Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730
Journal of Computational Physics
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
Transport and diffusion of material quantities on propagating interfaces via level set methods
Journal of Computational Physics
Regularization of Orthonormal Vector Sets using Coupled PDE's
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
A general framework for low level vision
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Color image enhancement via chromaticity diffusion
IEEE Transactions on Image Processing
Numerical methods for minimization problems constrained to S1 and S2
Journal of Computational Physics
Texture transfer during shape transformation
ACM Transactions on Graphics (TOG)
Fourth order partial differential equations on general geometries
Journal of Computational Physics
Maintaining the point correspondence in the level set framework
Journal of Computational Physics
Inverse-Consistent Surface Mapping with Laplace-Beltrami Eigen-Features
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
IEEE Transactions on Image Processing
Brain image registration using cortically constrained harmonic mappings
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Automated sulci identification via intrinsic modeling of cortical anatomy
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
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
Enhancing images painted on manifolds
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Denoising tensors via lie group flows
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Non-rigid shape comparison of implicitly-defined curves
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Regularization of mappings between implicit manifolds of arbitrary dimension and codimension
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Hi-index | 31.46 |
A framework for solving variational problems and partial differential equations that define maps onto a given generic manifold is introduced in this paper. We discuss the framework for arbitrary target manifolds, while the domain manifold problem was addressed in [J. Comput. Phys. 174(2) (2001) 759]. The key idea is to implicitly represent the target manifold as the level-set of a higher dimensional function, and then implement the equations in the Cartesian coordinate system where this embedding function is defined. In the case of variational problems, we restrict the search of the minimizing map to the class of maps whose target is the level-set of interest. In the case of partial differential equations, we re-write all the equation's geometric characteristics with respect to the embedding function. We then obtain a set of equations that, while defined on the whole Euclidean space, are intrinsic to the implicitly defined target manifold and map into it. This permits the use of classical numerical techniques in Cartesian grids, regardless of the geometry of the target manifold. The extension to open surfaces and submanifolds is addressed in this paper as well. In the latter case, the submanifold is defined as the intersection of two higher dimensional hypersurfaces, and all the computations are restricted to this intersection. Examples of the applications of the framework here described include harmonic maps in liquid crystals, where the target manifold is a hypersphere; probability maps, where the target manifold is a hyperplane; chroma enhancement; texture mapping; and general geometric mapping between high dimensional manifolds.