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  • 1.
    Curic, Vladimir
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction.
    Angulo, Jesus
    Morphological image regularization using adaptive structuring functionsManuscript (preprint) (Other academic)
  • 2.
    Curic, Vladimir
    et al.
    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.
    Hendriks Luengo, Cris L.
    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.
    Adaptive structuring elements based on salience information2012In: Computer Vision and Graphics / [ed] L. Bolc, K. Wojciechowski, R. Tadeusiewicz, L.J. Chmielewski, Springer, 2012, p. 321-328Conference paper (Other academic)
    Abstract [en]

    Adaptive structuring elements modify their shape and size according to the image content and may outperform fixed structuring elements. Without any restrictions, they suffer from a high computational complexity, which is often higher than linear with respect to the number of pixels in the image. This paper introduces adaptive structuring elements that have predefined shape, but where the size is adjusted to the local image structures. The size of adaptive structuring elements is determined by the salience map that corresponds to the salience of the edges in the image, which can be computed in linear time. We illustrate the difference between the new adaptive structuring elements and morphological amoebas. As an example of its usefulness, we show how the new adaptive morphological operations can isolate the text in historical documents.

  • 3.
    Curic, Vladimir
    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.
    Landström, Anders
    Thurley, Matthew J.
    Luengo Hendriks, Cris L.
    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.
    Adaptive Mathematical Morphology: a survey of the field2014In: Pattern Recognition Letters, ISSN 0167-8655, E-ISSN 1872-7344, Vol. 47, p. 18-28Article in journal (Refereed)
    Abstract [en]

    We present an up-to-date survey on the topic of adaptive mathematical morphology. A broad review of research performed within the field is provided, as well as an in-depth summary of the theoretical advances within the field. Adaptivity can come in many different ways, based on different attributes, measures, and parameters. Similarities and differences between a few selected methods for adaptive structuring elements are considered, providing perspective on the consequences of different types of adaptivity. We also provide a brief analysis of perspectives and trends within the field, discussing possible directions for future studies.

  • 4.
    Curic, Vladimir
    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.
    Lefèvre, Sébastien
    Luengo Hendriks, Cris L.
    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.
    Adaptive hit or miss transform2015In: Mathematical Morphology and Its Applications to Signal and Image Processing, Springer, 2015, p. 741-752Conference paper (Refereed)
    Abstract [en]

    The Hit or Miss Transform is a fundamental morphological operator, and can be used for template matching. In this paper, we present a framework for adaptive Hit or Miss Transform, where structuring elements are adaptive with respect to the input image itself. We illustrate the difference between the new adaptive Hit or Miss Transform and the classical Hit or Miss Transform. As an example of its usefulness, we show how the new adaptive Hit or Miss Transform can detect particles in single molecule imaging.

  • 5.
    Curic, Vladimir
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
    Lindblad, Joakim
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
    Sladoje, Natasa
    Centre for Mathematics and Statistics, Faculty of Technical Sciences, University of Novi Sad, Serbia.
    The Sum of minimal distances as a useful distance measure for image registration2010In: Proceedings SSBA 2010 / [ed] Cris Luengo and Milan Gavrilovic, Uppsala: Centre for Image Analysis , 2010, p. 55-58Conference paper (Other academic)
    Abstract [en]

    In this paper we study set distances which are used in image registration related problems. We introduced a new distance as a Sum of minimal distances with added linear weights. Linear weights are added in a way to reduce the impact of single outliers. An evaluation of observed distances with respect to applicability to image object registration is performed. A comparative study of set distances with respect to noise sensitivity as well as with respect to translation and rotation of objects in image is presented. Based on our experiments on synthetic images containing various types of noise, we determine that the proposed weighted sum of minimal distances has a good performances for object registration.

  • 6.
    Curic, Vladimir
    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.
    Lindblad, Joakim
    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. Faculty of Engineering, University of Novi Sad, Serbia.
    Sladoje, Natasa
    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. University of Novi Sad, Serbia.
    Sarve, Hamid
    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.
    Borgefors, Gunilla
    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 set distance and its application to shape registration2014In: Pattern Analysis and Applications, ISSN 1433-7541, E-ISSN 1433-755X, Vol. 17, no 1, p. 141-152Article in journal (Refereed)
  • 7.
    Curic, Vladimir
    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.
    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.
    Salience-Based Parabolic Structuring Functions2013In: Mathematical Morphology and Its Applications to Signal and Image Processing, Springer Berlin/Heidelberg, 2013, p. 183-194Conference paper (Refereed)
    Abstract [en]

    It has been shown that the use of the salience map based on the salience distance transform can be useful for the construction of spatially adaptive structuring elements. In this paper, we propose salience-based parabolic structuring functions that are defined for a fixed, predefined spatial support, and have low computational complexity. In addition, we discuss how to properly define adjunct morphological operators using the new spatially adaptive structuring functions. It is also possible to obtain flat adaptive structuring elements by thresholding the salience-based parabolic structuring functions.

