liu.seSearch for publications in DiVA
Change search
Link to record
Permanent link

Direct link
BETA
Bigün, Josef
Alternative names
Publications (10 of 13) Show all publications
Bigun, J., Bigun, T. & Nilsson, K. (2003). Orientation fields filtering by derivates of a Gaussian. In: Josef Bigun and Tomas Gustavsson (Ed.), Image Analysis: 13th Scandinavian Conference, SCIA 2003 Halmstad, Sweden, June 29 – July 2, 2003 Proceedings (pp. 307-313). Springer, 2749
Open this publication in new window or tab >>Orientation fields filtering by derivates of a Gaussian
2003 (English)In: Image Analysis: 13th Scandinavian Conference, SCIA 2003 Halmstad, Sweden, June 29 – July 2, 2003 Proceedings / [ed] Josef Bigun and Tomas Gustavsson, Springer, 2003, Vol. 2749, p. 307-313Chapter in book (Refereed)
Abstract [en]

We suggest a set of complex differential operators, symmetry derivatives, that can be used for matching and pattern recognition. We present results on the invariance properties of these. These show that all orders of symmetry derivatives of Gaussians yield a remarkable invariance : they are obtained by replacing the original differential polynomial with the same polynomial but using ordinary scalars. Moreover, these functions are closed under convolution and they are invariant to the Fourier transform. The revealed properties have practical consequences for local orientation based feature extraction. This is shown by two applications: i) tracking markers in vehicle tests ii) alignment of fingerprints.

Place, publisher, year, edition, pages
Springer, 2003
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 2749
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-48573 (URN)10.1007/3-540-45103-X_4 (DOI)3-540-40601-8 (ISBN)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2018-01-30
Bigun, J., Granlund, G. H. & Wiklund, J. (1991). Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Transaction on Pattern Analysis and Machine Intelligence, 13(8), 775-790
Open this publication in new window or tab >>Multidimensional orientation estimation with applications to texture analysis and optical flow
1991 (English)In: IEEE Transaction on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, E-ISSN 1939-3539, Vol. 13, no 8, p. 775-790Article in journal (Refereed) Published
Abstract [en]

The problem of detection of orientation in finite dimensional Euclidean spaces is solved in the least squares sense. In particular, the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n-dimensional Euclidean space. Detection of orientation is shown to correspond to fitting an axis or a plane to the Fourier transform of an n-dimensional structure. The solution of this problem is related to the solution of a well-known matrix eigenvalue problem. Moreover, it is shown that the necessary computations can be performed in the spatial domain without actually doing a Fourier transformation. Along with the orientation estimate, a certainty measure, based on the error of the fit, is proposed. Two applications in image analysis are considered: texture segmentation and optical flow. An implementation for 2-D (texture features) as well as 3-D (optical flow) is presented. In the case of 2-D, the method exploits the properties of the complex number field to by-pass the eigenvalue analysis, improving the speed and the numerical stability of the method. The theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise. The comparative results indicate that the proposed theory produces algorithms computing robust texture features as well as optical flow. The computations are highly parallelizable and can be used in realtime image analysis since they utilize only elementary functions in a closed form (up to dimension 4) and Cartesian separable convolutions.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 1991
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21590 (URN)10.1109/34.85668 (DOI)
Available from: 2009-10-04 Created: 2009-10-04 Last updated: 2018-09-06Bibliographically approved
Bigun, J., Granlund, G. H. & Wiklund, J. (1991). Multidimensional orientation: texture analysis and optical flow. In: Proceedings of the SSAB Symposium on Image Analysis: Stockholm. Paper presented at SSAB symposium on image analysis, 5-7 March, Stockholm (pp. 110-113).
Open this publication in new window or tab >>Multidimensional orientation: texture analysis and optical flow
1991 (English)In: Proceedings of the SSAB Symposium on Image Analysis: Stockholm, 1991, p. 110-113Conference paper, Published paper (Refereed)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21698 (URN)
Conference
SSAB symposium on image analysis, 5-7 March, Stockholm
Available from: 2009-10-08 Created: 2009-10-05 Last updated: 2014-01-28Bibliographically approved
Bigün, J. (1990). A Structure Feature for Some Image Processing Applications Based on Spiral Functions. Computer Vision, Graphics and Image Processing, 51(2), 166-194
Open this publication in new window or tab >>A Structure Feature for Some Image Processing Applications Based on Spiral Functions
1990 (English)In: Computer Vision, Graphics and Image Processing, ISSN 0734-189X, Vol. 51, no 2, p. 166-194Article in journal (Refereed) Published
Abstract [en]

