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  • 1.
    Andersson, Kenneth
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Andersson, Mats
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization, CMIV.
    Johansson, Peter
    ISY LiTH.
    Forchheimer, Robert
    Linköping University, Department of Electrical Engineering.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization, CMIV.
    Motion compensation using backward prediction and prediction refinement2003In: Signal Processing: Image Communication, ISSN 0923-5965, Vol. 18, no 5, p. 381-400Article in journal (Refereed)
    Abstract [en]

    This paper presents new methods for use of dense motion fields for motion compensation of interlaced video. The motion estimation is based on previously decoded field-images. The motion is then temporally predicted and used for motion compensated prediction of the field-image to be coded. The motion estimation algorithm is phase-based and uses two or three field-images to achieve motion estimates with sub-pixel accuracy. To handle non-constant motion and the specific characteristics of the field-image to be coded, the initially predicted image is refined using forward motion compensation, based on block-matching. Tests show that this approach achieves higher PSNR than forward block-based motion estimation, when coding the residual with the same coder. The subjective performance is also better.

  • 2.
    Andersson, Kenneth
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Andersson, Mats
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    A perception based velocity estimator and its use for motion compensated prediction2001In: SCIA 2001 Scandinavian Conference on Image Analysis,2001, 2001, p. 493-499Conference paper (Refereed)
    Abstract [en]

    The use of temporal redundancy is of vital importance for a successful video coding algorithm. An effective approach is the hybrid video coder where motion estimation is used for prediction of the next image frame and code the prediction error, and the motion field. The standard method for motion estimation is block matching as in MPEG-2, typically resulting in block artifacts. In this paper a perception based velocity estimator and its use for pixel based motion compensated prediction of interlaced video is presented.

  • 3.
    Andersson, Kenneth
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Johansson, Peter
    Linköping University, Department of Electrical Engineering, Image Coding. Linköping University, The Institute of Technology.
    Forchheimer, Robert
    Linköping University, Department of Electrical Engineering, Image Coding. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Backward-forward motion compensated prediction2002In: Proceedings of ACIVS 2002 (Advanced Concepts for Intelligent Vision Systems), Ghent, Belgium, September 9-11, 2002, 2002, p. 260-267Conference paper (Refereed)
    Abstract [en]

    This paper presents new methods for use of dense motion fields for motion compensation of interlaced video. The motion is estimated using previously decoded field-images. An initial motion compensated prediction is produced using the assumption that the motion is predictable in time. The motion estimation algorithm is phase-based and uses two or three field-images to achieve motion estimates with sub-pixel accuracy. To handle non-constant motion and the specific characteristics of the field-image to be coded, the initially predicted image is refined using forward motion compensation, based on block-matching. Tests show that this approach achieves higher PSNR than forward block-based motion estimation, when coding the residual with the same coder. The subjective performance is also better.

  • 4.
    Andersson, Kenneth
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Continuous normalized convolution2002In: Multimedia and Expo, 2002. ICME '02. Proceedings. 2002 IEEE International Conference on  (Volume:1), IEEE , 2002, p. 725-728Conference paper (Refereed)
    Abstract [en]

    The problem of signal estimation for sparsely and irregularly sampled signals is dealt with using continuous normalized convolution. Image values on real-valued positions are estimated using integration of signals and certainties over a neighbourhood employing a local model of both the signal and the used discrete filters. The result of the approach is that an output sample close to signals with high certainty is interpolated using a small neighbourhood. An output sample close to signals with low certainty is spatially predicted from signals in a large neighbourhood.

  • 5.
    Andersson, Kenneth
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Multiple hierarchical motion estimation2002In: Signal Processing, Pattern Recognition, and Applications - 2002 / [ed] M.H. Hamza, ACTA Press, 2002, p. 80-Conference paper (Refereed)
    Abstract [en]

    This paper introduce multiple hierarchical motion estimation to achieve motion estimates with high spatial resolution. The approach is based on phase-based motion estimation. Results show that the algorithm deal with the smooth motion field of hierarchical motion estimation while keeping the advantages of such an approach.