  • 8.
    Curic, Vladimir
    et al.
    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.
    Luengo Hendriks, Cris L.
    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.
    Borgefors, Gunilla
    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.
    Adaptive structuring elements based on salience distance transform2012In: In Proceedings of Swedish Society for Image Analysis, SSBA 2012, KTH, Stockholm, 2012Conference paper (Other academic)
    Abstract [en]

    Spatially adaptive structuring elements adjust their shape to the local structures in the image, and are often defined by a ball in a geodesic distance or gray-weighted distance metric space. This paper introduces salience adaptive structuring elements as spatially variant structuring elements that modify not only their shape, but also their size according to the salience of the edges in the image. Consequently they have good properties for filtering.

  • 9.
    Curic, Vladimir
    et al.
    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.
    Luengo Hendriks, Cris L.
    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.
    Borgefors, Gunilla
    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.
    Salience adaptive structuring elements2012In: IEEE Journal on Selected Topics in Signal Processing, ISSN 1932-4553, E-ISSN 1941-0484, Vol. 6, no 7, p. 809-819Article in journal (Refereed)
    Abstract [en]

    Spatially adaptive structuring elements adjust their shape to the local structures in the image, and are often defined by a ball in a geodesic distance or gray-weighted distance metric space. This paper introduces salience adaptive structuring elements as spatially variant structuring elements that modify not only their shape, but also their size according to the salience of the edges in the image. Morphological operators with salience adaptive structuring elements shift edges with high salience to a less extent than those with low salience. Salience adaptive structuring elements are less flexible than morphological amoebas and their shape is less affected by noise in the image. Consequently, morphological operators using salience adaptive structuring elements have better properties.

  • 10. Gonzalez-Castro, Victor
    et al.
    Debayle, Johan
    Curic, Vladimir
    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.
    Pixel Classification Using General Adaptive Neighborhood-Based Features2014In: Proceedings 22nd International Conference on Pattern Recognition (ICPR) 2014, 2014, p. 3750-3755Conference paper (Refereed)
    Abstract [en]

    This paper introduces a new descriptor for characterizing and classifying the pixels of texture images by means of General Adaptive Neighborhoods (GANs). The GAN of a pixel is a spatial region surrounding it and fitting its local image structure. The features describing each pixel are then region-based and intensity-based measurements of its corresponding GAN. In addition, these features are combined with the gray-level values of adaptive mathematical morphology operators using GANs as structuring elements. The classification of each pixel of images belonging to five different textures of the VisTex database has been carried out to test the performance of this descriptor. For the sake of comparison, other adaptive neighborhoods introduced in the literature have also been used to extract these features from: the Morphological Amoebas (MA), adaptive geodesic neighborhoods (AGN) and salience adaptive structuring elements (SASE). Experimental results show that the GAN-based method outperforms the others for the performed classification task, achieving an overall accuracy of 97.25% in the five-way classifications, and area under curve values close to 1 in all the five "one class vs. all classes" binary classification problems.

  • 11.
    Jones, Daniel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Leroy, Prune
    Uppsala University, Science for Life Laboratory, SciLifeLab. Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology.
    Unoson, Cecilia
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Microbiology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Fange, David
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Curic, Vladimir
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Lawson, Michael J.
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Elf, Johan
    Uppsala University, Science for Life Laboratory, SciLifeLab. Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology. Uppsala Univ, Dept Cell & Mol Biol, Sci Life Lab, Uppsala, Sweden..
    Kinetics of dCas9 target search in Escherichia coli2017In: Science, ISSN 0036-8075, E-ISSN 1095-9203, Vol. 357, no 6358, p. 1420-1423Article in journal (Refereed)
    Abstract [en]