A new low-level vision primitive based on logarithmic spirals is presented for various image processing tasks. The detection of such primitives is equivalent to detection of lines and edges in another coordinate system which has been used to model the mapping of the visual field to the striate cortex. Algorithms detecting the proposed primitives and pointing out a matched subclass are presented along with necessary theory. As a result, if the local structure is describable by the proposed primitives then a certainty parameter based on a well-defined mismatch (error) function will indicate this. Moreover, the best fit of a subclass of the proposed primitives in the least squares sense will be computed. The resulting images are unthresholded. They are computed by means of simple convolutions and pixelwise arithmetic operations which make the algorithms suitable for real time image processing applications. Since the resulting images contain information about the local structure, they can be used as feature images in applications like remote sensing, texture analysis, and object recognition. Experimental results on the latter including synthetic as well as natural images are presented along with noise sensitivity tests. The results exhibit good detection properties for the subclasses of the modeled primitives along with uniform and reliable behavior of the corresponding certainty measures.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21584 (URN)10.1016/0734-189X(90)90029-U (DOI)
Available from: 2009-10-04 Created: 2009-10-04 Last updated: 2009-10-04
Bigün, J. (1988). Local symmetry features in image processing. (Doctoral dissertation). Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Local symmetry features in image processing
1988 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

The extraction of features is necessary for all aspects of image processing and analysis such as classification, segmentation, enhancement and coding. In the course of developing models to describe images, a need arises for description of more complex structures than lines. This need does not reject the importance of line structures but indicates the need to complement and utilize them in a more systematic way.

In this thesis, some new methods for extraction of local symmetry features as well as experimental results and applications are presented. The local images are expanded in terms of orthogonal functions with iso-value curves being harmonic functions. Circular, linear, hyperbolic and parabolic structures are studied in particular and some two-step algorithms involving only convolutions are given for detection purposes. Confidence measures with a reliability verified by both theoretical and experimental studies, are proposed. The method is extended to symmetric patterns fulfilling certain general conditions. It is shown that in the general case the resulting algorithms are implementable through the same computing schemes used for detection of linear structures except for a use of different filters.

Multidimensional linear symmetry is studied and an application problem in 3-D or in particular, optical flow, and the solution proposed by this general framework is presented. The solution results in a closed form algorithm consisting of two steps, in which spatio-temporal gradient and Gaussian filtering are performed. The result consists of an optical flow estimate minimizing the linear symmetry criterion and a confidence measure based on the minimum error. The frequency band sensitivity of the obtained results is found to be possible to control. Experimental results are presented.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1988. p. 104
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 179
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-54889 (URN)91-7870-334-4 (ISBN)
Public defence
1988-05-06, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Available from: 2010-04-19 Created: 2010-04-19 Last updated: 2019-01-08Bibliographically approved
Bigun, J. & Granlund, G. H. (1988). Optical Flow Based on the Inertia Matrix of the Frequency Domain. In: Proceedings from SSAB Symposium on Picture Processing: Lund University, Sweden (pp. 132-135).
Open this publication in new window or tab >>Optical Flow Based on the Inertia Matrix of the Frequency Domain
1988 (English)In: Proceedings from SSAB Symposium on Picture Processing: Lund University, Sweden, 1988, p. 132-135Conference paper, Published paper (Refereed)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21722 (URN)
Available from: 2009-10-25 Created: 2009-10-05 Last updated: 2009-10-25
Bigun, J. (1988). Pattern Recognition by detection of local symmetries. In: E. S. Gelsema and L. N. Kanal (Ed.), Pattern Recognition and Artificial Intelligence: . Paper presented at Proceedings of Pattern Recognition in Practice III, May 18-20, Amsterdam, The Netherlands (pp. 75-90).
Open this publication in new window or tab >>Pattern Recognition by detection of local symmetries
1988 (English)In: Pattern Recognition and Artificial Intelligence / [ed] E. S. Gelsema and L. N. Kanal, 1988, p. 75-90Conference paper, Published paper (Refereed)
Abstract [en]

