Coordinate-free diffusion over compact lie-groups

Yaniv Gur*, Nir Sochen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540728221
StatePublished - 2007
Event1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007 - Ischia, Italy
Duration: 30 May 20072 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4485 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007


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