Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
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
A Riemannian Framework for Tensor Computing
International Journal of 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
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
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
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We have seen in recent years a need for regularization of complicated feature spaces: Vector fields, orientation fields, color perceptual spaces, the structure tensor and Diffusion Weighted Images (DWI) are few examples. In most cases we represent the feature space as a manifold. In the proposed formalism, the image is described as a section of a fiber bundle where the image domain is the base space and the feature space is the fiber. In some distinguished cases the feature space has algebraic structure as well. In the proposed framework we treat fibers which are compact Lie-group manifolds (e.g., O(N), SU(N)). We study here this case and show that the algebraic structure can help in defining a sensible regularization scheme. We solve the parameterization problem of compact manifold that is responsible for singularities anytime that one wishes to describe in one coordinate system a compact manifold. The proposed solution defines a coordinate-free diffusion process accompanied by an appropriate numerical scheme. We demonstrate this framework in an example of S1 feature space regularization which is known also as orientation diffusion.