    How fast can a cell locate a specific chromosomal DNA sequence specified by a single-stranded oligonucleotide? To address this question, we investigate the intracellular search processes of the Cas9 protein, which can be programmed by a guide RNA to bind essentially any DNA sequence. This targeting flexibility requires Cas9 to unwind the DNA double helix to test for correct base pairing to the guide RNA. Here we study the search mechanisms of the catalytically inactive Cas9 (dCas9) in living Escherichia coli by combining single-molecule fluorescence microscopy and bulk restriction-protection assays. We find that it takes a single fluorescently labeled dCas9 6 hours to find the correct target sequence, which implies that each potential target is bound for less than 30 milliseconds. Once bound, dCas9 remains associated until replication. To achieve fast targeting, both Cas9 and its guide RNA have to be present at high concentrations.

  • 12.
    Kipper, Kalle
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Lundius, Ebba G.
    Uppsala University, Science for Life Laboratory, SciLifeLab. Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology.
    Ćurić, Vladimir
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Nikic, Ivana
    European Mol Biol Lab, Cell Biol & Biophys Unit, Struct & Computat Biol Unit, D-69117 Heidelberg, Germany..
    Wiessler, Manfred
    Deutsch Krebsforschungszentrum, Biol Chem, D-69120 Heidelberg, Germany..
    Lemke, Edward A.
    European Mol Biol Lab, Cell Biol & Biophys Unit, Struct & Computat Biol Unit, D-69117 Heidelberg, Germany..
    Elf, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Application of Noncanonical Amino Acids for Protein Labeling in a Genomically Recoded Escherichia coli2017In: ACS Photonics, E-ISSN 2330-4022, Vol. 6, no 2, p. 233-255Article in journal (Refereed)
    Abstract [en]

    Small synthetic fluorophores are in many ways superior to fluorescent proteins as labels for imaging. A major challenge is to use them for a protein-specific labeling in living cells. Here, we report on our use of noncanonical amino acids that are genetically encoded via the pyrrolysyl-tRNA/pyrrolysyl-RNA synthetase pair at artificially introduced TAG codons in a recoded E. coli strain. The strain is lacking endogenous TAG codons and the TAG-specific release factor RF1. The amino acids contain bioorthogonal groups that can be clicked to externally supplied dyes, thus enabling protein-specific labeling in live cells. We find that the noncanonical amino acid incorporation into the target protein is robust for diverse amino acids and that the usefulness of the recoded E. coli strain mainly derives from the absence of release factor RF1. However, the membrane permeable dyes display high nonspecific binding in intracellular environment and the electroporation of hydrophilic nonmembrane permeable dyes severely impairs growth of the recoded strain. In contrast, proteins exposed on the outer membrane of E. coli can be labeled with hydrophilic dyes with a high specificity as demonstrated by labeling of the osmoporin OmpC. Here, labeling can be made sufficiently specific to enable single molecule studies as exemplified by OmpC single particle tracking.

  • 13.
    Lindblad, Joakim
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia.
    Curic, Vladimir
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis.
    Sladoje, Natasa
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Faculty of Technical Sciences, University of Novi Sad.
    On set distances and their application to image registration2009In: Proc. 6th International Symposium on Image and Signal Processing and Analysis, Salzburg, Austria: IEEE , 2009, p. 449-454Conference paper (Refereed)
    Abstract [en]

    In this paper we study set distances that are used in image processing. We propose a generalization of Sum of minimal distances and show that its special cases include a metric by Symmetric difference. The Hausdorff metric and the Chamfer matching distances are also closely related with the presented framework. In addition, we define the Complement set distance of a given distance. We evaluate the observed distance with respect to applicability to image object registration. We perform comparative evaluations with respect to noise sensitivity, as well as with respect to rigid body transformations. We conclude that the family of Generalized sum of minimal distances has many desirable properties for this application.

  • 14.
    Lindblad, Joakim
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
    Sladoje, Natasa
    Curic, Vladimir
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis.
    Sarve, Hamid
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis.
    Johansson, Carina B.
    Borgefors, Gunilla
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis.
    Improved Quantification of Bone Remodelling by Utilizing Fuzzy Based Segmentation2009In: Image Analysis: Proceedings SCIA 2009 / [ed] A.-B. Salberg, J. Y. Hardeberg, R. Jenssen, Berlin: Springer Verlag , 2009, p. 750-759Conference paper (Refereed)
    Abstract [en]

    We present a novel fuzzy theory based method for the segmentation of images required in histomorphometrical investigations of bone implant integration. The suggested method combines discriminant analysis classification controlled by an introduced uncertainty measure, and fuzzy connectedness segmentation method, so that the former is used for automatic seeding of the later. A thorough evaluation of the proposed segmentation method is performed. Comparison with previously published automatically obtained measurements, as well as with manually obtained ones, is presented. The proposed method improves the segmentation and, consequently, the accuracy of the automatic measurements, while keeping advantages with respect to the manual ones, by being fast, repeatable, and objective.

