Mapping & Warping shapesGeometry Acquisition
Zheng Hanlin2011.07.05
-- 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
Authors
• Alec Jacobson– Ph.D. Candidate
Authors
• Ilya Baran– Postdoc.– Disney Research in Zurich
Authors
Olga SorkineAssistant ProfessorETH Zurich
The Main Idea
• Shape deformation– Work freely with the most convenient
combination of handle types
bone
cage
points
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
Free-form Skeleton-based
Generalized barycentric coordinate
Advantage Nature control for rigid limbs
Provide smooth weights
automatically
Disadvantage Require regular structure
Less convenient for flexible regions
Need (nearly) closed cages
Algorithm
• Linear blending:
Affine transformation of handle HjNew position
Old position
Handle size
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– Insensitive to noise– Small topology changes– Parameter free– Practical to compute on a discrete mesh– …
Does there exist a measure cover all these properties?
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
Algorithm
• Discrete cases
• Can be proved:
Conformal discrete laplacian
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
Authors
• Vladimir G. Kim– Ph.D. Candidate– Princeton Univ.
– He has Canadian and Kyrgyz citizenships.
Authors
• Yaron Lipman • 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
Algorithm
• Blended map
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 AvronTel-Aviv
Univ.
Andrei SharfUC-Davis
Chen GreifUniv. of British
Columbia
Daniel Cohen-OrTel-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
GlobFit: Consistently Fitting Primitives by Discovering Global Relations
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
Authors
• Daniel Cohen-Or • 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
More Details
• re-RANSAC
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.
Data-Driven Suggestions for Creativity Support in 3D Modeling
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
Thanks!