Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
International Journal of Computer Vision
A PDE-based fast local level set method
Journal of Computational Physics
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Level set methods: an overview and some recent results
Journal of Computational Physics
Using Beltrami Framework for Orientation Diffusion in Image Processing
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Variational Problems and PDE's on Implicit Surfaces
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
The Beltrami Flow over Implicit Manifolds
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
Journal of Computational Physics
Local level set method in high dimension and codimension
Journal of Computational Physics
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
A general framework for low level vision
IEEE Transactions on Image Processing
Regularizing Flows over Lie Groups
Journal of Mathematical Imaging and Vision
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
Coordinate-free diffusion over compact Lie-groups
SSVM'07 Proceedings of the 1st international conference on Scale space and variational 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
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We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source and target manifold are represented implicitly, using multiple level set functions, or explicitly, as functions of the spatial coordinates. We derive the general implicit differential operators, and show how they can be used to generalize previous results concerning the Beltrami flow and other similar flows. As examples, We show how these results can be used to regularize gray level and color images on manifolds, and to regularize tangent vector fields and direction fields on manifolds.