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On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-6096-3648
2012 (English)Conference paper, Published paper (Refereed)
Abstract [en]

The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method compares favorably to current state-of-the-art color image denoising techniques.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2012. 215-228 p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 7574
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-79603DOI: 10.1007/978-3-642-33712-3_16ISBN: 978-3-642-33711-6 (print)ISBN: 978-3-642-33712-3 (print)OAI: oai:DiVA.org:liu-79603DiVA: diva2:543914
Conference
ECCV 2012: 12th European Conference on Computer Vision, 7-12 October, Firenze, Italy
Projects
NACIPGARNICSELLIIT
Available from: 2012-08-10 Created: 2012-08-10 Last updated: 2017-06-01Bibliographically approved
In thesis
1. A Variational Approach to Image Diffusion in Non-Linear Domains
Open this publication in new window or tab >>A Variational Approach to Image Diffusion in Non-Linear Domains
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Image filtering methods are designed to enhance noisy images captured in situations that are problematic for the camera sensor. Such noisy images originate from unfavourable illumination conditions, camera motion, or the desire to use only a low dose of ionising radiation in medical imaging. Therefore, in this thesis work I have investigated the theory of partial differential equations (PDE) to design filtering methods that attempt to remove noise from images. This is achieved by modeling and deriving energy functionals which in turn are minimized to attain a state of minimum energy. This state is obtained by solving the so called Euler-Lagrange equation. An important theoretical contribution of this work is that conditions are put forward determining when a PDE has a corresponding energy functional. This is in particular described in the case of the structure tensor, a commonly used tensor in computer vision.A primary component of this thesis work is to model adaptive image filtering such that any modification of the image is structure preserving, but yet is noise suppressing. In color image filtering this is a particular challenge since artifacts may be introduced at color discontinuities. For this purpose a non-Euclidian color opponent transformation has been analysed and used to separate the standard RGB color space into uncorrelated components.A common approach to achieve adaptive image filtering is to select an edge stopping function from a set of functions that have proven to work well in the past. The purpose of the edge stopping function is to inhibit smoothing of image features that are desired to be retained, such as lines, edges or other application dependent characteristics. Thus, a step from ad-hoc filtering based on experience towards an application-driven filtering is taken, such that only desired image features are processed. This improves what is characterised as visually relevant features, a topic which this thesis covers, in particular for medical imaging.The notion of what are relevant features is a subjective measure may be different from a layman's opinion compared to a professional's. Therefore, we advocate that any image filtering method should yield an improvement not only in numerical measures but also a visual improvement should be experienced by the respective end-user

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2013. 32 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1594
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-92788 (URN)LIU-TEK-LIC-2013:28 (Local ID)978-91-7519-606-0 (ISBN)LIU-TEK-LIC-2013:28 (Archive number)LIU-TEK-LIC-2013:28 (OAI)
Presentation
2013-06-13, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Projects
NACIP, VIDI, GARNICS
Available from: 2013-05-30 Created: 2013-05-22 Last updated: 2016-05-04Bibliographically approved

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On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising(3013 kB)972 downloads
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Program_code_ECCV2012(49 kB)3 downloads
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Type softwareMimetype application/zip

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