liu.seSök publikationer i DiVA
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Variational Tensor-Based Models for Image Diffusion in Non-Linear Domains
Linköpings universitet, Institutionen för systemteknik, Datorseende. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska högskolan.
2015 (Engelska)Doktorsavhandling, monografi (Övrigt vetenskapligt)
Abstract [en]

This dissertation addresses the problem of adaptive image filtering.

Although the topic has a long history in the image processing community, researchers continuously present novel methods to obtain ever better image restoration results.

With an expanding market for individuals who wish to share their everyday life on social media, imaging techniques such as compact cameras and smart phones are important factors. Naturally, every producer of imaging equipment desires to exploit cheap camera components while supplying high quality images. One step in this pipeline is to use sophisticated imaging software including, e.g., noise reduction to reduce manufacturing costs, while maintaining image quality.

This thesis is based on traditional formulations such as isotropic and tensor-based anisotropic diffusion for image denoising. The difference from main-stream denoising methods is that this thesis explores the effects of introducing contextual information as prior knowledge for image denoising into the filtering schemes. To achieve this, the adaptive filtering theory is formulated from an energy minimization standpoint. The core contributions of this work is the introduction of a novel tensor-based functional which unifies and generalises standard diffusion methods. Additionally, the explicit Euler-Lagrange equation is derived which, if solved, yield the stationary point for the minimization problem. Several aspects of the functional are presented in detail which include, but are not limited to, tensor symmetry constraints and convexity. Also, the classical problem of finding a variational formulation to a given tensor-based partial differential equation is studied.

The presented framework is applied in problem formulation that includes non-linear domain transformation, e.g., visualization of medical images.

Additionally, the framework is also used to exploit locally estimated probability density functions or the channel representation to drive the filtering process.

Furthermore, one of the first truly tensor-based formulations of total variation is presented. The key to the formulation is the gradient energy tensor, which does not require spatial regularization of its tensor components. It is shown empirically in several computer vision applications, such as corner detection and optical flow, that the gradient energy tensor is a viable replacement for the commonly used structure tensor. Moreover, the gradient energy tensor is used in the traditional tensor-based anisotropic diffusion scheme. This approach results in significant improvements in computational speed when the scheme is implemented on a graphical processing unit compared to using the commonly used structure tensor.

Ort, förlag, år, upplaga, sidor
Linköping: Linköping University Electronic Press, 2015. , s. 156
Serie
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1646
Nyckelord [en]
image diffusion, variational formulation, denoising, tensor, non-linear
Nationell ämneskategori
Matematisk analys
Identifikatorer
URN: urn:nbn:se:liu:diva-114279DOI: 10.3384/diss.diva-114279ISBN: 978-91-7519-113-3 (tryckt)OAI: oai:DiVA.org:liu-114279DiVA, id: diva2:789680
Disputation
2015-03-31, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 09:15 (Engelska)
Opponent
Handledare
Projekt
VIDINACIPGARNICSEMC^2Tillgänglig från: 2015-02-20 Skapad: 2015-02-16 Senast uppdaterad: 2016-08-31Bibliografiskt granskad

Open Access i DiVA

fulltext(13979 kB)1036 nedladdningar
Filinformation
Filnamn FULLTEXT02.pdfFilstorlek 13979 kBChecksumma SHA-512
3a09002be6d2ff755fd75396936a4df87bd12f37ed03291b4a6aa9605e4c673223883e8c6b32810daef6fff7df804e9a4949d3fba0659550afebdfa4659a02c1
Typ fulltextMimetyp application/pdf
omslag(2786 kB)47 nedladdningar
Filinformation
Filnamn COVER01.pdfFilstorlek 2786 kBChecksumma SHA-512
7b3c10e8c796a0c94f1cc70b4c9c134f738ab8f65b51a381bcfe8f7d5ecc682b25e483a6e1d088b930e763e3cf1f63d697a9e499612341cd1ed8a5dec171f1ce
Typ coverMimetyp application/pdf

Övriga länkar

Förlagets fulltext

Personposter BETA

Åström, Freddie

Sök vidare i DiVA

Av författaren/redaktören
Åström, Freddie
Av organisationen
DatorseendeCentrum för medicinsk bildvetenskap och visualisering, CMIVTekniska högskolan
Matematisk analys

Sök vidare utanför DiVA

GoogleGoogle Scholar
Totalt: 1050 nedladdningar
Antalet nedladdningar är summan av nedladdningar för alla fulltexter. Det kan inkludera t.ex tidigare versioner som nu inte längre är tillgängliga.

doi
isbn
urn-nbn

Altmetricpoäng

doi
isbn
urn-nbn
Totalt: 2870 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf