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Brun, Anders
Publications (10 of 29) Show all publications
Cammoun, L., Castano-Moraga, C., Munoz-Moreno, E., Sosa-Cabrera, D., Acar, B., Rodriguez-Florido, M., . . . Thiran, J. (2009). A Review of Tensors and Tensor Signal Processing. In: S. Aja-Fernandez, R. de Luis Garcia, D. Tao, and X. Li (Ed.), Tensors in Image Processing and Computer Vision: . Paper presented at Tensors in Image Processing and Computer Vision (pp. 1-32). Paper presented at Tensors in Image Processing and Computer Vision. Springer London
Open this publication in new window or tab >>A Review of Tensors and Tensor Signal Processing
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2009 (English)In: Tensors in Image Processing and Computer Vision / [ed] S. Aja-Fernandez, R. de Luis Garcia, D. Tao, and X. Li, Springer London, 2009, p. 1-32Chapter in book (Refereed)
Abstract [en]

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Place, publisher, year, edition, pages
Springer London, 2009
Series
Advances in Pattern Recognition, ISSN 1617-7916
National Category
Engineering and Technology Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-58092 (URN)10.1007/978-1-84882-299-3_1 (DOI)978-1-84882-298-6 (ISBN)
Conference
Tensors in Image Processing and Computer Vision
Available from: 2010-07-29 Created: 2010-07-29 Last updated: 2013-08-28
Svensson, B., Brun, A., Andersson, M. & Knutsson, H. (2009). On Geometric Transformations of Local Structure Tensors. In: S. Aja-Fernandez, R. de Luis Garcia, D. Tao, X. Li (Ed.), Tensors in Image Processing and Computer Vision: Part 2. Paper presented at Tensors in Image Processing and Computer Vision (pp. 179-193). Paper presented at Tensors in Image Processing and Computer Vision. Springer London
Open this publication in new window or tab >>On Geometric Transformations of Local Structure Tensors
2009 (English)In: Tensors in Image Processing and Computer Vision: Part 2 / [ed] S. Aja-Fernandez, R. de Luis Garcia, D. Tao, X. Li, Springer London, 2009, p. 179-193Chapter in book (Refereed)
Abstract [en]

The structure of images has been studied for decades and the use of local structure tensor fields appeared during the eighties [3, 14, 6, 9, 11]. Since then numerous varieties of tensors and estimation schemes have been developed. Tensors have for instance been used to represent orientation [7], velocity, curvature [2] and diffusion [19] with applications to adaptive filtering [8], motion analysis [10] and segmentation [17]. Even though sampling in non-Cartesian coordinate system are common, analysis and processing of local structure tensor fields in such systems is less developed. Previous work on local structure in non-Cartesian coordinate systems include [21, 16, 1, 18].

Place, publisher, year, edition, pages
Springer London, 2009
Series
Advances in Pattern Recognition, ISSN 1617-7916
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-60131 (URN)10.1007/978-1-84882-299-3_8 (DOI)978-1-84882-298-6 (ISBN)978-1-84882-299-3 (ISBN)
Conference
Tensors in Image Processing and Computer Vision
Funder
Swedish Research CouncilVINNOVA
Available from: 2010-10-06 Created: 2010-10-06 Last updated: 2015-08-19Bibliographically approved
Brun, A., Martin-Fernandez, M., Acar, B., Munoz-Moreno, E., Cammoun, L., Sigfridsson, A., . . . Knutsson, H. (2009). Similar Tensor Arrays - A Framework for Storage of Tensor Array Data (1ed.). In: Santiago Aja-Fern´andez, Rodrigo de Luis Garc´ıa, Dacheng Tao, Xuelong Li (Ed.), Santiago Aja-Fern´andez, Rodrigo de Luis Garc´ıa, Dacheng Tao, Xuelong Li (Ed.), Tensors in Image Processing and Computer Vision: . Paper presented at Tensor in Image Processing and Computer Vision (pp. 407-428). Paper presented at Tensor in Image Processing and Computer Vision. Springer Science+Business Media B.V.
Open this publication in new window or tab >>Similar Tensor Arrays - A Framework for Storage of Tensor Array Data
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2009 (English)In: Tensors in Image Processing and Computer Vision / [ed] Santiago Aja-Fern´andez, Rodrigo de Luis Garc´ıa, Dacheng Tao, Xuelong Li, Springer Science+Business Media B.V., 2009, 1, p. 407-428Chapter in book (Refereed)
Abstract [en]

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2009 Edition: 1
Series
Advances in Pattern Recognition, ISSN 1617-7916
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:liu:diva-58091 (URN)10.1007/978-1-84882-299-3_19 (DOI)978-1-84882-298-6 (ISBN)978-1-84882-299-3 (ISBN)
Conference
Tensor in Image Processing and Computer Vision
Available from: 2010-07-29 Created: 2010-07-29 Last updated: 2018-01-12Bibliographically approved
Brun, A. & Knutsson, H. (2009). Tensor Glyph Warping - Visualizing Metric Tensor Fields using Riemannian Exponential Maps. In: Laidlaw, David H.; Weickert, Joachim (Ed.), Visualization and Processing of Tensor Fields: Advances and Perspectives (pp. 139-160). Springer Berlin/Heidelberg
Open this publication in new window or tab >>Tensor Glyph Warping - Visualizing Metric Tensor Fields using Riemannian Exponential Maps
2009 (English)In: Visualization and Processing of Tensor Fields: Advances and Perspectives / [ed] Laidlaw, David H.; Weickert, Joachim, Springer Berlin/Heidelberg, 2009, p. 139-160Chapter in book (Refereed)
Abstract [en]

The Riemannian exponential map, and its inverse the Riemannian logarithm map, can be used to visualize metric tensor fields. In this chapter we first derive the well-known metric sphere glyph from the geodesic equations, where the tensor field to be visualized is regarded as the metric of a manifold. These glyphs capture the appearance of the tensors relative to the coordinate system of the human observer. We then introduce two new concepts for metric tensor field visualization: geodesic spheres and geodesically warped glyphs. These additions make it possible not only to visualize tensor anisotropy, but also the curvature and change in tensorshape in a local neighborhood. The framework is based on the exp maps, which can be computed by solving a second order Ordinary Differential Equation (ODE) or by manipulating the geodesic distance function. The latter can be found by solving the eikonal equation, a non-linear Partial Differential Equation (PDE), or it can be derived analytically for some manifolds. To avoid heavy calculations, we also include first and second order Taylor approximations to exp and log. In our experiments, these are shown to be sufficiently accurate to produce glyphs that visually characterize anisotropy, curvature and shape-derivatives in smooth tensor fields. 

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2009
Series
Mathematics and Visualization, ISSN 1612-3786
National Category
Biomedical Laboratory Science/Technology
Identifiers
urn:nbn:se:liu:diva-58090 (URN)10.1007/978-3-540-88378-4_7 (DOI)978-3-540-88377-7 (ISBN)978-3-540-88378-4 (ISBN)
Available from: 2010-08-19 Created: 2010-07-29 Last updated: 2013-08-28Bibliographically approved
Ohlsson, H., Roll, J., Brun, A., Knutsson, H., Andersson, M. & Ljung, L. (2008). Direct Weight Optimization Applied to Discontinuous Functions. In: 47th IEEE Conference on Decision and Control, 2008. CDC 2008: . Paper presented at 47th IEEE Conference on Decision and Control, Cancun, Mexico, December, 2008 (pp. 117-122). IEEE
Open this publication in new window or tab >>Direct Weight Optimization Applied to Discontinuous Functions
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2008 (English)In: 47th IEEE Conference on Decision and Control, 2008. CDC 2008, IEEE , 2008, p. 117-122Conference paper, Published paper (Refereed)
Abstract [en]

The Direct Weight Optimization (DWO) approach is a nonparametric estimation approach that has appeared in recent years within the field of nonlinear system identification. In previous work, all function classes for which DWO has been studied have included only continuous functions. However, in many applications it would be desirable also to be able to handle discontinuous functions. Inspired by the bilateral filter method from image processing, such an extension of the DWO framework is proposed for the smoothing problem. Examples show that the properties of the new approach regarding the handling of discontinuities are similar to the bilateral filter, while at the same time DWO offers a greater flexibility with respect to different function classes handled.

