRF
2
p
q
Planemap MRF
3
p
q
Planemap MRF
8
p
q
Comparison
Standard	
  method Manha9an	
  Planemap
Kitchen	
  -­‐	
  22	
  images
house	
  -­‐	
  148	
  images
gallery	
  -­‐	
  492	
  images
Reconstruction Results
How to enforce piecewise planar
1. Advanced MRF and optimization
• Global Stereo Reconstruction under Second Order Smoothness Priors [Woodford et al., CVPR
2008] Best Paper Award
2. Integrate with top-down (primitive) approach
• Manhattan World Stereo [Furukawa et al., CVPR 2009]
• Piecewise Planar Stereo for Image-based rendering [Sinha et al., ICCV 2009]
• Fusion of Feature- and Area-Based Information for Urban Buildings Modeling from Aerial
Imagery [Zebedin et al., ECCV 2008]
• Piecewise Planar and Non-Planar Stereo for urban Scene Reconstruction [Gallup et al., CVPR
2010]
20 seconds break
How to enforce piecewise planar
1. Advanced MRF and optimization
• Global Stereo Reconstruction under Second Order Smoothness Priors [Woodford et al., CVPR
2008] Best Paper Award
2. Integrate with top-down (primitive) approach
• Manhattan World Stereo [Furukawa et al., CVPR 2009]
• Piecewise Planar Stereo for Image-based rendering [Sinha et al., ICCV 2009]
• Fusion of Feature- and Area-Based Information for Urban Buildings Modeling from Aerial
Imagery [Zebedin et al., ECCV 2008]
• Piecewise Planar and Non-Planar Stereo for urban Scene Reconstruction [Gallup et al., CVPR
2010]
Relaxing Mahnattan
Piecewise Planar Stereo for Image-based rendering [Sinha et al., ICCV 2009]
• Use sparse lines + sparse points to detect planes
• MRF + Graph-cuts
Relaxing Manhattan
[Sinha et al.]
Relaxing Manhattan
[Sinha et al.]
Enable Curved Surfaces
• Building reconstruction from a top down view
Fusion of Feature- and Area-Based Information for Urban Buildings Modeling from Aerial
Imagery [Zebedin et al., ECCV 2008]
Enable Curved Surfaces[Zebedin et al.]
How to enforce piecewise planar
1. Advanced MRF and optimization
• Global Stereo Reconstruction under Second Order Smoothness Priors [Woodford et al., CVPR
2008] Best Paper Award
2. Integrate with top-down (primitive) approach
• Manhattan World Stereo [Furukawa et al., CVPR 2009]
• Piecewise Planar Stereo for Image-based rendering [Sinha et al., ICCV 2009]
• Fusion of Feature- and Area-Based Information for Urban Buildings Modeling from Aerial
Imagery [Zebedin et al., ECCV 2008]
• Piecewise Planar and Non-Planar Stereo for urban Scene Reconstruction [Gallup et al., CVPR
2010]
Piecewise	
  Planar	
  and	
  Non-­‐Planar	
  Stereo	
  
for	
  Urban	
  Scene	
  Reconstruction
David	
  Gallup	
  	
  
Jan-­‐Michael	
  Frahm	
  
Marc	
  Pollefeys	
  
University	
  of	
  North	
  Carolina	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  ETH	
  	
  Zurich
3D	
  Reconstruction	
  from	
  Video
Street-­‐Side	
  Video Real-­‐Time	
  Stereo
106
Idea
3D	
  ReconstructionVideo	
  Frames
107
Enforce planarity where it looks like a building
First	
  step:	
  Planar	
  and	
  Non-­‐Planar	
  Stereo
108
Video
Real-­‐Time	
  Stereo Plane	
  Detection	
   Planemap	
  (w/	
  non-­‐planar))
Labels	
  =	
  
planes non-­‐plane discard
Second	
  step:	
  Appearance	
  Prior
109
Video	
  Frames
Classification
• divide	
  image	
  into	
  regular	
  grid	
  
• RGB,	
  HSV,	
  hue	
  histogram,	
  edge	
  orientation	
  histogram	
  
• 5000	
  human-­‐labeled	
  examples	
  (5	
  images)	
  
• k-­‐nearest-­‐neighbor	
  classifier
non-­‐planar planar
110
Hoiem	
  et	
  al.	
  2005,	
  
Xiao	
  et	
  al.	
  2009
Algorithm
Video
Real-­‐Time	
  Stereo
Planar/Non-­‐Planar	
  
Classification
Plane	
  Detection	
  
Planar	
  and	
  Non-­‐Planar	
  
MRF
111
non-­‐planar planar
Effect	
  of	
  Classifier
112
Without	
  image	
  prior With	
  image	
  prior
non-­‐planar planar
Results
113
Video	
  Frame Plane	
  Detection
Planar	
  Classification Reconstruction
non-­‐planar
planar
Results
114
Summary: Shape priors

in Depthmap MVS
MRF with a triple term
Manhattan planemap Planemap
Planemap w/ curved surfaces
Mix of planemap
and depthmap
Outline
• Why priors?
• Prior enforcement through MRF
• Prior enforcement through primitives
• Prior enforcement through shortest-path
Priors through primitives for
large-scale indoor modeling