  • 6.
    Andersson, Kenneth
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Westin, Carl-Fredrik
    Laboratory of Mathematics in Imaging, Harvard Medical School, Brigham and Women's Hospital, Boston, USA.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Prediction from off-grid samples using continuous normalized convolution2007In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 87, no 3, p. 353-365Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel method for performing fast estimation of data samples on a desired output grid from samples on an irregularly sampled grid. The output signal is estimated using integration of signals over a neighbourhood employing a local model of the signal using discrete filters. The strength of the method is demonstrated in motion compensation examples by comparing to traditional techniques.

  • 7.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Global search strategies for solving multilinear least-squares problems2012In: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, no 1, p. 12-21Article in journal (Refereed)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

  • 8.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Report (Other academic)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

  • 9.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Report (Other academic)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 10.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, no 2, p. 259-277Article in journal (Refereed)
    Abstract [en]

    Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

    An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 11.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Adaptive Spatio-temporal Filtering of 4D CT-Heart2013In: Image Analyses: Image Processing, Computer Vision, Pattern Recognition, and Graphics / [ed] Joni-Kristian Kämäräinen, Markus Koskela, Berlin Heidelberg: Springer, 2013, p. 246-255Conference paper (Refereed)
    Abstract [en]

    The aim of this project is to keep the x-ray exposure of the patient as low as reasonably achievable while improving the diagnostic image quality for the radiologist. The means to achieve these goals is to develop and evaluate an efficient adaptive filtering (denoising/image enhancement) method that fully explores true 4D image acquisition modes.

    The proposed prototype system uses a novel filter set having directional filter responses being monomials. The monomial filter concept is used both for estimation of local structure and for the anisotropic adaptive filtering. Initial tests on clinical 4D CT-heart data with ECG-gated exposure has resulted in a significant reduction of the noise level and an increased detail compared to 2D and 3D methods. Another promising feature is that the reconstruction induced streak artifacts which generally occur in low dose CT are remarkably reduced in 4D.

  • 12.
    Andersson, Mats
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Controllable 3-D Filters1993In: Proceedings of the SSAB Symposium on Image Analysis: Gothenburg, 1993Conference paper (Refereed)
  • 13.
    Andersson, Mats
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Orientation Estimation in Ambiguous Neighbourhoods1992In: Theory & Applications of Image Analysis: eds P. Johansen and S. Olsen / [ed] P. Johansen and S. Olsen, Singapore: World Scientific Publishing Co , 1992, p. 189-210Chapter in book (Refereed)
  • 14.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Transformation of local spatio-temporal structure tensor fields2003In: Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on  (Volume:3 ), IEEE , 2003, p. 285-288Conference paper (Refereed)
    Abstract [en]

    Tensors and tensor fields are commonly used in multidimensional signal processing to represent the local structure of the signal. This paper focuses on the case where the sampling on the original signal is anisotropic, e.g when the resolution of the multidimensional image varies depending on the direction which is common e.g. in medical imaging devices. To obtain a geometrically correct description of the local structure there are mainly two possibilities. To resample the image prior to the computation of the local structure tensor field or to compute the tensor field on the original grid and transform the result to obtain a correct geometry of the local structure. This paper deals with the latter alternative and contains an in depth theoretical analysis establishing the appropriate rules for tensor transformations induced by changes in space-time geometry with emphasis on velocity and motion estimation.

  • 15.
    Andersson, Mats
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Granlund, Gösta H.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Implementation of Image Processing Operations from Analogue Convolver Responses1989In: Proceedings of the SSAB Conference on Image Analysis: Gothenburg, Sweden, 1989, p. 67-74Conference paper (Refereed)
  • 16.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Kronander, Torbjorn
    Velocity Adaptive Filtered Angiography1999Patent (Other (popular science, discussion, etc.))
    Abstract [en]

    A method of imaging a blood vessel in a body using X-rays and an injectable contrast medium is described. The contrast medium is injected into the body, and signals constituted by an X-ray image sequence depicting X-ray attenuation values is recorded. The X-ray attenuated values in each spaced-time neighborhood are combined in a way that is dependent on the processed image sequence and separately established for each neighborhood, and separating, from background and vessel signals, flow signals having energy contributions mainly in an area of frequency domain bounded by surfaces corresponding to threshold velocities separately established for each neighborhood, which surfaces are shifted a specified amount along a temporal frequency axis.

