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  • 1.
    Bigun, Josef
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Optimal Orientation Detection of Linear Symmetry1987Report (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.

  • 2.
    Bigun, Josef
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Pattern Recognition by detection of local symmetries1988In: Pattern Recognition and Artificial Intelligence / [ed] E. S. Gelsema and L. N. Kanal, 1988, p. 75-90Conference 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.

  • 3.
    Bigun, Josef
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Recognition of Local Symmetries in Gray Value Images by Harmonic Functions1988In: Proceedings of the 9th International Conference on Pattern Recognition, Vol. 1, 1988, p. 345-347Conference 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.

  • 4.
    Bigun, Josef
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Some Mathematical Tools of Computers for Vision Purposes1987In: Proceedings of the 7th Nordic Conference on Teaching of Matematics at Technical Universities: Aalborg University, Denmark, 1987Conference paper (Refereed)
  • 5.
    Bigun, Josef
    et al.
    Halmstad University.
    Bigun, Tomas
    TietoEnator ArosTech, Linköping.
    Nilsson, Kenneth
    Halmstad University.
    Orientation fields filtering by derivates of a Gaussian2003In: 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.

  • 6.
    Bigun, Josef
    et al.
    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.
    Central Symmetry Modelling1986Report (Other academic)
    Abstract [en]

    A definition of central symmetry for local neighborhoods of 2-D images is given. A complete ON-set of centrally symmetric basis functions is proposed. The local neighborhoods are expanded in this basis. The behavior of coefficient spectrum obtained by this expansion is proposed to be the foundation of central symmetry parameters of the neighbqrhoods. Specifically examination of two such behaviors are proposed: Point concentration and line concentration of the energy spectrum. Moreover, the study of these types of behaviors of the spectrum are shown to be possible to do in the spatial domain.

  • 7.
    Bigun, Josef
    et al.
    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.
    Central Symmetry Modelling1986In: Proceedings of EUSIPCO-86, Third European Signal Processing Conference / [ed] Ian T. Young, 1986, p. 883-886Conference paper (Refereed)
    Abstract [en]

    A definition of central symmetry for local neighborhoods of 2-D images is given. A complete ON-set of centrally symmetric basis functions is proposed. The local neighborhoods are expanded in this basis. The behavior of coefficient spectrum obtained by this expansion is proposed to be the foundation of central symmetry parameters of the neighbqrhoods. Specifically examination of two such behaviors are proposed: Point concentration and line concentration of the energy spectrum. Moreover, the study of these types of behaviors of the spectrum are shown to be possible to do in the spatial domain.

  • 8.
    Bigun, Josef
    et al.
    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.
    Optical Flow Based on the Inertia Matrix of the Frequency Domain1988In: Proceedings from SSAB Symposium on Picture Processing: Lund University, Sweden, 1988, p. 132-135Conference paper (Refereed)
  • 9.
    Bigun, Josef
    et al.
    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.
    Optimal Orientation Detection of Linear Symmetry1987In: Proceedings of the IEEE First International Conference on Computer Vision, 1987, p. 433-438Conference 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.

  • 10.
    Bigun, Josef
    et al.
    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.
    Wiklund, Johan
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Multidimensional orientation estimation with applications to texture analysis and optical flow1991In: 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)
    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.

  • 11.
    Bigun, Josef
    et al.
    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.
    Wiklund, Johan
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Multidimensional orientation: texture analysis and optical flow1991In: Proceedings of the SSAB Symposium on Image Analysis: Stockholm, 1991, p. 110-113Conference paper (Refereed)
  • 12.
    Bigün, Josef
    Linköping University, Department of Electrical Engineering, Computer Vision . Linköping University, The Institute of Technology.
    A Structure Feature for Some Image Processing Applications Based on Spiral Functions1990In: Computer Vision, Graphics and Image Processing, ISSN 0734-189X, Vol. 51, no 2, p. 166-194Article in journal (Refereed)
    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.

  • 13.
    Bigün, Josef
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Local symmetry features in image processing1988Doctoral 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.

1 - 13 of 13
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  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • en-GB
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  • nn-NO
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