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A Multidimensional Filtering Framework with Applications to Local Structure Analysis and Image Enhancement
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Filtering is a fundamental operation in image science in general and in medical image science in particular. The most central applications are image enhancement, registration, segmentation and feature extraction. Even though these applications involve non-linear processing a majority of the methodologies available rely on initial estimates using linear filters. Linear filtering is a well established cornerstone of signal processing, which is reflected by the overwhelming amount of literature on finite impulse response filters and their design.

Standard techniques for multidimensional filtering are computationally intense. This leads to either a long computation time or a performance loss caused by approximations made in order to increase the computational efficiency. This dissertation presents a framework for realization of efficient multidimensional filters. A weighted least squares design criterion ensures preservation of the performance and the two techniques called filter networks and sub-filter sequences significantly reduce the computational demand.

A filter network is a realization of a set of filters, which are decomposed into a structure of sparse sub-filters each with a low number of coefficients. Sparsity is here a key property to reduce the number of floating point operations required for filtering. Also, the network structure is important for efficiency, since it determines how the sub-filters contribute to several output nodes, allowing reduction or elimination of redundant computations.

Filter networks, which is the main contribution of this dissertation, has many potential applications. The primary target of the research presented here has been local structure analysis and image enhancement. A filter network realization for local structure analysis in 3D shows a computational gain, in terms of multiplications required, which can exceed a factor 70 compared to standard convolution. For comparison, this filter network requires approximately the same amount of multiplications per signal sample as a single 2D filter. These results are purely algorithmic and are not in conflict with the use of hardware acceleration techniques such as parallel processing or graphics processing units (GPU). To get a flavor of the computation time required, a prototype implementation which makes use of filter networks carries out image enhancement in 3D, involving the computation of 16 filter responses, at an approximate speed of 1MVoxel/s on a standard PC.

Place, publisher, year, edition, pages
Institutionen för medicinsk teknik , 2008.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1171
Keyword [en]
Medical image science, multidimensional filtering, image enhancement, image registration, image segmentation, filter networks, graphics processing units (GPU)
National Category
Medical Laboratory and Measurements Technologies
Identifiers
URN: urn:nbn:se:liu:diva-11271ISBN: 978-91-7393-943-0 (print)OAI: oai:DiVA.org:liu-11271DiVA: diva2:17689
Public defence
2008-04-18, Linden, Hus 421, Campus US, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2015-06-02
List of papers
1. On Geometric Transformations of Local Structure Tensors
Open this publication in new window or tab >>On Geometric Transformations of Local Structure Tensors
Manuscript (Other academic)
Identifiers
urn:nbn:se:liu:diva-13022 (URN)
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2010-01-13
2. Estimation of Non-Cartesian Local Structure Tensor Fields
Open this publication in new window or tab >>Estimation of Non-Cartesian Local Structure Tensor Fields
2007 (English)In: Image Analysis: 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007 / [ed] Bjarne Kjær Ersbøll, Kim Steenstrup Pedersen, Springer Berlin/Heidelberg, 2007, Vol. 4522/2007, 948-957 p.Conference paper, Published paper (Refereed)
Abstract [en]

In medical imaging, signals acquired in non-Cartesian coordinate systems are common. For instance, CT and MRI often produce significantly higher resolution within scan planes, compared to the distance between two adjacent planes. Even oblique sampling occurs, by the use of gantry tilt. In ultrasound imaging, samples are acquired in a polar coordinate system, which implies a spatially varying metric.