  • 17.
    Andersson, Mats
    et al.
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Smedby, Örjan
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Medical and Health Sciences, Radiology. Linköping University, Faculty of Health Sciences. Östergötlands Läns Landsting, Center for Diagnostics, Department of Radiology in Linköping.
    Sandborg, Michael
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Medical and Health Sciences, Radiation Physics. Linköping University, Faculty of Health Sciences. Östergötlands Läns Landsting, Center for Surgery, Orthopaedics and Cancer Treatment, Department of Radiation Physics.
    Farnebäck, Gunnar
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Hans, Knutsson
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Adaptiv filtering of 4D-heart CT for image denoising and patient safety2010Conference paper (Other academic)
    Abstract [en]

    The aim of this medical image science project is to increase patient safety in terms of improved image quality and reduced exposure to ionizing radiation in CT. The means to achieve these goals is to develop and evaluate an efficient adaptive filtering (denoising/image enhancement) method that fully explores true 4D image acquisition modes. Four-dimensional (4D) medical image data are captured as a time sequence of image volumes. During 4D image acquisition, a 3D image of the patient is recorded at regular time intervals. The resulting data will consequently have three spatial dimensions and one temporal dimension. Increasing the dimensionality of the data impose a major increase the computational demands. The initial linear filtering which is the cornerstone in all adaptive image enhancement algorithms increase exponentially with the dimensionality. On the other hand the potential gain in Signal to Noise Ratio (SNR) also increase exponentially with the dimensionality. This means that the same gain in noise reduction that can be attained by performing the adaptive filtering in 3D as opposed to 2D can be expected to occur once more by moving from 3D to 4D. The initial tests on on both synthetic and clinical 4D images has resulted in a significant reduction of the noise level and an increased detail compared to 2D and 3D methods. When tuning the parameters for adaptive filtering is extremely important to attain maximal diagnostic value which not necessarily coincide with an an eye pleasing image for a layman. Although this application focus on CT the resulting adaptive filtering methods will be beneficial for a wide range of 3D/4D medical imaging modalities e.g. shorter acquisition time in MRI and improved elimination of noise in 3D or 4D ultrasound datasets.

  • 18.
    Andersson, Mats T.
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Controllable 3-D Filters for Low Level Computer Vision1993In: SCIA8: Tromso, 1993Conference paper (Refereed)
    Abstract [en]

    Three-dimensional data processing is becoming more and more common. Typical operations are for example estimation of optical flow in video sequences and orientation estimation in 3-D MR images. This paper proposes an efficient approach to robust low level feature extraction for 3-D image analysis. In contrast to many earlier algorithms the methods proposed in this paper support the use of relatively complex models at the initial processing steps. The aim of this approach is to provide the means to handle complex events at the initial processing steps and to enable reliable estimates in the presence of noise. A limited basis filter set is proposed which forms a basis on the unit sphere and is related to spherical harmonics. From these basis filters, different types of orientation selective filters are synthesized. An interpolation scheme that provides a rotation as well as a translation of the synthesized filter is presented. The purpose is to obtain a robust and invariant feature extraction at a manageable computational cost.

  • 19.
    Andersson, Mats T.
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Controllable 3-D Filters for Low Level Computer Vision1993Report (Other academic)
    Abstract [en]

    Three-dimensional data processing is becoming more and more common. Typical operations are for example estimation of optical flow in video sequences and orientation estimation in 3-D MR images. This paper proposes an efficient approach to robust low level feature extraction for 3-D image analysis. In contrast to many earlier algorithms the methods proposed in this paper support the use of relatively complex models at the initial processing steps. The aim of this approach is to provide the means to handle complex events at the initial processing steps and to enable reliable estimates in the presence of noise. A limited basis filter set is proposed which forms a basis on the unit sphere and is related to spherical harmonics. From these basis filters, different types of orientation selective filters are synthesized. An interpolation scheme that provides a rotation as well as a translation of the synthesized filter is presented. The purpose is to obtain a robust and invariant feature extraction at a manageable computational cost.

