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  • 1.
    Asplund, Teo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Precise Image-Based Measurements through Irregular Sampling2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Mathematical morphology is a theory that is applicable broadly in signal processing, but in this thesis we focus mainly on image data. Fundamental concepts of morphology include the structuring element and the four operators: dilation, erosion, closing, and opening. One way of thinking about the role of the structuring element is as a probe, which traverses the signal (e.g. the image) systematically and inspects how well it "fits" in a certain sense that depends on the operator.

    Although morphology is defined in the discrete as well as in the continuous domain, often only the discrete case is considered in practice. However, commonly digital images are a representation of continuous reality and thus it is of interest to maintain a correspondence between mathematical morphology operating in the discrete and in the continuous domain. Therefore, much of this thesis investigates how to better approximate continuous morphology in the discrete domain. We present a number of issues relating to this goal when applying morphology in the regular, discrete case, and show that allowing for irregularly sampled signals can improve this approximation, since moving to irregularly sampled signals frees us from constraints (namely those imposed by the sampling lattice) that harm the correspondence in the regular case. The thesis develops a framework for applying morphology in the irregular case, using a wide range of structuring elements, including non-flat structuring elements (or structuring functions) and adaptive morphology. This proposed framework is then shown to better approximate continuous morphology than its regular, discrete counterpart.

    Additionally, the thesis contains work dealing with regularly sampled images using regular, discrete morphology and weighting to improve results. However, these cases can be interpreted as specific instances of irregularly sampled signals, thus naturally connecting them to the overarching theme of irregular sampling, precise measurements, and mathematical morphology.

    List of papers
    1. Mathematical morphology on irregularly sampled data in one dimension
    Open this publication in new window or tab >>Mathematical morphology on irregularly sampled data in one dimension
    2017 (English)In: Mathematical Morphology - Theory and Applications, ISSN 2353-3390, Vol. 2, no 1, p. 1-24Article in journal (Refereed) Published
    National Category
    Computer Sciences
    Research subject
    Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-337288 (URN)10.1515/mathm-2017-0001 (DOI)
    Funder
    Swedish Research Council, 2014-5983
    Available from: 2017-12-29 Created: 2017-12-21 Last updated: 2019-10-17Bibliographically approved
    2. Mathematical Morphology on Irregularly Sampled Signals
    Open this publication in new window or tab >>Mathematical Morphology on Irregularly Sampled Signals
    2017 (English)In: Computer Vision – ACCV 2016 Workshops. ACCV 2016, Springer, 2017, Vol. 10117, p. 506-520Conference paper, Published paper (Refereed)
    Abstract [en]

    This paper introduces a new operator that can be used to approximate continuous-domain mathematical morphology on irregularly sampled surfaces. We define a new way of approximating the continuous domain dilation by duplicating and shifting samples according to a flat continuous structuring element. We show that the proposed algorithm can better approximate continuous dilation, and that dilations may be sampled irregularly to achieve a smaller sampling without greatly compromising the accuracy of the result.

    Place, publisher, year, edition, pages
    Springer, 2017
    Series
    Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10117
    National Category
    Computer Sciences Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-309921 (URN)10.1007/978-3-319-54427-4_37 (DOI)000426193700037 ()978-3-319-54427-4 (ISBN)978-3-319-54426-7 (ISBN)
    Conference
    13th Asian Conference on Computer Vision (ACCV), Taipei, Taiwan, November 20-24, 2016
    Funder
    Swedish Research Council, 2014-5983
    Available from: 2016-12-08 Created: 2016-12-08 Last updated: 2019-10-17Bibliographically approved
    3. Mathematical Morphology on Irregularly Sampled Data Applied to Segmentation of 3D Point Clouds of Urban Scenes
    Open this publication in new window or tab >>Mathematical Morphology on Irregularly Sampled Data Applied to Segmentation of 3D Point Clouds of Urban Scenes
    Show others...
    2019 (English)In: International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, 2019Conference paper, Published paper (Refereed)
    Abstract [en]

    This paper proposes an extension of mathematical morphology on irregularly sampled signals to 3D point clouds. The proposed method is applied to the segmentation of urban scenes to show its applicability to the analysis of point cloud data. Applying the proposed operators has the desirable side-effect of homogenizing signals that are sampled heterogeneously. In experiments we show that the proposed segmentation algorithm yields good results on the Paris-rue-Madame database and is robust in terms of sampling density, i.e. yielding similar labelings for more sparse samplings of the same scene.

