Mapping & Warping shapes Geometry Acquisition Zheng Hanlin 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 Sorkine Assistant Professor ETH 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-formSkeleton- 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 Hj New 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

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 LipmanRaif 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

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 & 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

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

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 T.J. Watson Research Center – Research field: Numerical linear algebra High performance computing

Authors Chen Greif – Associate Professor – Scientific Computing Laboratory Department of Computer 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 signalbasis 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 & 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 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

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 – Stanford Univ. – Research area: Richer tools for 3D content creation

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

Thanks!