  • 20.
    Andersson, Mats T.
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Orientation Estimation in Ambiguous Neighbourhoods1991In: Proceedings of SCIA91: Aalborg, Denmark, 1991Conference paper (Refereed)
    Abstract [en]

    This paper describes a new algorithm for local orientation estimation. The proposed algorithm detects and separates interfering events in ambiguous neighbourhoods and produces robust estimates of the two most dominant events. A representation suitable for simultaneous representation of two orientations is introduced. The main purpose of this representation is to make averaging of outputs for neigbourhoods containing two orientations possible. The feature extraction is performed by a set of quadrature filters. A method to obtain a large set of quadrature filter responses from a limited basis filter set is introduced. The estimation of the neighbourhood and the separation of the present events are based upon the quadrature responses in terms of local magnitude and phase. The performance of the algorithm is demonstrated using test images.

  • 21.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Wiklund, Johan
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Filter Networks1999In: Proceedings of Signal and Image Processing (SIP'99), Nassau, Bahamas: IASTED , 1999, p. 213-217Conference paper (Refereed)
    Abstract [en]

    This paper presents a new and efficient approach for optimization and implementation of filter banks e.g. velocity channels, orientation channels and scale spaces. The multi layered structure of a filter network enable a powerful decomposition of complex filters into simple filter components and the intermediary results may contribute to several output nodes. Compared to a direct implementation a filter network uses only a fraction of the coefficients to provide the same result. The optimization procedure is recursive and all filters on each level are optimized simultaneously. The individual filters of the network, in general, contain very few non-zero coefficients, but there are are no restrictions on the spatial position of the coefficients, they may e.g. be concentrated on a line or be sparsely scattered. An efficient implementation of a quadrature filter hierarchy for generic purposes using sparse filter components is presented.

  • 22.
    Andersson, Mats
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Wiklund, Johan
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Sequential Filter Trees for Efficient 2D 3D and 4D Orientation Estimation1998Report (Other academic)
    Abstract [en]

    A recursive method to condense general multidimensional FIR-filters into a sequence of simple kernels with mainly one dimensional extent has been worked out. Convolver networks adopted for 2, 3 and 4D signals is presented and the performance is illustrated for spherically separable quadrature filters. The resulting filter responses are mapped to a non biased tensor representation where the local tensor constitutes a robust estimate of both the shape and the orientation (velocity) of the neighbourhood. A qualitative evaluation of this General Sequential Filter concept results in no detectable loss in accuracy when compared to conventional FIR (Finite Impulse Response) filters but the computational complexity is reduced several orders in magnitude. For the examples presented in this paper the attained speed-up is 5, 25 and 300 times for 2D, 3D and 4D data respectively The magnitude of the attained speed-up implies that complex spatio-temporal analysis can be performed using standard hardware, such as a powerful workstation, in close to real time. Due to the soft implementation of the convolver and the tree structure of the sequential filtering approach the processing is simple to reconfigure for the outer as well as the inner (vector length) dimensionality of the signal. The implementation was made in AVS (Application Visualization System) using modules written in C.

  • 23.
    Borga, Magnus
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Andersson, Mats
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Generation of representations for supervised learning - A velocity estimation example2001In: SCIA 2001,2001, 2001Conference paper (Refereed)
  • 24.
    Borga, Magnus
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Friman, Ola
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Lundberg, Peter
    Linköping University, Department of Medical and Health Sciences, Radiation Physics. Linköping University, Faculty of Health Sciences. Östergötlands Läns Landsting, Center for Surgery, Orthopaedics and Cancer Treatment, Department of Radiation Physics.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    A canonical correlation approach to exploratory data analysis in fMRI2002Conference paper (Other academic)
    Abstract [en]

    A computationally efficient data-driven method for exploratory analysis of functional MRI data is presented. The basic idea is to reveal underlying components in the fMRI data that have maximum autocorrelation. The tool for accomplishing this task is Canonical Correlation Analysis. The proposed method is more robust and much more computationally efficient than independent component analysis, which previously has been applied in fMRI.

