Geometric modeling in shape space

Authors:
Martin Kilian;Niloy J. Mitra;Helmut Pottmann
Affiliations:
Vienna University of Technology;Vienna University of Technology;Vienna University of Technology
Venue:
ACM SIGGRAPH 2007 papers
Year:
2007

Citing 28
Cited 47

On the limited memory BFGS method for large scale optimization

Mathematical Programming: Series A and B
Progressive meshes

SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics

Proceedings of the 24th annual conference on Computer graphics and interactive techniques
As-rigid-as-possible shape interpolation

Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Shape by example

I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730

Journal of Computational Physics
Computational Line Geometry

Computational Line Geometry
Shape Space from Deformation

PG '98 Proceedings of the 6th Pacific Conference on Computer Graphics and Applications
The space of human body shapes: reconstruction and parameterization from range scans

ACM SIGGRAPH 2003 Papers
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces

IEEE Transactions on Pattern Analysis and Machine Intelligence
Deformation transfer for triangle meshes

ACM SIGGRAPH 2004 Papers
Cross-parameterization and compatible remeshing of 3D models

ACM SIGGRAPH 2004 Papers
Inter-surface mapping

ACM SIGGRAPH 2004 Papers
Comparing point clouds

Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Laplacian surface editing

Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

Foundations of Computational Mathematics
Poisson shape interpolation

Proceedings of the 2005 ACM symposium on Solid and physical modeling
SCAPE: shape completion and animation of people

ACM SIGGRAPH 2005 Papers
Linear rotation-invariant coordinates for meshes

ACM SIGGRAPH 2005 Papers
Mean value coordinates for closed triangular meshes

ACM SIGGRAPH 2005 Papers
As-rigid-as-possible shape manipulation

ACM SIGGRAPH 2005 Papers
Conformal Metrics and True "Gradient Flows" for Curves

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Designing Spatially Coherent Minimizing Flows for Variational Problems Based on Active Contours

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Vector field based shape deformations

ACM SIGGRAPH 2006 Papers
Subspace gradient domain mesh deformation

ACM SIGGRAPH 2006 Papers
Volume and shape preservation via moving frame manipulation

ACM Transactions on Graphics (TOG)
PriMo: coupled prisms for intuitive surface modeling

SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Isometric embedding of facial surfaces into S3

Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision

Generalized surface flows for mesh processing

SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Curved folding

ACM SIGGRAPH 2008 papers
Interactive physically-based shape editing

Proceedings of the 2008 ACM symposium on Solid and physical modeling
A genus oblivious approach to cross parameterization

Computer Aided Geometric Design
Topology-Invariant Similarity of Nonrigid Shapes

International Journal of Computer Vision
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates

Journal of Mathematical Imaging and Vision
A Shape Representation with Elastic Quadratic Polynomials--Preservation of High Curvature Points under Noisy Conditions

International Journal of Computer Vision
Semantic deformation transfer

ACM SIGGRAPH 2009 papers
Interactive physically-based shape editing

Computer Aided Geometric Design
Shape Metrics Based on Elastic Deformations

Journal of Mathematical Imaging and Vision
Geodesics in Shape Space via Variational Time Discretization

EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Meshless modeling of deformable shapes and their motion

Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Recognition of multiple configurations of objects with limited data

Pattern Recognition
Non-rigid registration under isometric deformations

SGP '08 Proceedings of the Symposium on Geometry Processing
A Computational Model of Multidimensional Shape

International Journal of Computer Vision
A simple geometric model for elastic deformations

ACM SIGGRAPH 2010 papers
Generalized surface flows for deformable registration and cortical matching

MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Style-content separation by anisotropic part scales

ACM SIGGRAPH Asia 2010 papers
Generating shapes by analogies: An application to hearing aid design

Computer-Aided Design
Comparative analysis of quasi-conformal deformations in shape space

MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Nonparametric Regression between General Riemannian Manifolds

SIAM Journal on Imaging Sciences
An Elasticity-Based Covariance Analysis of Shapes

International Journal of Computer Vision
Exploration of continuous variability in collections of 3D shapes

ACM SIGGRAPH 2011 papers
Example-based elastic materials

ACM SIGGRAPH 2011 papers
A Continuum Mechanical Approach to Geodesics in Shape Space

International Journal of Computer Vision
Shape space exploration of constrained meshes

Proceedings of the 2011 SIGGRAPH Asia Conference
A New Geometric Metric in the Space of Curves, and Applications to Tracking Deforming Objects by Prediction and Filtering

SIAM Journal on Imaging Sciences
Interactive spacetime control of deformable objects

ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Continuous deformations by isometry preserving shape integration

Proceedings of the 7th international conference on Curves and Surfaces
A blendshape model that incorporates physical interaction

Computer Animation and Virtual Worlds
A Reparameterisation Based Approach to Geodesic Constrained Solvers for Curve Matching

International Journal of Computer Vision
A continuous, editable representation for deforming mesh sequences with separate signals for time, pose and shape

Computer Graphics Forum
Pose space surface manipulation

International Journal of Computer Games Technology
Modeling Polyhedral Meshes with Affine Maps

Computer Graphics Forum
Time-Discrete Geodesics in the Space of Shells

Computer Graphics Forum
Lie bodies: a manifold representation of 3D human shape

ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Elastic shape matching of parameterized surfaces using square root normal fields

ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Efficient simulation of example-based materials

EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Dynamic multi-view exploration of shape spaces

EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Efficient simulation of example-based materials

Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Map-based exploration of intrinsic shape differences and variability

ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Generating and exploring good building layouts

ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Planar shape interpolation with bounded distortion

ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Technical Section: Planar shape interpolation using relative velocity fields

Computers and Graphics
Pose analysis using spectral geometry

The Visual Computer: International Journal of Computer Graphics
Structure-aware shape processing

SIGGRAPH Asia 2013 Courses
Deformation similarity measurement in quasi-conformal shape space

Graphical Models

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes -- triangular meshes or more generally straight line graphs in Euclidean space -- are treated as points in a shape space. We introduce useful Riemannian metrics in this space to aid the user in design and modeling tasks, especially to explore the space of (approximately) isometric deformations of a given shape. Much of the work relies on an efficient algorithm to compute geodesics in shape spaces; to this end, we present a multi-resolution framework to solve the interpolation problem -- which amounts to solving a boundary value problem -- as well as the extrapolation problem -- an initial value problem -- in shape space. Based on these two operations, several classical concepts like parallel transport and the exponential map can be used in shape space to solve various geometric modeling and geometry processing tasks. Applications include shape morphing, shape deformation, deformation transfer, and intuitive shape exploration.