On the geometry of images

Joel Bosveld

    Research output: ThesisDoctoral Thesis

    77 Downloads (Pure)

    Abstract

    Measurements within the space of images are necessary for many problems in computer vision. Geometry goes beyond measurements and considers the symmetries of the space. We understand images as maps between smooth manifolds and consider Lie groups acting on the domain and codomain. We constrain distances to be invariant to the action and compute the discrepancy: the energy to deform one image to another through the group action.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • The University of Western Australia
    Award date23 Oct 2017
    DOIs
    Publication statusUnpublished - 2017

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    geometry
    computer vision
    symmetry
    energy

    Cite this

    Bosveld, Joel. / On the geometry of images. 2017.
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    title = "On the geometry of images",
    abstract = "Measurements within the space of images are necessary for many problems in computer vision. Geometry goes beyond measurements and considers the symmetries of the space. We understand images as maps between smooth manifolds and consider Lie groups acting on the domain and codomain. We constrain distances to be invariant to the action and compute the discrepancy: the energy to deform one image to another through the group action.",
    keywords = "Geometry, Image space, Computer vision, Discrepancy",
    author = "Joel Bosveld",
    year = "2017",
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    school = "The University of Western Australia",

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    Bosveld, J 2017, 'On the geometry of images', Doctor of Philosophy, The University of Western Australia. https://doi.org/10.4225/23/5a0a5065297b7

    On the geometry of images. / Bosveld, Joel.

    2017.

    Research output: ThesisDoctoral Thesis

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    AB - Measurements within the space of images are necessary for many problems in computer vision. Geometry goes beyond measurements and considers the symmetries of the space. We understand images as maps between smooth manifolds and consider Lie groups acting on the domain and codomain. We constrain distances to be invariant to the action and compute the discrepancy: the energy to deform one image to another through the group action.

    KW - Geometry

    KW - Image space

    KW - Computer vision

    KW - Discrepancy

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    DO - 10.4225/23/5a0a5065297b7

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