  • 25.
    Borga, Magnus
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Friman, Ola
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Lundberg, Peter
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Medical and Health Sciences, Radiology. Linköping University, Faculty of Health Sciences.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Blind Source Separation of Functional MRI Data2002Conference paper (Other academic)
  • 26.
    Borga, Magnus
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    A Binary Competition Tree for Reinforcement Learning1994Report (Other academic)
    Abstract [en]

    A robust, general and computationally simple reinforcement learning system is presented. It uses a channel representation which is robust and continuous. The accumulated knowledge is represented as a reward prediction function in the outer product space of the input- and output channel vectors. Each computational unit generates an output simply by a vector-matrix multiplication and the response can therefore be calculated fast. The response and a prediction of the reward are calculated simultaneously by the same system, which makes TD-methods easy to implement if needed. Several units can cooperate to solve more complicated problems. A dynamic tree structure of linear units is grown in order to divide the knowledge space into a sufficiently number of regions in which the reward function can be properly described. The tree continuously tests split- and prune criteria in order to adapt its size to the complexity of the problem.

  • 27.
    Borga, Magnus
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    A canonical correlation approach to blind source separation2001Report (Other academic)
  • 28.
    Borga, Magnus
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    An Adaptive Stereo Algorithm Based on Canonial Correlation Analysis1998Conference paper (Refereed)
    Abstract [en]

    This paper presents a novel algorithm that uses CCA and phase analysis to detect the disparity in stereo images. The algorithm adapts filters in each local neighbourhood of the image in a way which maximizes the correlation between the filtered images. The adapted filters are then analysed to find the disparity. This is done by a simple phase analysis of the scalar product of the filters. The algorithm can even handle cases where the images have different scales. The algorithm can also handle depth discontinuities and give multiple depth estimates for semitransparent images.

  • 29.
    Borga, Magnus
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    An Adaptive Stereo Algorithm Based on Canonical Correlation Analysis1998In: Proceedings of the Second IEEE International Conference on Intelligent Processing Systems: Gold Coast, Austalia, 1998, p. 177-182Conference paper (Refereed)
    Abstract [en]

    This paper presents a novel algorithm that uses CCA and phase analysis to detect the disparity in stereo images. The algorithm adapts filters in each local neighbourhood of the image in a way which maximizes the correlation between the filtered images. The adapted filters are then analyzed to find the disparity. This is done by a simple phase analysis of the scalar product of the filters. The algorithm can even handle cases where the images have different scales. The algorithm can also handle depth discontinuities and give multiple depth estimates for semi-transparent images.

  • 30.
    Borga, Magnus
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    An Adaptive Stereo Algorithm Based on Canonical Correlation Analysis1998Report (Other academic)
  • 31.
    Borga, Magnus
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Canonical correlation analysis in early version processing2001In: European Symposium on Artificial neural Networks ESANN,2001, 2001Conference paper (Refereed)
  • 32.
    Borga, Magnus
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Estimating Multiple Depths in Semi-transparent Stereo Images1999In: Proceedings of the 11th Scandinavian Conference on Image Analysis, 1999Conference paper (Refereed)
    Abstract [en]

    A stereo algorithm that can estimate multiple depths in semi-transparent images is presented. The algorithm is based on a combination of phase analysis and canonical correlation analysis. The algorithm adapts filters in each local neighbourhood of the image in a way which maximizes the correlation between the filtered images. The adapted filters are then analysed to find the disparity. This is done by a simple phase analysis of the scalar product of the filters. For images with different but constant depths, a simple reconstruction procedure is suggested.

  • 33.
    Borga, Magnus
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Finding Efficient Nonlinear Visual Operators using Canonical Correlation Analysis2000In: Proceedings of the SSAB Symposium on Image Analysis: Halmstad, Linköping: Linköpings universitet , 2000, p. 13-16Conference paper (Refereed)
    Abstract [en]

    This paper presents a general strategy for designing efficient visual operators. The approach is highly task oriented and what constitutes the relevant information is defined by a set of examples. The examples are pairs of images displaying a strong dependence in the chosen feature but are otherwise independent. Particularly important concepts in the work are mutual information and canonical correlation. Visual operators learned from examples are presented, e.g. local shift invariant orientation operators and image content invariant disparity operators. Interesting similarities to biological vision functions are observed.

