Mapping & Warping shapes
Geometry Acquisition
Zheng Hanlin
2011.07.05
-- Summer Seminar

Papers
• Bounded Biharmonic Weight for Real-Time Deformation (SIG11)
• Biharmonic Distance (TOG11)
• Blended Intrinsic Maps (SIG11)
• Photo-Inspired Model-Driven 3D Object Modeling (SIG11)
• Style-Content Separation by Anisotropic Part Scales (SIGA10)
• L1-Sparse Reconstruction of Sharp Point Set Surfaces (TOG)
• GlobFit: Consistently Fitting Primitives by Discovering Global Relations
(SIG11)
• Data-Driven Suggestions for Creativity Support in 3D Modeling (SIGA10)

Bounded Biharmonic Weight for
Real-Time Deformation
Sig11

• Alec Jacobson
– Ph.D. Candidate
Authors

Authors
• Ilya Baran
– Postdoc.
– Disney Research in Zurich

Authors
Olga Sorkine
Assistant Professor
ETH Zurich

The Main Idea
• Shape deformation
– Work freely with the most convenient combination of handle types bone points cage

Motivation(Video)
• Typical flow for deformation
– Bind the object to handles ( bind time )
– Manipulate the handles ( pose time )
• Different handle types have different advantages and disadvantages
• Design the weights for a linear blending scheme
• Real-time responce

Motivations
Deformation
Type
Advantage
Free-form
Disadvantage Require regular structure
Skeletonbased
Nature control for rigid limbs
Less convenient for flexible regions
Generalized barycentric coordinate
Provide smooth weights automatically
Need (nearly) closed cages

• Linear blending:
Algorithm
Handle size
New position
Old position
Affine transformation of handle Hj
Weight function
Bounded biharmonic weights

Algorithm
• Bounded biharmonic weights:

Algorithm
• Bounded biharmonic weights:
– Properties:
• Smoothness
• Non-negativity
• Shape-awareness
• Partition of unity
• Locality and sparsity
• No local maxima

Algorithm
• Bounded v.s. Unbounded

Results & Comparison

Results

Results

Results

Results

Performance

Limitation
• The optimization is not fast enough
– Bind-time
• This weights do NOT have the linear precision property

Conclusion
• Unify all popular types of control armatures
• Intuitive design of real-time blending deformation

Biharmonic Distance
TOG11

Authors
Yaron Lipman Raif M. Rustamov Thomas Funkhouser

The Main Idea
• A new distance measure based on the biharmonic differential operator

Motivation
• The most important properties for a distance
– metric
– smooth
– Locally isotropic
– Globally shape-aware
– Isometry invariant
Does there exist a measure cover all these properties?
– Insensitive to noise
– Small topology changes
– Parameter free
– Practical to compute on a discrete mesh
– …

Related works
• Geodesic distance
– Not smooth, insensitive to topology
• Diffusion distance
– Not locally isotropic
– Not global shape-aware
– Depending on parameter
• Commute-time distance (Graph)
– Cannot define on surfaces
– Depending on the conformal structure

Algorithm
• Continuous cases:
• Biharmonic:
Green’s function

• Discrete cases
Algorithm
Conformal discrete laplacian
• Can be proved:

Results & Comparisons

Results & Comparisons

Applications
• Function interpolation on surfaces

Applications
• Surface matching

Performances

Conclusions
• A novel surface distance
– Has good properties

Blended Intrinsic Maps
Sig11

• Vladimir G. Kim
– Ph.D. Candidate
– Princeton Univ.
Authors
– He has Canadian and Kyrgyz citizenships.

• Yaron Lipman
Authors
• Thomas Funkhouser

The Main Idea
• Find the maps between two genus 0 surfaces

Related Works
• Inter-surface mapping
• Finding sparse correspondences
• Iterative closest points
• Finding dense correspondences
• Surface embedding
• Exploring Mobius Transformations

• Blended map
Algorithm
Candidate maps
Smooth blending weights

Algorithm
• Generating maps (candidate conformal maps)
• Defining confidence weights
– How much distorting is induced
• Finding consistency weights
– Lower values for incorrect matches
• Blend map

More Details
• Finding Consistency Weights
– Objective Function
– Similarity measure
– Optimizing

Results & Comparisons

Results & Comparisons

Results & Performances

Results & Performances

Limitation & Conclusion
• Limitations:
– Not guaranteed to work in case of partial near-isometric matching
– Only for genus zero surfaces now
• An automatic method for finding a map between surfaces (including non-isometric surfaces)