Place, publisher, year, edition, pages
IEEE, 2008
Series
IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
Keywords
Function estimation, Non-parametric identification, Discontinuous functions
National Category
Control Engineering Biomedical Laboratory Science/Technology
Identifiers
urn:nbn:se:liu:diva-60135 (URN)10.1109/CDC.2008.4738761 (DOI)000307311600020 ()978-1-4244-3123-6 (ISBN)e-978-1-4244-3124-3 (ISBN)
Conference
47th IEEE Conference on Decision and Control, Cancun, Mexico, December, 2008
Available from: 2010-10-06 Created: 2010-10-06 Last updated: 2015-10-08Bibliographically approved
Ohlsson, H., Rydell, J., Brun, A., Roll, J., Andersson, M., Ynnerman, A. & Knutsson, H. (2008). Enabling Bio-Feedback using Real-Time fMRI. In: 47th IEEE Conference on Decision and Control, 2008, CDC 2008: . Paper presented at 47th IEEE Conference on Decision and Control, Cancun, Mexico, December, 2008 (pp. 3336-3341). IEEE
Open this publication in new window or tab >>Enabling Bio-Feedback using Real-Time fMRI
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2008 (English)In: 47th IEEE Conference on Decision and Control, 2008, CDC 2008, IEEE , 2008, p. 3336-3341Conference paper, Published paper (Refereed)
Abstract [en]

Despite the enormous complexity of the human mind, fMRI techniques are able to partially observe the state of a brain in action. In this paper we describe an experimental setup for real-time fMRI in a bio-feedback loop. One of the main challenges in the project is to reach a detection speed, accuracy and spatial resolution necessary to attain sufficient bandwidth of communication to close the bio-feedback loop. To this end we have banked on our previous work on real-time filtering for fMRI and system identification, which has been tailored for use in the experiment setup. In the experiments presented the system is trained to estimate where a person in the MRI scanner is looking from signals derived from the visual cortex only. We have been able to demonstrate that the user can induce an action and perform simple tasks with her mind sensed using real-time fMRI. The technique may have several clinical applications, for instance to allow paralyzed and "locked in" people to communicate with the outside world. In the meanwhile, the need for improved fMRI performance and brain state detection poses a challenge to the signal processing community. We also expect that the setup will serve as an invaluable tool for neuro science research in general.

Place, publisher, year, edition, pages
IEEE, 2008
Series
IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
Keywords
fMRI, System identification, Bio-feedback
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-44641 (URN)10.1109/CDC.2008.4738759 (DOI)000307311603077 ()77222 (Local ID)978-1-4244-3123-6 (ISBN)e-978-1-4244-3124-3 (ISBN)77222 (Archive number)77222 (OAI)
Conference
47th IEEE Conference on Decision and Control, Cancun, Mexico, December, 2008
Note

©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Henrik Ohlsson, Joakim Rydell, Anders Brun, Jacob Roll, Mats Andersson, Anders Ynnerman and Hans Knutsson, Enabling Bio-Feedback Using Real-Time fMRI, 2008, Proceedings of the 47th IEEE Conference on Decision and Control, 2008, 3336.

Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2015-10-08Bibliographically approved
Svensson, B., Brun, A., Andersson, M. & Knutsson, H. (2007). Estimation of Non-Cartesian Local Structure Tensor Fields. In: Bjarne Kjær Ersbøll, Kim Steenstrup Pedersen (Ed.), Bjarne Kjær Ersbøll, Kim Steenstrup Pedersen (Ed.), Image Analysis: 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007. Paper presented at 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007 (pp. 948-957). Springer Berlin/Heidelberg, 4522/2007
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, p. 948-957Conference 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, E-ISSN 1611-3349 ; 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: 2018-02-15Bibliographically approved
Brun, A., Svensson, B., Westin, C.-F., Herberthson, M., Wrangsjö, A. & Knutsson, H. (2007). Filtering Vector-Valued Images using Importance Sampling. In: Proceedings of the {SSBA} Symposium on Image Analysis,2007: . Paper presented at Symposium on Image Analysis {SSBA}, Linköping, Sweden March 14-15 2007.
Open this publication in new window or tab >>Filtering Vector-Valued Images using Importance Sampling
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2007 (English)In: Proceedings of the {SSBA} Symposium on Image Analysis,2007, 2007Conference paper, Published paper (Other academic)
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:liu:diva-38749 (URN)45479 (Local ID)45479 (Archive number)45479 (OAI)
Conference
Symposium on Image Analysis {SSBA}, Linköping, Sweden March 14-15 2007
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-08-28
Brun, A., Westin, C.-F., Herberthson, M. & Knutsson, H. (2007). Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation. In: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007: . Paper presented at IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. Honolulu, HI, USA, APR 15-20, 2007 (pp. III-1053-III-1056). New York, USA: IEEE
Open this publication in new window or tab >>Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation
2007 (English)In: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007, New York, USA: IEEE , 2007, p. III-1053-III-1056Conference paper, Published paper (Refereed)
Abstract [en]