  • 34.
    Borga, Magnus
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Landelius, Tomas
    n/a.
    Learning Canonical Correlations1997In: SCIA10: Lappeenranta, Finland, 1997Conference paper (Refereed)
  • 35.
    Borga, Magnus
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Landelius, Tomas
    n/a.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    A Unified Approach to PCA, PLS, MLR and CCA1997Report (Other academic)
    Abstract [en]

    This paper presents a novel algorithm for analysis of stochastic processes. The algorithm can be used to find the required solutions in the cases of principal component analysis (PCA), partial least squares (PLS), canonical correlation analysis (CCA) or multiple linear regression (MLR). The algorithm is iterative and sequential in its structure and uses on-line stochastic approximation to reach an equilibrium point. A quotient between two quadratic forms is used as an energy function and it is shown that the equilibrium points constitute solutions to the generalized eigenproblem.

  • 36.
    Borga, Magnus
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Malmgren, Helge
    Dept of Philosophy Göteborgs universitet.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics.
    Feature selective edge detektion2000In: International Conference on Pattern Recognition,2000, IEEE , 2000, p. 229-232 vol.1Conference paper (Refereed)
    Abstract [en]

    We present a method that finds edges between certain image features, e.g. gray-levels, and disregards edges between other features. The method uses a channel representation of the features and performs normalized convolution using the channel values as certainties. This means that areas with certain features can be disregarded by the edge filter. The method provides an important tool for finding tissue specific edges in medical images, as demonstrated by an MR-image example

  • 37.
    Borga, Magnus
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Malmgren, Helge
    n/a.
    Knutsson, Hans
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    FSED - Feature Selective Edge Detection2000In: ICPR15: Barcelona, Spain, IEEE , 2000, Vol. 1, p. 229-232 vol.1Conference paper (Refereed)
    Abstract [en]

    We present a novel method that finds edges between certain image features, e.g. gray-levels, and disregards edges between other features. The method uses a channel representation of the features and performs normalized convolution using the channel values as certainties. This means that areas with certain features can be disregarded by the edge filter. The method provides an important new tool for finding tissue specific edges in medical images, as demonstrated by an MR-image example.

  • 38.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Tensor Glyph Warping - Visualizing Metric Tensor Fields using Riemannian Exponential Maps2009In: 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. 

  • 39.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Park, Hae-Jeong
    Clinical Neuroscience Division, Laboratory of Neuroscience, Boston VA, USA Health Care System-Brockton Division, Department of Psychiatry, Harvard Medical School, Boston, MA, USA.
    Shenton, Martha E.
    Clinical Neuroscience Division, Laboratory of Neuroscience, Boston VA, USA Health Care System-Brockton Division, Department of Psychiatry, Harvard Medical School, Boston, MA, USA.
    Westin, Carl-Fredrik
    Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
    Clustering Fiber Traces Using Normalized Cuts2004In: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004: 7th International Conference, Saint-Malo, France, September 26-29, 2004. Proceedings, Part I, Springer Berlin/Heidelberg, 2004, p. 368-375Conference paper (Refereed)
    Abstract [en]

    In this paper we present a framework for unsupervised segmentation of white matter fiber traces obtained from diffusion weighted MRI data. Fiber traces are compared pairwise to create a weighted undirected graph which is partitioned into coherent sets using the normalized cut (Ncut) criterion. A simple and yet effective method for pairwise comparison of fiber traces is presented which in combination with the Ncut criterion is shown to produce plausible segmentations of both synthetic and real fiber trace data. Segmentations are visualized as colored stream-tubes or transformed to a segmentation of voxel space, revealing structures in a way that looks promising for future explorative studies of diffusion weighted MRI data.

  • 40.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV). Centre for Image Analysis, SLU, Uppsala, Sweden.
    Martin-Fernandez, Marcos
    Universidad de Valladolid Laboratorio de Procesado de Imagen (LPI), Dept. Teoría de la Señal y Comunicaciones e Ingeniería Telemática Spain.
    Acar, Burac
    Boğaziçi University 5 Electrical & Electronics Engineering Department Istanbul Turkey.
    Munoz-Moreno, Emma
    Universidad de Valladolid Laboratorio de Procesado de Imagen (LPI), Dept. Teoría de la Señal y Comunicaciones e Ingeniería Telemática Spain.
    Cammoun, Leila
    Signal Processing Institute (ITS), Ecole Polytechnique Fédérale Lausanne (EPFL) Lausanne Switzerland.
    Sigfridsson, Andreas
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV). Center for Technology in Medicine, Dept. Señales y Comunicaciones, University of Las Palmas de Gran Canaria, Spain.
    Sosa-Cabrera, Dario
    Center for Technology in Medicine, Dept. Señales y Comunicaciones, University of Las Palmas de Gran Canaria, Spain.
    Svensson, Björn
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Similar Tensor Arrays - A Framework for Storage of Tensor Array Data2009In: 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.