  • 15.
    Lindén, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology.
    Curic, Vladimir
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology.
    Amselem, Elias
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology.
    Elf, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular Systems Biology.
    Pointwise error estimates in localization microscopy2017In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 8, article id 15115Article in journal (Refereed)
    Abstract [en]

    Pointwise localization of individual fluorophores is a critical step in super-resolution localization microscopy and single particle tracking. Although the methods are limited by the localization errors of individual fluorophores, the pointwise localization precision has so far been estimated using theoretical best case approximations that disregard, for example, motion blur, defocus effects and variations in fluorescence intensity. Here, we show that pointwise localization precision can be accurately estimated directly from imaging data using the Bayesian posterior density constrained by simple microscope properties. We further demonstrate that the estimated localization precision can be used to improve downstream quantitative analysis, such as estimation of diffusion constants and detection of changes in molecular motion patterns. Finally, the quality of actual point localizations in live cell super-resolution microscopy can be improved beyond the information theoretic lower bound for localization errors in individual images, by modelling the movement of fluorophores and accounting for their pointwise localization uncertainty.

  • 16.
    Ćurić, Vladimir
    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.
    Distance Functions and Their Use in Adaptive Mathematical Morphology2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    One of the main problems in image analysis is a comparison of different shapes in images. It is often desirable to determine the extent to which one shape differs from another. This is usually a difficult task because shapes vary in size, length, contrast, texture, orientation, etc. Shapes can be described using sets of points, crisp of fuzzy. Hence, distance functions between sets have been used for comparing different shapes.

    Mathematical morphology is a non-linear theory related to the shape or morphology of features in the image, and morphological operators are defined by the interaction between an image and a small set called a structuring element. Although morphological operators have been extensively used to differentiate shapes by their size, it is not an easy task to differentiate shapes with respect to other features such as contrast or orientation. One approach for differentiation on these type of features is to use data-dependent structuring elements.

    In this thesis, we investigate the usefulness of various distance functions for: (i) shape registration and recognition; and (ii) construction of adaptive structuring elements and functions.

    We examine existing distance functions between sets, and propose a new one, called the Complement weighted sum of minimal distances, where the contribution of each point to the distance function is determined by the position of the point within the set. The usefulness of the new distance function is shown for different image registration and shape recognition problems. Furthermore, we extend the new distance function to fuzzy sets and show its applicability to classification of fuzzy objects.

    We propose two different types of adaptive structuring elements from the salience map of the edge strength: (i) the shape of a structuring element is predefined, and its size is determined from the salience map; (ii) the shape and size of a structuring element are dependent on the salience map. Using this salience map, we also define adaptive structuring functions. We also present the applicability of adaptive mathematical morphology to image regularization. The connection between adaptive mathematical morphology and Lasry-Lions regularization of non-smooth functions provides an elegant tool for image regularization.

    List of papers
    1. On set distances and their application to image registration
    Open this publication in new window or tab >>On set distances and their application to image registration
    2009 (English)In: Proc. 6th International Symposium on Image and Signal Processing and Analysis, Salzburg, Austria: IEEE , 2009, p. 449-454Conference paper, Published paper (Refereed)
    Abstract [en]

    In this paper we study set distances that are used in image processing. We propose a generalization of Sum of minimal distances and show that its special cases include a metric by Symmetric difference. The Hausdorff metric and the Chamfer matching distances are also closely related with the presented framework. In addition, we define the Complement set distance of a given distance. We evaluate the observed distance with respect to applicability to image object registration. We perform comparative evaluations with respect to noise sensitivity, as well as with respect to rigid body transformations. We conclude that the family of Generalized sum of minimal distances has many desirable properties for this application.