    National Category
    Signal Processing
    Research subject
    Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-388524 (URN)10.1007/978-3-030-20867-7_29 (DOI)978-3-030-20866-0 (ISBN)978-3-030-20867-7 (ISBN)
    Conference
    International Symposium on Mathematical Morphology (ISMM 2019)
    Funder
    Swedish Research Council, 2014-5983
    Available from: 2019-07-01 Created: 2019-07-01 Last updated: 2019-10-17
    4. Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions
    Open this publication in new window or tab >>Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions
    (English)In: Article in journal (Refereed) Submitted
    National Category
    Signal Processing
    Research subject
    Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-395204 (URN)
    Funder
    Swedish Research Council, 2014-5983
    Available from: 2019-10-15 Created: 2019-10-15 Last updated: 2019-10-25
    5. Estimating the Gradient for Images with Missing Samples Using Elliptical Structuring Elements
    Open this publication in new window or tab >>Estimating the Gradient for Images with Missing Samples Using Elliptical Structuring Elements
    (English)In: Article in journal (Refereed) Submitted
    National Category
    Signal Processing
    Research subject
    Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-395200 (URN)
    Funder
    Swedish Research Council, 2014-5983
    Available from: 2019-10-15 Created: 2019-10-15 Last updated: 2019-10-25
    6. A Faster, Unbiased Path Opening by Upper Skeletonization and Weighted Adjacency Graphs
    Open this publication in new window or tab >>A Faster, Unbiased Path Opening by Upper Skeletonization and Weighted Adjacency Graphs
    2016 (English)In: IEEE Transactions on Image Processing, ISSN 1057-7149, E-ISSN 1941-0042, Vol. 25, no 12, p. 5589-5600Article in journal (Refereed) Published
    Abstract [en]

    The path opening is a filter that preserves bright regions in the image in which a path of a certain length L fits. A path is a (not necessarily straight) line defined by a specific adjacency relation. The most efficient implementation known scales as O(min(L, d, Q)N) with the length of the path, L, the maximum possible path length, d, the number of graylevels, Q, and the image size, N. An approximation exists (parsimonious path opening) that has an execution time independent of path length. This is achieved by preselecting paths, and applying 1D openings along these paths. However, the preselected paths can miss important structures, as described by its authors. Here, we propose a different approximation, in which we preselect paths using a grayvalue skeleton. The skeleton follows all ridges in the image, meaning that no important line structures will be missed. An H-minima transform simplifies the image to reduce the number of branches in the skeleton. A graph-based version of the traditional path opening operates only on the pixels in the skeleton, yielding speedups up to one order of magnitude, depending on image size and filter parameters. The edges of the graph are weighted in order to minimize bias. Experiments show that the proposed algorithm scales linearly with image size, and that it is often slightly faster for longer paths than for shorter paths. The algorithm also yields the most accurate results- as compared with a number of path opening variants-when measuring length distributions.

    Keywords
    graph theory, image filtering, transforms, 1D openings, H-minima transform, filter parameters, graph edges, grayvalue skeleton, image analysis, image filtering, image size, unbiased path opening, upper skeletonization, weighted adjacency graphs, Approximation algorithms, Gray-scale, Image edge detection, Length measurement, Periodic structures, Skeleton, Transforms, Path opening, granulometry, image analysis, length distribution, line segment, mathematical morphology, unbiased
    National Category
    Other Computer and Information Science
    Research subject
    Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-309087 (URN)10.1109/TIP.2016.2609805 (DOI)000388205100007 ()
    Funder
    Swedish Research Council, 2014-5983
    Available from: 2016-12-02 Created: 2016-12-02 Last updated: 2019-10-17Bibliographically approved
  • 2.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Bengtsson Bernander, Karl
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Breznik, Eva
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    CNNs on Graphs: A New Pooling Approach and Similarities to Mathematical Morphology2019Conference paper (Other academic)
  • 3.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Luengo, Cris
    Flagship Biosci Inc, Westminster, CO USA.
    Thurley, Matthew
    Lulea Univ Technol, Lulea, Sweden.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    A New Approach to Mathematical Morphology on One Dimensional Sampled Signals2016In: IEEE Proceedings, International Conference on Pattern Recognition (ICPR 2016), Cancun, Mexico, 2016, 2016Conference paper (Refereed)
    Abstract [en]