For data samples in Rn, the mean is a well known estimator. When the data set belongs to an embedded manifold M in Rn, e.g. the unit circle in R2, the definition of a mean can be extended and constrained to M by choosing either the intrinsic Riemannian metric of the manifold or the extrinsic metric of the embedding space. A common view has been that extrinsic means are approximate solutions to the intrinsic mean problem. This paper study both means on the unit circle and reveal how they are related to the ML estimate of independent samples generated from a Brownian distribution. The conclusion is that on the circle, intrinsic and extrinsic means are maximum likelihood estimators in the limits of high SNR and low SNR respectively

Place, publisher, year, edition, pages
New York, USA: IEEE, 2007
Series
IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings, ISSN 1520-6149 ; 3
Keywords
Diffusion equations, Maximum likelihood estimation, Signal Processing, Signal representations
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-38748 (URN)10.1109/ICASSP.2007.366864 (DOI)000248906600264 ()45478 (Local ID)1-4244-0727-3 (ISBN)e-1-4244-0728-1 (ISBN)45478 (Archive number)45478 (OAI)
Conference
IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. Honolulu, HI, USA, APR 15-20, 2007
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2015-10-09Bibliographically approved
Brun, A. (2007). Manifolds in Image Science and Visualization. (Doctoral dissertation). : Institutionen för medicinsk teknik
Open this publication in new window or tab >>Manifolds in Image Science and Visualization
2007 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

A Riemannian manifold is a mathematical concept that generalizes curved surfaces to higher dimensions, giving a precise meaning to concepts like angle, length, area, volume and curvature. A glimpse of the consequences of a non-flat geometry is given on the sphere, where the shortest path between two points – a geodesic – is along a great circle. Different from Euclidean space, the angle sum of geodesic triangles on the sphere is always larger than 180 degrees.

Signals and data found in applied research are sometimes naturally described by such curved spaces. This dissertation presents basic research and tools for the analysis, processing and visualization of such manifold-valued data, with a particular emphasis on future applications in medical imaging and visualization.

Two-dimensional manifolds, i.e. surfaces, enter naturally into the geometric modelling of anatomical entities, such as the human brain cortex and the colon. In advanced algorithms for processing of images obtained from computed tomography (CT) and ultrasound imaging (US), images themselves and derived local structure tensor fields may be interpreted as two- or three-dimensional manifolds. In diffusion tensor magnetic resonance imaging (DT-MRI), the natural description of diffusion in the human body is a second-order tensor field, which can be related to the metric of a manifold. A final example is the analysis of shape variations of anatomical entities, e.g. the lateral ventricles in the brain, within a population by describing the set of all possible shapes as a manifold.

Work presented in this dissertation include: Probabilistic interpretation of intrinsic and extrinsic means in manifolds. A Bayesian approach to filtering of vector data, removing noise from sampled manifolds and signals. Principles for the storage of tensor field data and learning a natural metric for empirical data.

The main contribution is a novel class of algorithms called LogMaps, for the numerical estimation of logp (x) from empirical data sampled from a low-dimensional manifold or geometric model embedded in Euclidean space. The logp (x) function has been used extensively in the literature for processing data in manifolds, including applications in medical imaging such as shape analysis. However, previous approaches have been limited to manifolds where closed form expressions of logp (x) have been known. The introduction of the LogMap framework allows for a generalization of the previous methods. The application of LogMaps to texture mapping, tensor field visualization, medial locus estimation and exploratory data analysis is also presented.

Place, publisher, year, edition, pages
Institutionen för medicinsk teknik, 2007. p. 151
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1157
Keywords
manifold learning, image analysis, signal processing, diffusion tensor mri
National Category
Medical Laboratory and Measurements Technologies
Identifiers
urn:nbn:se:liu:diva-10475 (URN)978-91-85715-02-2 (ISBN)
Public defence
2008-01-25, Linden, 421, Universitetssjukhuset i Linköping, Linköping, 10:15 (English)
Opponent
Supervisors
Note
The electronic version is corrected for grammatical and spelling errors.Available from: 2008-03-17 Created: 2008-03-17 Last updated: 2013-08-28
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