    Place, publisher, year, edition, pages
    Salzburg, Austria: IEEE, 2009
    National Category
    Computer Vision and Robotics (Autonomous Systems)
    Research subject
    Computerized Image Analysis; Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-110684 (URN)10.1109/ISPA.2009.5297672 (DOI)978-953-184-135-1 (ISBN)
    Conference
    6th International Symposium on Image and Signal Processing and Analysis, Salzburg, Austria, 16-18 September, 2009
    Available from: 2009-11-26 Created: 2009-11-23 Last updated: 2018-12-18
    2. A new set distance and its application to shape registration
    Open this publication in new window or tab >>A new set distance and its application to shape registration
    Show others...
    2014 (English)In: Pattern Analysis and Applications, ISSN 1433-7541, E-ISSN 1433-755X, Vol. 17, no 1, p. 141-152Article in journal (Refereed) Published
    National Category
    Discrete Mathematics
    Identifiers
    urn:nbn:se:uu:diva-220413 (URN)10.1007/s10044-012-0290-x (DOI)000330839400011 ()
    Available from: 2012-08-23 Created: 2014-03-13 Last updated: 2018-12-18Bibliographically approved
    3. Distance measures between digital fuzzy objects and their applicability in image processing
    Open this publication in new window or tab >>Distance measures between digital fuzzy objects and their applicability in image processing
    2011 (English)In: Combinatorial Image Analysis / [ed] Jake Aggarwal, Reneta Barneva, Valentin Brimkov, Kostadin Koroutchev, Elka Koroutcheva, Springer Berlin/Heidelberg, 2011, p. 385-397Conference paper, Published paper (Refereed)
    Abstract [en]

    We present two different extensions of the Sum of minimal distances and the Complement weighted sum of minimal distances to distances between fuzzy sets. We evaluate to what extent the proposed distances show monotonic behavior with respect to increasing translation and rotation of digital objects, in noise free, as well as in noisy conditions. Tests show that one of the extension approaches leads to distances exhibiting very good performance. Furthermore, we evaluate distance based classification of crisp and fuzzy representations of objects at a range of resolutions. We conclude that the proposed distances are able to utilize the additional information available in a fuzzy representation, thereby leading to improved performance of related image processing tasks.

    Place, publisher, year, edition, pages
    Springer Berlin/Heidelberg, 2011
    Series
    Lecture Notes in Computer Science ; 6636
    Keywords
    Fuzzy sets, set distance, registration, classification
    National Category
    Computer Vision and Robotics (Autonomous Systems) Discrete Mathematics
    Research subject
    Computerized Image Analysis; Computerized Image Processing
    Identifiers
    urn:nbn:se:uu:diva-157186 (URN)10.1007/978-3-642-21073-0_34 (DOI)978-3-642-21072-3 (ISBN)
    Conference
    Internatiional Workshop on Combinatorial Image Analysis, IWCIA 2011
    Available from: 2011-08-18 Created: 2011-08-18 Last updated: 2018-12-18
    4. Salience adaptive structuring elements
    Open this publication in new window or tab >>Salience adaptive structuring elements
    2012 (English)In: IEEE Journal on Selected Topics in Signal Processing, ISSN 1932-4553, E-ISSN 1941-0484, Vol. 6, no 7, p. 809-819Article in journal (Refereed) Published
    Abstract [en]

    Spatially adaptive structuring elements adjust their shape to the local structures in the image, and are often defined by a ball in a geodesic distance or gray-weighted distance metric space. This paper introduces salience adaptive structuring elements as spatially variant structuring elements that modify not only their shape, but also their size according to the salience of the edges in the image. Morphological operators with salience adaptive structuring elements shift edges with high salience to a less extent than those with low salience. Salience adaptive structuring elements are less flexible than morphological amoebas and their shape is less affected by noise in the image. Consequently, morphological operators using salience adaptive structuring elements have better properties.

    Keywords
    Adaptive mathematical morphology, anisotropic filtering, morphological amoebas, salience distance transform
    National Category
    Other Mathematics
    Identifiers
    urn:nbn:se:uu:diva-181248 (URN)10.1109/JSTSP.2012.2207371 (DOI)000310138400007 ()
    Available from: 2012-09-20 Created: 2012-09-20 Last updated: 2017-12-07Bibliographically approved
    5. Adaptive structuring elements based on salience information
    Open this publication in new window or tab >>Adaptive structuring elements based on salience information
    2012 (English)In: Computer Vision and Graphics / [ed] L. Bolc, K. Wojciechowski, R. Tadeusiewicz, L.J. Chmielewski, Springer, 2012, p. 321-328Conference paper, Published paper (Other academic)
    Abstract [en]

    Adaptive structuring elements modify their shape and size according to the image content and may outperform fixed structuring elements. Without any restrictions, they suffer from a high computational complexity, which is often higher than linear with respect to the number of pixels in the image. This paper introduces adaptive structuring elements that have predefined shape, but where the size is adjusted to the local image structures. The size of adaptive structuring elements is determined by the salience map that corresponds to the salience of the edges in the image, which can be computed in linear time. We illustrate the difference between the new adaptive structuring elements and morphological amoebas. As an example of its usefulness, we show how the new adaptive morphological operations can isolate the text in historical documents.