  • 41.
    Brun, Anders
    et al.
    Centre for Image Analysis, Swedish University of Agricultural Sciences, Sweden.
    Nilsson, Ola
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Reimers, Martin
    Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway.
    Museth, Ken
    Linköping University, Department of Science and Technology, Digital Media. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Computing Riemannian Normal Coordinates on Triangle MeshesManuscript (preprint) (Other academic)
    Abstract [en]

    Imagine an ant walking around on the curved surface of a plant, a radio amateur planning to broadcast to a distant location across the globe or a pilot taking o from an airport - all of them are helped by egocentric maps of the world around them that shows directions and distances to various remote places. It is not surprising that this idea has already been used in cartography, where it is known as Azimuthal Equidistant Projection (AEP). If Earth is approximated by a sphere, distances and directions between two places are computed from arcs along great circles. In physics and mathematics, the same idea is known as Riemannian Normal Coordinates (RNC). It has been given a precise and general denition for surfaces (2-D), curved spaces (3-D) and generalized to smooth manifolds (N-D). RNC are the Cartesian coordinates of vectors that index points on the surface (or manifold) through the so called exponential map, which is a well known concept in dierential geometry. They are easily computed for a particular point if the inverse of the exponential map, the logarithm map, is known. Recently, RNC and similar coordinate systems have been used in computer graphics, visualization and related areas of research. In Fig. 1 for instance, RNC are used to produce a texture on the Stanford bunny through decal compositing. Given the growing use of RNC, which is further elaborated on in the next section, it is meaningful to develop accurate and reproducible techniques to compute this parameterization. In this paper, we describe a technique to compute RNC for surfaces represented by triangular meshes, which is the predominant representation of surfaces in computer graphics. The method that we propose has similarities to the Logmap framework, which has previously been developed for dimension reduction of unorganized point clouds in high-dimensional spaces, a.k.a. manifold learning. For this reason we sometimes refer to it as "Logmap for triangular meshes" or simply Logmap.

  • 42.
    Brun, Anders
    et al.
    Laboratory of Mathematics in Imaging, Brigham and Women’s Hospital, Harvard Medical School, Boston, USA .
    Park, Hae-Jeong
    Clinical Neuroscience Div., Lab. of Neuroscience, Boston VA Health Care System-Brockton Division, Dep. of Psychiatry, Harvard Medical School, and Surgical Planning Laboratory, Brigham and Women’s Hospital, Harvard Medical School, .
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl-Fredrik
    Laboratory of Mathematics in Imaging, Brigham and Women’s Hospital, Harvard Medical School, Boston, USA .
    Coloring of DT-MRI fiber traces using Laplacian Eigenmaps2003In: Computer Aided Systems Theory - EUROCAST 2003: 9th International Workshop on Computer Aided Systems Theory Las Palmas de Gran Canaria, Spain, February 24-28, 2003 Revised Selected Papers / [ed] Roberto Moreno-Díaz and Franz Pichler, Springer Berlin/Heidelberg, 2003, Vol. 2809, p. 518-529Conference paper (Refereed)
    Abstract [en]

    We propose a novel post processing method for visualization of fiber traces from DT-MRI data. Using a recently proposed non-linear dimensionality reduction technique, Laplacian eigenmaps [3], we create a mapping from a set of fiber traces to a low dimensional Euclidean space. Laplacian eigenmaps constructs this mapping so that similar traces are mapped to similar points, given a custom made pairwise similarity measure for fiber traces. We demonstrate that when the low-dimensional space is the RGB color space, this can be used to visualize fiber traces in a way which enhances the perception of fiber bundles and connectivity in the human brain.