The symmetries in a neighbourhood of a gray value image are modelled by conjugate harmonic function pairs. These are shown to be a suitable curve linear coordinate pair, in which the model represents a neighbourhood. In this representation the image parts, which are symmetric with respect to the chosen function pair, have iso-gray value curves which are simple lines or parallel line patterns. The detection is modelled in the special Fourier domain corresponding to the new variables by minimizing an error function. It is shown that the  minimization process or detection of these patterns can be carried out for the whole image entirely in the spatial domain by convolutions. What will be defined as the partial derivative image is the image which takes part in the convolution. The convolution kernel is complex valued, as are the partial derivative image and the result. The magnitudes of the result are shown to correspond to a well defined certainty measure, while the orientation is the least square estimate of an orientation in the Fourier transform corresponding to the harmonic coordinates. Applications to four symmetries are given. These are circular, linear, hyperbolic and parabolic symmetries. Experimental results are presented.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21693 (URN)
Conference
Proceedings of Pattern Recognition in Practice III, May 18-20, Amsterdam, The Netherlands
Available from: 2009-10-08 Created: 2009-10-05 Last updated: 2014-01-28Bibliographically approved
Bigun, J. (1988). Recognition of Local Symmetries in Gray Value Images by Harmonic Functions. In: Proceedings of the 9th International Conference on Pattern Recognition, Vol. 1: . Paper presented at 9th International Conference on Pattern Recognition, November 14-17, Rome, Italy (pp. 345-347).
Open this publication in new window or tab >>Recognition of Local Symmetries in Gray Value Images by Harmonic Functions
1988 (English)In: Proceedings of the 9th International Conference on Pattern Recognition, Vol. 1, 1988, p. 345-347Conference paper, Published paper (Refereed)
Abstract [en]

A method for modeling symmetries of the neighborhoods in gray-value images is derived. It is based on the form of the iso-gray-value curves. For every neighborhood a complex number is obtained through a convolution of a complex-valued image with a complex-valued filter. The magnitude of the complex number is the degree of symmetry with respect to the a priori chosen harmonic function pair. The degree of symmetry has a clear definition which is based on the error in the Fourier domain. The argument of the complex number is the angle representing the relative dominance of one of the pair of harmonic functions compared to the other.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21713 (URN)10.1109/ICPR.1988.28238 (DOI)0-8186-0878-1 (ISBN)
Conference
9th International Conference on Pattern Recognition, November 14-17, Rome, Italy
Available from: 2009-10-25 Created: 2009-10-05 Last updated: 2014-01-28Bibliographically approved
Bigun, J. (1987). Optimal Orientation Detection of Linear Symmetry. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Optimal Orientation Detection of Linear Symmetry
1987 (English)Report (Other academic)
Abstract [en]

The problem of optimal detection of orientation in arbitrary neighborhoods is solved in the least squares sense. It is shown that this corresponds to fitting an axis in the Fourier domain of the n-dimensional neighborhood, the solution of which is a well known solution of a matrix eigenvalue problem. The eigenvalues are the variance or inertia with respect to the axes given by their respective eigen vectors. The orientation is taken as the axis given by the least eigenvalue. Moreover it is shown that the necessary computations can be pursued in the spatial domain without doing a Fourier transformation. An implementation for 2-D is presented. Two certainty measures are given corresponding to the orientation estimate. These are the relative or the absolute distances between the two eigenvalues, revealing whether the fitted axis is much better than an axis orthogonal to it. The result of the implementation is verified by experiments which confirm an accurate orientation estimation and reliable certainty measure in the presence of additive noise at high level as well as low levels.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1987. p. 13
Series
LiTH-ISY-I, ISSN 8765-4321 ; 828
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-103805 (URN)L iTH-ISY-I-0828 (ISRN)
Available from: 2014-01-28 Created: 2014-01-28 Last updated: 2014-01-28Bibliographically approved
Bigun, J. & Granlund, G. H. (1987). Optimal Orientation Detection of Linear Symmetry. In: Proceedings of the IEEE First International Conference on Computer Vision: . Paper presented at The IEEE First International Conference on Computer Vision, June 8-11, London, Great Britain (pp. 433-438).
Open this publication in new window or tab >>Optimal Orientation Detection of Linear Symmetry
1987 (English)In: Proceedings of the IEEE First International Conference on Computer Vision, 1987, p. 433-438Conference paper, Published paper (Refereed)
Abstract [en]

The problem of optimal detection of orientation in arbitrary neighborhoods is solved in the least squares sense. It is shown that this corresponds to fitting an axis in the Fourier domain of the n-dimensional neighborhood, the solution of which is a well known solution of a matrix eigenvalue problem. The eigenvalues are the variance or inertia with respect to the axes given by their respective eigen vectors. The orientation is taken as the axis given by the least eigenvalue. Moreover it is shown that the necessary computations can be pursued in the spatial domain without doing a Fourier transformation. An implementation for 2-D is presented. Two certainty measures are given corresponding to the orientation estimate. These are the relative or the absolute distances between the two eigenvalues, revealing whether the fitted axis is much better than an axis orthogonal to it. The result of the implementation is verified by experiments which confirm an accurate orientation estimation and reliable certainty measure in the presence of additive noise at high level as well as low levels.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-51315 (URN)
Conference
The IEEE First International Conference on Computer Vision, June 8-11, London, Great Britain
Available from: 2009-10-26 Created: 2009-10-26 Last updated: 2014-01-14Bibliographically approved
Organisations

Search in DiVA

Show all publications