abstraction of man-made shapes ravish mehra 1,2, qingnan zhou 1, jeremy long 4, alla sheffer 1, amy...
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Abstraction of Man-Made Shapes
Ravish Mehra1,2, Qingnan Zhou1, Jeremy Long4, Alla Sheffer1, Amy Gooch4, Niloy J. Mitra2,3
1Univ. of British Columbia 2 IIT Delhi 3 KAUST 4Univ. of Victoria
Abstraction of Man-Made ShapesAbstraction of Man-Made ShapesAbstraction of Man-Made ShapesAbstraction of Man-Made Shapes
Abstraction of Man-Made Shapes
Human Perception
Abstraction of Man-Made Shapes
Observation
© Succession Picasso
Abstraction of Man-Made Shapes
Observation
o Man-Made objects dominated by flat/smooth faces.o Sharp creases define the shape.
Cole et al. 2008
Abstraction of Man-Made Shapes
Abstract Representation
o Abstraction algorithm - curves as building blocks o Extract sparse network of curves + normalso Abstract shape - union of smooth patches
Abstraction of Man-Made Shapes
o Curve based NPR• Suggestive contours [DeCarlo et al. 2003]• Apparent ridges [Judd et al. 2007]
o Curve based surface modeling• Wires [Singh et al. 1998]• Fiber Mesh [Nealen et al. 2007]• iWires [Gal et al. 2009]
o Vector representation• Diffusion Curves [Orzan et al. 2008]
Related Works
Abstraction of Man-Made Shapes
Abstraction Pipeline
1. Original model 2. Envelope 3. Curve Network 4. Reconstructionresult
ReconstructionVectorization Envelopegeneration
Abstraction of Man-Made Shapes
Challenge
o Input contains multiple self-intersecting components.o Can even be a polygon soup.
Abstraction of Man-Made Shapes
Envelope Generation
o Envelope: A tight closed manifold approximation of the original surface.
Abstraction of Man-Made Shapes
Envelope Generation: Initialization
o Initial envelope: A manifold surface loosely follow input’s geometry.
Abstraction of Man-Made Shapes
Envelope Generation: Iterative Fitting
Preserves local detailsPulls each vertex towards its original position
Pulls each vertex towards its mapped position
Abstraction of Man-Made Shapes
Envelope Generation
Abstraction of Man-Made Shapes
Vectorization
o Purpose: extract a vector representation o Encodes shape-defining features; concise & enables
reconstruction
Envelope Vector Representation
Abstraction of Man-Made Shapes
Vectorization as Mesh Segmentation
o Man-made shapes - union of smooth patches.
o Vectorization as mesh segmentation problem.• Segmentation – collection of charts• Each chart should be smooth
o Vector representation = boundary of segmentation + associated normals
Abstraction of Man-Made Shapes
Initial Segmentation
o Variational Shape Approximation [Cohen-Steiner et al. 2004]. • Speed and simplicity• Satisfies smoothness criteria
o Topological Simplification• Merging small charts• Straightening boundaries
[ Julius et al. 2005 ]
Abstraction of Man-Made Shapes
Iterative Improvement
o Optimization for each chart• Smooth surface
smoothly varying normals
• Approximate the original shape
• Smooth boundary helps subsequent
regularization phase
Abstraction of Man-Made Shapes
Iterative Improvement
o Normal solve • trade-off between smoothness and original normals
o Per-triangle solve• vertex positions satisfying desired normals• stay close to original positions
o Global assembly• reconcile different per-triangle vertex positions
Abstraction of Man-Made Shapes
Iterative Improvement
Abstraction of Man-Made Shapes
Regularization and Simplification
o Regularity• local : linear, circular, planar • global : parallel, orthogonal,
symmetric
o Hierarchical simplification• higher levels of abstraction• simplify network• regularize again
Abstraction of Man-Made Shapes
Curve Extraction
Vector representation of 3D Shapes
Abstraction of Man-Made Shapes
Reconstruction
o Reconstruct the abstract model• Embed each boundary loop
into a plane[Kruskal and Wish 1978]
• Triangulate the planar loops [Shewchuk 1996]
• Deform the planar patches using curve’s position and normal as constraints[Popa et al. 2006]
Abstraction of Man-Made Shapes
Results
Abstraction of Man-Made Shapes
Eiffel tower
15.6K triangles 2417 components 85 curves140 curves
Abstraction of Man-Made Shapes
Empire state
16K triangles 17 components 38 curves152 curves
Abstraction of Man-Made Shapes
Arc de Triomphe
13K triangles 8 components 139 curves193 curves
Abstraction of Man-Made Shapes
Dome of the Rock
3.8K triangles 2 components 26 curves145 curves
Abstraction of Man-Made Shapes
Limitations and Future Work
o Thin long features that affect topology
o Not well-known objects
Abstraction of Man-Made Shapes
Summary
o Algorithm for generating abstractions of 3D man-made models.
o Simple yet robust mechanism for approximating polygon soup by a manifold surface.
o Novel vector-based representation of 3D geometry.
Abstraction of Man-Made Shapes
Video
Abstraction of Man-Made Shapes
Acknowledgements
Sponsored by
Adobe Inc.MITACS NCEMicrosoft Outstanding YoungFaculty FellowshipNSERC Discover Program
Thanks
Benjamin CecchettoDerek BradleyKaran SinghTiberiu PopaVladislav KraevoyXi ChenAnonymous reviewers
Abstraction of Man-Made Shapes