Mapping & Warping shapes Geometry Acquisition

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!