Tensor-based image diffusions derived from generalizations of the total variation and beltrami functionals

Roussos, A; Maragos, P

dc.contributor.author	Roussos, A	en
dc.contributor.author	Maragos, P	en
dc.date.accessioned	2014-03-01T02:47:06Z
dc.date.available	2014-03-01T02:47:06Z
dc.date.issued	2010	en
dc.identifier.issn	15224880	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32994
dc.subject	Anisotropic Diffusion	en
dc.subject	High Dimensionality	en
dc.subject	Total Variation	en
dc.subject	Variational Approach	en
dc.subject	Variational Method	en
dc.subject	Diffusion Tensor	en
dc.subject.other	Beltrami	en
dc.subject.other	Beltrami flow	en
dc.subject.other	Diffusion method	en
dc.subject.other	Diffusion tensor	en
dc.subject.other	Embeddings	en
dc.subject.other	Functionals	en
dc.subject.other	High dimensional spaces	en
dc.subject.other	Image diffusion	en
dc.subject.other	Image patches	en
dc.subject.other	Image Structures	en
dc.subject.other	Non-linear anisotropic diffusion	en
dc.subject.other	Structure tensors	en
dc.subject.other	Total variation	en
dc.subject.other	Variational approaches	en
dc.subject.other	Variational methods	en
dc.subject.other	Vector-valued images	en
dc.subject.other	Diffusion	en
dc.subject.other	Image processing	en
dc.subject.other	Imaging systems	en
dc.subject.other	Tensors	en
dc.title	Tensor-based image diffusions derived from generalizations of the total variation and beltrami functionals	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1109/ICIP.2010.5653241	en
heal.identifier.secondary	5653241	en
heal.identifier.secondary	http://dx.doi.org/10.1109/ICIP.2010.5653241	en
heal.publicationDate	2010	en
heal.abstract	We introduce a novel functional for vector-valued images that generalizes several variational methods, such as the Total Variation and Beltrami Functionals. This functional is based on the structure tensor that describes the geometry of image structures within the neighborhood of each point. We first generalize the Beltrami functional based on the image patches and using embeddings in high dimensional spaces. Proceeding to the most general form of the proposed functional, we prove that its minimization leads to a nonlinear anisotropic diffusion that is regularized, in the sense that its diffusion tensor contains convolutions with a kernel. Using this result we propose two novel diffusion methods, the Generalized Beltrami Flow and the Tensor Total Variation. These methods combine the advantages of the variational approaches with those of the tensor-based diffusion approaches. © 2010 IEEE.	en
heal.journalName	Proceedings - International Conference on Image Processing, ICIP	en
dc.identifier.doi	10.1109/ICIP.2010.5653241	en
dc.identifier.spage	4141	en
dc.identifier.epage	4144	en