  • 43.
    Brun, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Svensson, Björn
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl-Fredrik
    Herberthson, Magnus
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Wrangsjö, Andreas
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Filtering Vector-Valued Images using Importance Sampling2007In: Proceedings of the {SSBA} Symposium on Image Analysis,2007, 2007Conference paper (Other academic)
  • 44.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Svensson, Björn
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Westin, Carl-Fredrik
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Wrangsjö, Andreas
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Using Importance Sampling for Bayesian Feature Space Filtering2007In: Proceedings of the 15th Scandinavian conference on image analysis / [ed] Kjær Bjarne Ersbøll and Kim Steenstrup Pedersen, Berlin, Heidelberg: Springer-Verlag , 2007, p. 818-827Conference paper (Refereed)
    Abstract [en]

    We present a one-pass framework for filtering vector-valued images and unordered sets of data points in an N-dimensional feature space. It is based on a local Bayesian framework, previously developed for scalar images, where estimates are computed using expectation values and histograms. In this paper we extended this framework to handle N-dimensional data. To avoid the curse of dimensionality, it uses importance sampling instead of histograms to represent probability density functions. In this novel computational framework we are able to efficiently filter both vector-valued images and data, similar to e.g. the well-known bilateral, median and mean shift filters.

  • 45.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl_Fredrik
    Haker, S.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    A novel approach to averaging, filtering and interpolation of 3-D object orientation data2004In: Proceedings of the Swedish Symposium on Image Analysis (2004), 2004, p. 5-8Conference paper (Other academic)
  • 46.
    Brun, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
    Westin, Carl-Fredrik
    Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
    Haker, Steven
    Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    A tensor-like representation for averaging, filtering and interpolation of 3D object orientation data2005In: Image Processing, 2005. ICIP 2005. IEEE International Conference on  (Volume:3 ), 2005, p. 1092-1095Conference paper (Refereed)
    Abstract [en]

    Averaging, filtering and interpolation of 3-D object orientation data is important in both computer vision and computer graphics, for instance to smooth estimates of object orientation and interpolate between keyframes in computer animation. In this paper we present a novel framework in which the non-linear nature of these problems is avoided by embedding the manifold of 3-D orientations into a 16-dimensional Euclidean space. Linear operations performed in the new representation can be shown to be rotation invariant, and defining a projection back to the orientation manifold results in optimal estimates with respect to the Euclidean metric. In other words, standard linear filters, interpolators and estimators may be applied to orientation data, without the need for an additional machinery to handle the non-linear nature of the problems. This novel representation also provides a way to express uncertainty in 3-D orientation, analogous to the well known tensor representation for lines and hyperplanes.

  • 47.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl-Fredrik
    Laboratory of Mathematics in Imaging Harvard Medical School, Boston, USA.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Fast manifold learning based on Riemannian normal coordinates2005In: Image Analysis: 14th Scandinavian Conference, SCIA 2005, Joensuu, Finland, June 19-22, 2005. Proceedings / [ed] Heikki Kalviainen, Jussi Parkkinen, Arto Kaarna., Springer Berlin/Heidelberg, 2005, p. 920-Conference paper (Refereed)
    Abstract [en]

    We present a novel method for manifold learning, i.e. identification of the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space. The main idea is derived from the concept of Riemannian normal coordinates. This coordinate system is in a way a generalization of Cartesian coordinates in Euclidean space. We translate this idea to a cloud of data points in order to perform dimension reduction. Our implementation currently uses Dijkstra’s algorithm for shortest paths in graphs and some basic concepts from differential geometry. We expect this approach to open up new possibilities for analysis of e.g. shape in medical imaging and signal processing of manifold-valued signals, where the coordinate system is “learned” from experimental high-dimensional data rather than defined analytically using e.g. models based on Lie-groups.

  • 48.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Westin, Carl-Fredrik
    Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
    Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation2007In: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007, New York, USA: IEEE , 2007, p. III-1053-III-1056Conference 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

  • 49.
    Brun, Anders
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl-Fredrik
    Lab of Mathematics in Imaging Harvard Medical School, Boston, USA.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    LOGMAP: Preliminary results using a new method for manifold learning2005In: Symposium on Image Analysis SSBA,2005, 2005, p. 101-105Conference paper (Other academic)
  • 50.
    Brun, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl-Fredrik
    Harvard Medical School Boston.
    Herberthson, Magnus
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Knutsson, Hans
    Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Sample Logmaps - Intrinsic processing of empirical manifold data2006In: SSBA Symposium on Image Analysis,2006, 2006, p. 13-16Conference paper (Other academic)
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