In order to produce a geometrically correct image, signals are generally resampled to a Cartesian coordinate system. This paper concerns estimation of local structure tensors directly from the non-Cartesian coordinate system, thus avoiding deteriorated signal and noise characteristics caused by resampling. In many cases processing directly in the warped coordinate system is also less time-consuming. A geometrically correct tensor must obey certain transformation rules originating from fundamental differential geometry. Subsequently, this fact also affects the tensor estimation. As the local structure tensor is estimated using filters, a change of coordinate system also change the shape of the spatial support of these filters. Implications and limitations brought on by sampling require the filter design criteria to be adapted to the coordinate system.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2007
Series
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 4522
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-13023 (URN)10.1007/978-3-540-73040-8_96 (DOI)000247364000096 ()978-3-540-73039-2 (ISBN)978-3-540-73040-8 (ISBN)
Conference
15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2015-10-08Bibliographically approved
3. Efficient 3-D Adaptive Filtering for Medical Image Enhancement
Open this publication in new window or tab >>Efficient 3-D Adaptive Filtering for Medical Image Enhancement
2006 (English)In: 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006., IEEE , 2006, 996-999 p.Conference paper, Published paper (Refereed)
Abstract [en]

Tensor based orientation adaptive filtering, an explicit methodology for anisotropic filtering, constitutes a flexible framework for medical image enhancement. The technique features post-filtering steerability and allows user interaction and direct control over the high-frequency contents of the signal. A new class of filters for local structure analysis together with filter networks significantly lowers the complexity to meet the requirements of computation time for clinical use, while maintaining accuracy. In this paper the technique is applied to low-dose CT-images, magnetic resonance angiography and T2-weighted MRI.

Place, publisher, year, edition, pages
IEEE, 2006
Series
International Symposium on Biomedical Imaging. Proceedings, ISSN 1945-7928
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13024 (URN)10.1109/ISBI.2006.1625088 (DOI)000244446000252 ()0-7803-9576-X (ISBN)
Conference
3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 6-9 April 2006, Arlington, VA, USA
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2014-01-31Bibliographically approved
4. Approximate Spectral Factorization for Design of Efficient Sub-Filter Sequences
Open this publication in new window or tab >>Approximate Spectral Factorization for Design of Efficient Sub-Filter Sequences
2008 (English)Manuscript (preprint) (Other (popular science, discussion, etc.))
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13025 (URN)
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2015-06-02
5. Filter Networks for Efficient Estimation of Local 3-D Structure
Open this publication in new window or tab >>Filter Networks for Efficient Estimation of Local 3-D Structure
2005 (English)In: IEEE International Conference on Image Processing (ICIP). 11-14 Sept, Genoa, Italy, 2005, Vol. 3, 573-576 p.Conference paper, Published paper (Refereed)
Abstract [en]

Linear filtering is a fundamental operation in signal processing, but for multidimensional signals the practical use is severely limited by the computer power available. Decomposition of filters into a layered structure of sparse subfilters, i.e. a filter network, significantly reduces the number of multiplications required for each data sample. A filter network, here used for phase invariant estimation of local 3-D structure, provides a flexible solution for linear filtering, especially suited for applying a set of filters on signals of higher dimensionality. The filter network presented, is twice as efficient as convolution based on the fast Fourier transform (FFT) and outperforms standard convolution by a factor exceeding 50 in terms of multiplications and additions performed.

Keyword
filter design, filter network, sparse filters, efficient filtering, local structure
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13026 (URN)10.1109/ICIP.2005.1530456 (DOI)
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2013-08-28
6. A Graph Representation of Filter Networks
Open this publication in new window or tab >>A Graph Representation of Filter Networks
2005 (English)In: Scandinavian Conference on Image Analysis (SCIA). Joensuu, Finland, 2005, 1086-1095 p.Conference paper, Published paper (Refereed)
Abstract [en]

Filter networks, i.e. decomposition of a filter set into a layered structure of sparse subfilters has been proven successful for e.g. efficient convolution using finite impulse response filters. The efficiency is due to the significantly reduced number of multiplications and additions per data sample that is required. The computational gain is dependent on the choice of network structure and the graph representation compactly incorporates the network structure in the design objectives. Consequently the graph representation forms a framework for searching the optimal network structure. It also removes the requirement of a layered structure, at the cost of a less compact representation.

Keyword
filters, orientation_frequency_phase, tensors, CMIV
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13027 (URN)
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2013-08-28

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Svensson, Björn

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