“Reconstructing the World’s Museums” [Xiao and Furukawa, 2012]
(Best Student Paper Award)
Technical Contributions
• Architectural shape priors through primitives
• Single consistent 3D model
Technical Contributions
• Architectural shape priors through primitives
• Single consistent 3D model
Inverse Constructive Solid Geometry (CSG)
Technical Contributions
Inverse Constructive Solid Geometry (CSG)
• Architectural shape priors through primitives!
• Single consistent 3D model (real merging)
+
Technical Contributions
Inverse Constructive Solid Geometry (CSG)
• Architectural shape priors through primitives
• Single consistent 3D model (real merging)
+
+
-
+
+
-
CGAL
• From CSG to a mesh
Algorithm
Cut into Slices
gravity
side view
Cut into Slices
point count
Cut into Slices
2D CSG Reconstruction
Bottom-up approach
point
2D line
2D rectangle
2D CSG
2D CSG Reconstruction
point à line
2D CSG Reconstruction
point à line
line à rectangle
From 4 line segments
2D CSG Reconstruction
point à line
line à rectangle
rectangle à 2D CSG
2D CSG Reconstruction
Explain the data	

• Laser points 	

• Free space	

!
2D CSG Reconstruction
Repeat in each slice
3D CSG Reconstruction
Bottom-up approach
point
2D line
2D rectangle
2D CSG
Bottom-up approach
point
2D line
2D rectangle
2D CSG
Bottom-up approach
point
2D line
2D rectangle
point
2D line
2D rectangle
3D rectangle
3D CSG
2D CSG to 3D CSG
2D CSG
Rectangle	

primitive
2D CSG to 3D CSG
2D CSG
Rectangle	

primitive
2D CSG to 3D CSG
1. Generate primitives (cuboids)
2D CSG
Rectangle	

primitive
2D CSG to 3D CSG
3D CSG Reconstruction
1. Generate primitives (cuboids)
2. Build a 3D CSG
Algorithm on Run
Last Step
1. Remove Ceiling	

2. Texture Mapping
Challenging Navigation
Frick Collection Gallery (NewYork City)
Goal
Start
Statistics
# of sub problems
Ground Ground+Aerial
Outdoor
Indoor
Ground vs. Aerial à Ground+Aerial
Google Streetview Google MapsGL
Furukawa et al.
Aerial
Google/Bing/NASA …
This paper This paper
So, museum recons.
from
very high-end devices
“museums”
“restaurants”
“grocery stores”
{# of museums} <<
{# of restaurants} +	

{# of grocery stores} +

{# of clinic} + ...
Millions of small/medium-
scale businesses
• Image-based for scalable deployment

(especially for emerging markets)	

• Compact model

(for browser on low-end PCs)
Millions of small/medium-
scale businesses
• Image-based for scalable deployment

(especially for emerging markets)	

• Compact mesh model

(for browser on low-end PCs)
[ Cabral and Furukawa, 2014 ]
Outline
• Why priors?
• Prior enforcement through MRF
• Prior enforcement through primitives
• Prior enforcement through shortest-path
2D outline reconstruction
2D outline reconstruction
Why priors?
• Only reconstruct planar outline
• Texture mapping looks better
• Challenge is how to IGNORE clutter
Pipeline (standard)
1. Panorama images 2. MVS points
3. Point evidence 4. Free-space evidence
5. 2D room outline 6. 3D model
2D room outline reconstruction
3. Point evidence 4. Free-space evidence
Outline should pass
through this point
Threshold
2D room outline reconstruction
4. Free-space evidence3. Point evidence
5. Shortest path formulation
Standard way
Standard way
Standard way
2D room outline reconstruction
5. Shortest path formulation
2D room outline reconstruction
5. Shortest path formulation
2D room outline reconstruction
5. Shortest path formulation
Model complexity penalty

added to each edge
2D room outline reconstruction
5. Shortest path formulation
2D room outline reconstruction
Standard
Ours
Features
• Regularize on {# of line segments}
• Piecewise planarity enforcement
• With Dynamic Programming,

exactly control the number of vertices
13 vertices
Exact complexity
control
Exact complexity
control
15 vertices
Exact complexity
control
17 vertices
Exact complexity
control
19 vertices
Exact complexity
control
23 vertices
Exact complexity
control
27 vertices
Exact complexity control
13 verts. 15 verts. 17 verts.
19 verts. 23 verts.
. . . . . .
MVS points
Volumetric
graph-cuts
Ours
Summary
• Why priors?
• Prior enforcement through MRF
• Prior enforcement through primitives
• Prior enforcement through shortest-path
Questions
A. Who owns the Haniwa in the volumetric graph-cuts paper?
1. Yasutaka Furukawa.
2. Roberto Cipolla.
3. British Museum.
B. What is Uncanny valley for 3D reconstruction?
1. As the number of authors in a paper goes up, the model quality goes down.
2. As the face realism goes up, the model looks creepier.
3. As the model accuracy goes up, the rendering quality goes down.
C. How can one enforce piecewise planarity with a standard MRF formulation easily?
1. Use super-pixel segmentation.
2. Use primitive detection.
3. Use object recognition.
Lunch Time!

Lecture 02 yasutaka furukawa - 3 d reconstruction with priors