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Mapping & Warping shapes Geometry Acquisition Zheng Hanlin 2011.07.05 -- Summer Seminar
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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)
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Bounded Biharmonic Weight for Real-Time Deformation Sig11
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Authors Alec Jacobson – Ph.D. Candidate
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Authors Ilya Baran – Postdoc. – Disney Research in Zurich
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Authors Olga Sorkine Assistant Professor ETH Zurich
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The Main Idea Shape deformation – Work freely with the most convenient combination of handle types bone cage points
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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
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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
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Algorithm Linear blending: Affine transformation of handle Hj New position Old position Handle size Weight function Bounded biharmonic weights
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Algorithm Bounded biharmonic weights:
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Algorithm Bounded biharmonic weights: – Properties: Smoothness Non-negativity Shape-awareness Partition of unity Locality and sparsity No local maxima
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Algorithm Bounded v.s. Unbounded
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Results & Comparison
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Results
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Performance
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Limitation The optimization is not fast enough – Bind-time This weights do NOT have the linear precision property
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Conclusion Unify all popular types of control armatures Intuitive design of real-time blending deformation
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Biharmonic Distance TOG11
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Authors Yaron LipmanRaif M. Rustamov Thomas Funkhouser
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The Main Idea A new distance measure based on the biharmonic differential operator
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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?
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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
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Algorithm Continuous cases: Biharmonic: Green’s function
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Algorithm Discrete cases Can be proved: Conformal discrete laplacian
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Results & Comparisons
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Applications Function interpolation on surfaces
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Applications Surface matching
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Performances
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Conclusions A novel surface distance – Has good properties
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Blended Intrinsic Maps Sig11
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Authors Vladimir G. Kim – Ph.D. Candidate – Princeton Univ. – He has Canadian and Kyrgyz citizenships.
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Authors Yaron Lipman Thomas Funkhouser
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The Main Idea Find the maps between two genus 0 surfaces
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Related Works Inter-surface mapping Finding sparse correspondences Iterative closest points Finding dense correspondences Surface embedding Exploring Mobius Transformations
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Algorithm Blended map Candidate maps Smooth blending weights
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Algorithm Generating maps (candidate conformal maps) Defining confidence weights – How much distorting is induced Finding consistency weights – Lower values for incorrect matches Blend map
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More Details Finding Consistency Weights – Objective Function – Similarity measure – Optimizing
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Results & Comparisons
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Results & Performances
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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)
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Photo-Inspired Model-Driven 3D Object Modeling Sig11
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The Main Idea Modeling – From single photo
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Workflow
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Algorithm Model-driven object analysis – Part-based retrieval Silhouette-guided structure-preserving deformation – Controller construction – Structure-preserving controller optimization
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Algorithm Model-driven object analysis – Part-based retrieval Silhouette-guided structure-preserving deformation – Controller construction – Structure-preserving controller optimization
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Results
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Limitations Limitations: – Candidate sets: new geometric variations but not new structure – Only considered reflectional symmetry
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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
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Style-Content Separation by Anisotropic Part Scales SigA10
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The Main Idea
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Workflow
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Results
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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
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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
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Authors Haim Avron – Postdoctoral Researcher @IBM T.J. Watson Research Center – Research field: Numerical linear algebra High performance computing
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Authors Chen Greif – Associate Professor – Scientific Computing Laboratory Department of Computer Science @ UBC – Research Interests: Iterative solvers Saddle-point linear systems Preconditioning techniques PageRank
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The Main Idea Reconstruction
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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.
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Related Works 3D Surface Reconstruction Sparse Signal Reconstruction continuous signalbasis functions
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Workflow Orientation Reconstruction Position Reconstruction
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More Details Orientation Reconstruction – Assume the surface can be approximated well by local planes
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More Details Position Reconstruction Second-Order Cone Problem(SOCP) Slover: CVX [Grant and Boyd 2009]
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Results
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Results & Comparisons
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Performance
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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
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GlobFit: Consistently Fitting Primitives by Discovering Global Relations Sig11
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Authors Yangyan Li ( 李扬彦 ) – Ph.D. Candidate – Visual Computing Center of SIAT – Chinese Academy of Sciences Xiaokun Wu ( 吴晓堃 )
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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.
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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
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Authors Daniel Cohen-Or Niloy J. Mitra
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The Main Idea Recover the global mutual relations
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Related Works Surface Reconstruction Feature Detection Reverse engineering …
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The Workflow
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Main Contributions A global approach to constrain and optimize the local RANSAC based primitives
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More Details Greedy v.s. Global
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More Details re-RANSAC
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Evaluation Synthetic datasets – Compare face normals and distances Scanned datasets
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Results
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Limitations Noise will make the results bad
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Conclusion A method for incorporating global relations for man-made objects.
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Data-Driven Suggestions for Creativity Support in 3D Modeling
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Authors Siddhartha Chaudhuri – Ph.D. Student – CS @ Stanford Univ. – Research area: Richer tools for 3D content creation
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Authors Vladlen Koltun – Assistant Prof. – CS @ Stanford Univ. – Research area: Computer graphics Interactive techniques
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Thanks!
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