Photo-Inspired Model-Driven 3D
Object Modeling
Sig11

The Main Idea
• Modeling
– From single photo

Workflow

Algorithm
• Model-driven object analysis
– Part-based retrieval
• Silhouette-guided structure-preserving deformation
– Controller construction
– Structure-preserving controller optimization

Algorithm
• Model-driven object analysis
– Part-based retrieval
• Silhouette-guided structure-preserving deformation
– Controller construction
– Structure-preserving controller optimization

Results

Results

Limitations
• Limitations:
– Candidate sets: new geometric variations but not new structure
– Only considered reflectional symmetry

Future works
• More effective means of structure modification and editing fine-detailed features
• Using model-driven approach to allow more reusability
• More means to inspire the user in creative 3D modeling

Style-Content Separation by
Anisotropic Part Scales
SigA10

The Main Idea

Workflow

Results

Results

Limitations & Conclusions
• Limitation
– Input set should be in the same semantic class
– The initial segmentation should be sufficiently meaningful
– The synthesis method limits itself to creating new variations of an existing example model
• Analyze a set of 3D objects belonging to the same class while exhibiting significant shape variations, particularly in part scale

L1-Sparse Reconstruction of
Sharp Point Set Surfaces
Haim Avron
Tel-Aviv Univ.
Andrei Sharf
UC-Davis
Chen Greif
Univ. of British
Columbia
Daniel Cohen-Or
Tel-Aviv Univ.
TOG11

Authors
• Haim Avron
– Postdoctoral Researcher
@IBM T.J. Watson
Research Center
– Research field:
• Numerical linear algebra
• High performance computing

Authors
• Chen Greif
– Associate Professor
– Scientific Computing Laboratory
Department of Computer Science @
UBC
– Research Interests:
• Iterative solvers
• Saddle-point linear systems
• Preconditioning techniques
• PageRank

The Main Idea
• Reconstruction

Motivation
• L1-sparsity paradigm avoid the pitfalls such as least squares, namely smoothed out error
– L2 norm tends to severely penalize outliers and propagate the residual in the objective function uniformly
• Sharp features
– Outliers are not excessively penalized
– Objective function is expected to be more concentrated near the sharp features.

Related Works
• 3D Surface Reconstruction
• Sparse Signal Reconstruction continuous signal basis functions

Workflow
• Orientation Reconstruction
• Position Reconstruction

More Details
• Orientation Reconstruction
– Assume the surface can be approximated well by local planes

More Details
• Position Reconstruction
Second-Order Cone Problem(SOCP)
Slover: CVX [Grant and Boyd 2009]

Results

Results

Results & Comparisons

Results & Comparisons

Performance

Limitation & Conclusion
• Limitations:
– Difficult to correctly project points lying exactly on edge singularities.
– High computational cost
• A l1-sparse approach for reconstruction of point set surface with sharp features

Sig11

Authors
• Yangyan Li ( 李扬彦 )
– Ph.D. Candidate
– Visual Computing Center of SIAT
– Chinese Academy of Sciences
• Xiaokun Wu ( 吴晓堃 )

Authors
• Yiorgos Chrysanthou
– Associate Professor
– Univ. of Syprus
– The head of the Graphics Lab @ the University of Cyprus
– His current research interests:
• real-time rendering
• visibility, crowd rendering and simulation
• virtual and augmented reality and applications to cultural heritage.

Authors
• Andrei Sharf
– Computer Science Department
– Ben-Gurion Univ.
– Research interests:
• Geometry processing and 3D modeling
• Interactive techniques
• Topology, parallel data structures on the GPU
• Large scale 3D urban modeling

• Daniel Cohen-Or
Authors
• Niloy J. Mitra

The Main Idea
• Recover the global mutual relations

Related Works
• Surface Reconstruction
• Feature Detection
• Reverse engineering
• …

The Workflow

Main Contributions
• A global approach to constrain and optimize the local RANSAC based primitives

More Details
• Greedy v.s. Global

• re-RANSAC
More Details

Evaluation
• Synthetic datasets
– Compare face normals and distances
• Scanned datasets

Results

Results

Results

Limitations
• Noise will make the results bad

Conclusion
• A method for incorporating global relations for man-made objects.

Authors
• Siddhartha Chaudhuri
– Ph.D. Student
– CS @ Stanford Univ.
– Research area:
• Richer tools for 3D content creation

Authors
• Vladlen Koltun
– Assistant Prof.
– CS @ Stanford Univ.
– Research area:
• Computer graphics
• Interactive techniques