A variational level set approach to multiphase motion
Journal of Computational Physics
International Journal of Computer Vision
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
A Variational Framework for Joint Segmentation and Registration
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
SMI '04 Proceedings of the Shape Modeling International 2004
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
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
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Integral Invariants for Shape Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Gradients: Priors on Minimization Flows
International Journal of Computer Vision
International Journal of Computer Vision
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Multiscale Joint Segmentation and Registration of Image Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Transport of Relational Structures in Groups of Diffeomorphisms
Journal of Mathematical Imaging and Vision
Large Deformation Diffeomorphic Metric Curve Mapping
International Journal of Computer Vision
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
Region matching with missing parts
Image and Vision Computing
A Computational Model of Multidimensional Shape
International Journal of Computer Vision
Shape matching by variational computation of geodesics on a manifold
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
IEEE Transactions on Image Processing
An Image Morphing Technique Based on Optimal Mass Preserving Mapping
IEEE Transactions on Image Processing
Example-based elastic materials
ACM SIGGRAPH 2011 papers
Time-Discrete Geodesics in the Space of Shells
Computer Graphics Forum
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In this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation. A geodesic path is defined as the family of shapes such that the total amount of viscous dissipation caused by an optimal material transport along the path is minimized. The approach can easily be generalized to shapes given as segment contours of multi-labeled images and to geodesic paths between partially occluded objects. The proposed computational framework for finding such a minimizer is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1---1 correspondence along the induced flow in shape space. When decreasing the time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the underlying shape space. If the constraint of pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, one obtains for decreasing time step size an optical flow term controlling the transport of the shape by the underlying motion field. The method is implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations. The numerical relaxation of the energy is performed via an efficient multi-scale procedure in space and time. Various examples for 2D and 3D shapes underline the effectiveness and robustness of the proposed approach.