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A Variational Approach to Image Diffusion in Non-Linear Domains
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, Center for Medical Image Science and Visualization, CMIV. Linköping University, The Institute of Technology.
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: urn:nbn:se:liu:diva-92788Local ID: LIU-TEK-LIC-2013:28ISBN: 978-91-7519-606-0 (print)OAI: oai:DiVA.org:liu-92788DiVA: diva2:622727
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
List of papers
1. Color Persistent Anisotropic Diffusion of Images
Open this publication in new window or tab >>Color Persistent Anisotropic Diffusion of Images
2011 (English)In: Image Analysis / [ed] Anders Heyden, Fredrik Kahl, Heidelberg: Springer, 2011, 262-272 p.Conference paper, Published paper (Refereed)
Abstract [en]

Techniques from the theory of partial differential equations are often used to design filter methods that are locally adapted to the image structure. These techniques are usually used in the investigation of gray-value images. The extension to color images is non-trivial, where the choice of an appropriate color space is crucial. The RGB color space is often used although it is known that the space of human color perception is best described in terms of non-euclidean geometry, which is fundamentally different from the structure of the RGB space. Instead of the standard RGB space, we use a simple color transformation based on the theory of finite groups. It is shown that this transformation reduces the color artifacts originating from the diffusion processes on RGB images. The developed algorithm is evaluated on a set of real-world images, and it is shown that our approach exhibits fewer color artifacts compared to state-of-the-art techniques. Also, our approach preserves details in the image for a larger number of iterations.

Place, publisher, year, edition, pages
Heidelberg: Springer, 2011
Series
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 6688
Keyword
Non-linear diffusion, color image processing, perceptual image quality
National Category
Information Science Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:liu:diva-68999 (URN)10.1007/978-3-642-21227-7_25 (DOI)978-3-642-21226-0 (ISBN)978-3-642-21227-7 (ISBN)
Conference
The 17th Scandinavian Conference on Image Analysis, 23-27 May 2011, Ystad Sweden
Note

Original Publication: Åström Freddie, Felsberg Michael and Lenz Reiner, Color Persistent Anisotropic Diffusion of Images, 2011, Image Analysis, SCIA conference, 23-27 May 2011, Ystad Sweden, 262-272. http://dx.doi.org/10.1007/978-3-642-21227-7_25 Copyright: Springer

Available from: 2011-06-17 Created: 2011-06-15 Last updated: 2016-08-31Bibliographically approved
2. On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising
Open this publication in new window or tab >>On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising
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
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 7574
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-79603 (URN)10.1007/978-3-642-33712-3_16 (DOI)978-3-642-33711-6 (ISBN)978-3-642-33712-3 (ISBN)
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
3. Targeted Iterative Filtering
Open this publication in new window or tab >>Targeted Iterative Filtering
2013 (English)Conference paper, Published paper (Refereed)
Abstract [en]

The assessment of image denoising results depends on the respective application area, i.e. image compression, still-image acquisition, and medical images require entirely different behavior of the applied denoising method. In this paper we propose a novel, nonlinear diffusion scheme that is derived from a linear diffusion process in a value space determined by the application. We show that application-driven linear diffusion in the transformed space compares favorably with existing nonlinear diffusion techniques. 

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2013
Series
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 7893
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-89674 (URN)10.1007/978-3-642-38267-3_1 (DOI)978-3-642-38266-6 (ISBN)978-3-642-38267-3 (ISBN)
Conference
Fourth International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2013), 2-6 June 2013, Schloss Seggau, Graz region, Austria
Projects
VIDIGARNICSSM10-002BILDLAB
Available from: 2013-04-03 Created: 2013-03-01 Last updated: 2016-05-04Bibliographically approved

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