    We present a new approach to approximate continuous-domain mathematical morphology operators. The approach is applicable to irregularly sampled signals. We define a dilation under this new approach, where samples are duplicated and shifted according to the flat, continuous structuring element. We define the erosion by adjunction, and the opening and closing by composition. These new operators will significantly increase precision in image measurements. Experiments show that these operators indeed approximate continuous-domain operators better than the standard operators on sampled one-dimensional signals, and that they may be applied to signals using structuring elements smaller than the distance between samples. We also show that we can apply the operators to scan lines of a two-dimensional image to filter horizontal and vertical linear structures.

  • 4.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Luengo Hendriks, Cris L.
    Flagship Biosciences Inc, Colorado, USA..
    Thurley, Matthew J.
    Luleå tekniska universitet.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Surgical Sciences, Radiology.
    Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two DimensionsIn: Article in journal (Refereed)
  • 5.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Luengo Hendriks, Cris L.
    Flagship Biosciences Inc, Colorado, USA..
    Thurley, Matthew J.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Surgical Sciences, Radiology.
    Estimating the Gradient for Images with Missing Samples Using Elliptical Structuring ElementsIn: Article in journal (Refereed)
  • 6.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Luengo Hendriks, Cris L.
    Thurley, Matthew J.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Mathematical morphology on irregularly sampled data in one dimension2017In: Mathematical Morphology - Theory and Applications, ISSN 2353-3390, Vol. 2, no 1, p. 1-24Article in journal (Refereed)
  • 7.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Luengo Hendriks, Cris L.
    Flagship Biosciences Inc., Westminster, USA.
    Thurley, Matthew
    Luleå University of Technology, Luleå, Sweden.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Mathematical Morphology on Irregularly Sampled Signals2017In: Computer Vision – ACCV 2016 Workshops. ACCV 2016, Springer, 2017, Vol. 10117, p. 506-520Conference paper (Refereed)
    Abstract [en]

    This paper introduces a new operator that can be used to approximate continuous-domain mathematical morphology on irregularly sampled surfaces. We define a new way of approximating the continuous domain dilation by duplicating and shifting samples according to a flat continuous structuring element. We show that the proposed algorithm can better approximate continuous dilation, and that dilations may be sampled irregularly to achieve a smaller sampling without greatly compromising the accuracy of the result.

  • 8.
    Asplund, Teo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Serna, Andrés
    Terra3D.
    Marcotegui, Beatriz
    MINES ParisTech, PSL Research University, CMM - Centre for Mathematical Morphology.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Surgical Sciences, Radiology.
    Luengo Hendriks, Cris L.
    Flagship Biosciences Inc..
    Mathematical Morphology on Irregularly Sampled Data Applied to Segmentation of 3D Point Clouds of Urban Scenes2019In: International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, 2019Conference paper (Refereed)
    Abstract [en]

    This paper proposes an extension of mathematical morphology on irregularly sampled signals to 3D point clouds. The proposed method is applied to the segmentation of urban scenes to show its applicability to the analysis of point cloud data. Applying the proposed operators has the desirable side-effect of homogenizing signals that are sampled heterogeneously. In experiments we show that the proposed segmentation algorithm yields good results on the Paris-rue-Madame database and is robust in terms of sampling density, i.e. yielding similar labelings for more sparse samplings of the same scene.

1 - 8 of 8
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