    Place, publisher, year, edition, pages
    Springer, 2012
    Series
    Lecture Notes in Computer Science, ISSN 03029743 ; 7594
    National Category
    Other Mathematics Other Computer and Information Science
    Identifiers
    urn:nbn:se:uu:diva-181246 (URN)10.1007/978-3-642-33564-8-39 (DOI)000313005700039 ()978-3-642-33564-8 (ISBN)
    Conference
    International Conference on Computer Vision and Graphics, September 24-26, 2012, Warsaw, Poland
    Available from: 2012-09-20 Created: 2012-09-20 Last updated: 2018-01-12Bibliographically approved
    6. Salience-Based Parabolic Structuring Functions
    Open this publication in new window or tab >>Salience-Based Parabolic Structuring Functions
    2013 (English)In: Mathematical Morphology and Its Applications to Signal and Image Processing, Springer Berlin/Heidelberg, 2013, p. 183-194Conference paper, Published paper (Refereed)
    Abstract [en]

    It has been shown that the use of the salience map based on the salience distance transform can be useful for the construction of spatially adaptive structuring elements. In this paper, we propose salience-based parabolic structuring functions that are defined for a fixed, predefined spatial support, and have low computational complexity. In addition, we discuss how to properly define adjunct morphological operators using the new spatially adaptive structuring functions. It is also possible to obtain flat adaptive structuring elements by thresholding the salience-based parabolic structuring functions.

    Place, publisher, year, edition, pages
    Springer Berlin/Heidelberg, 2013
    Series
    Lecture Notes in Computer Science, ISSN 0302-9743 ; 7883
    National Category
    Other Mathematics
    Research subject
    Mathematics with specialization in Applied Mathematics; Computerized Image Analysis
    Identifiers
    urn:nbn:se:uu:diva-204715 (URN)10.1007/978-3-642-38294-9_16 (DOI)978-3-642-38293-2 (ISBN)
    Conference
    11th International Symposium on Mathematical Morphology
    Available from: 2013-08-09 Created: 2013-08-09 Last updated: 2014-04-29Bibliographically approved
    7. Morphological image regularization using adaptive structuring functions
    Open this publication in new window or tab >>Morphological image regularization using adaptive structuring functions
    (English)Manuscript (preprint) (Other academic)
    National Category
    Other Mathematics
    Identifiers
    urn:nbn:se:uu:diva-221161 (URN)
    Available from: 2014-03-25 Created: 2014-03-25 Last updated: 2014-04-29
    8. Adaptive Mathematical Morphology: a survey of the field
    Open this publication in new window or tab >>Adaptive Mathematical Morphology: a survey of the field
    2014 (English)In: Pattern Recognition Letters, ISSN 0167-8655, E-ISSN 1872-7344, Vol. 47, p. 18-28Article in journal (Refereed) Published
    Abstract [en]

    We present an up-to-date survey on the topic of adaptive mathematical morphology. A broad review of research performed within the field is provided, as well as an in-depth summary of the theoretical advances within the field. Adaptivity can come in many different ways, based on different attributes, measures, and parameters. Similarities and differences between a few selected methods for adaptive structuring elements are considered, providing perspective on the consequences of different types of adaptivity. We also provide a brief analysis of perspectives and trends within the field, discussing possible directions for future studies.

    Keywords
    Overview, Mathematical morphology, Adaptive morphology, Adaptive structuring elements, Adjunction property
    National Category
    Computer Vision and Robotics (Autonomous Systems)
    Identifiers
    urn:nbn:se:uu:diva-221159 (URN)10.1016/j.patrec.2014.02.022 (DOI)000339999200003 ()
    Available from: 2014-03-18 Created: 2014-03-25 Last updated: 2018-01-11Bibliographically approved
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