Growth of discrete projection ghosts created by iteration

Imants Svalbe, Shekhar Chandra

    Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

    5 Citations (Scopus)

    Abstract

    Ghost images find use in synthesizing the content of missing rows of image or projection space from data that contains some deliberate level of information redundancy. Here we examine the properties of ghost images that are constructed through a process of iterated convolution. An initial ghost is propagated by cumulative displacements into other discrete directions to expand the range of angles that have zero-sum projections. The discrete projection scheme used here is the finite Radon transform (FRT). We examine these accumulating ghosts to quantify the growth of their dynamic range of their pixel values and the spread of their spatial extent. After N propagations, a pair of points with intensity A?1 can replicate to produce a maximum total intensity of 2N . For the discrete projections of the FRT, we show that column-oriented iterations better suppress the range and rate of growth of ghost image values. After N row-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.8N . After N column-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.7N . The slower rate of expansion of pixel values for column iteration comes at the expense of fragmenting the compactness of the set of FRT projection angles that are chosen to sum to zero.
    Original languageEnglish
    Title of host publicationDiscrete Geometry for Computer Imagery
    EditorsIsabelle Debled-Rennesson, Eric Domenjoud, Bertrand Kerautret, Philippe Even
    Place of PublicationGermany
    PublisherSpringer
    Pages406 - 416
    Number of pages11
    Volume6607
    ISBN (Print)0302-9743
    DOIs
    Publication statusPublished - 2011
    EventInternational Conference on Discrete Geometry for Computer Imagery 2011 - Nancy, France
    Duration: 6 Apr 20118 Apr 2011
    Conference number: 16th
    http://www.springer.com/gp/book/9783642198663

    Conference

    ConferenceInternational Conference on Discrete Geometry for Computer Imagery 2011
    Abbreviated titleDGCI 2011
    CountryFrance
    CityNancy
    Period6/04/118/04/11
    Internet address

    Cite this

    Svalbe, I., & Chandra, S. (2011). Growth of discrete projection ghosts created by iteration. In I. Debled-Rennesson, E. Domenjoud, B. Kerautret, & P. Even (Eds.), Discrete Geometry for Computer Imagery (Vol. 6607, pp. 406 - 416). Germany: Springer. https://doi.org/10.1007/978-3-642-19867-0_34
    Svalbe, Imants ; Chandra, Shekhar. / Growth of discrete projection ghosts created by iteration. Discrete Geometry for Computer Imagery. editor / Isabelle Debled-Rennesson ; Eric Domenjoud ; Bertrand Kerautret ; Philippe Even. Vol. 6607 Germany : Springer, 2011. pp. 406 - 416
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    title = "Growth of discrete projection ghosts created by iteration",
    abstract = "Ghost images find use in synthesizing the content of missing rows of image or projection space from data that contains some deliberate level of information redundancy. Here we examine the properties of ghost images that are constructed through a process of iterated convolution. An initial ghost is propagated by cumulative displacements into other discrete directions to expand the range of angles that have zero-sum projections. The discrete projection scheme used here is the finite Radon transform (FRT). We examine these accumulating ghosts to quantify the growth of their dynamic range of their pixel values and the spread of their spatial extent. After N propagations, a pair of points with intensity A?1 can replicate to produce a maximum total intensity of 2N . For the discrete projections of the FRT, we show that column-oriented iterations better suppress the range and rate of growth of ghost image values. After N row-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.8N . After N column-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.7N . The slower rate of expansion of pixel values for column iteration comes at the expense of fragmenting the compactness of the set of FRT projection angles that are chosen to sum to zero.",
    author = "Imants Svalbe and Shekhar Chandra",
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    Svalbe, I & Chandra, S 2011, Growth of discrete projection ghosts created by iteration. in I Debled-Rennesson, E Domenjoud, B Kerautret & P Even (eds), Discrete Geometry for Computer Imagery. vol. 6607, Springer, Germany, pp. 406 - 416, International Conference on Discrete Geometry for Computer Imagery 2011, Nancy, France, 6/04/11. https://doi.org/10.1007/978-3-642-19867-0_34

    Growth of discrete projection ghosts created by iteration. / Svalbe, Imants; Chandra, Shekhar.

    Discrete Geometry for Computer Imagery. ed. / Isabelle Debled-Rennesson; Eric Domenjoud; Bertrand Kerautret; Philippe Even. Vol. 6607 Germany : Springer, 2011. p. 406 - 416.

    Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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    AB - Ghost images find use in synthesizing the content of missing rows of image or projection space from data that contains some deliberate level of information redundancy. Here we examine the properties of ghost images that are constructed through a process of iterated convolution. An initial ghost is propagated by cumulative displacements into other discrete directions to expand the range of angles that have zero-sum projections. The discrete projection scheme used here is the finite Radon transform (FRT). We examine these accumulating ghosts to quantify the growth of their dynamic range of their pixel values and the spread of their spatial extent. After N propagations, a pair of points with intensity A?1 can replicate to produce a maximum total intensity of 2N . For the discrete projections of the FRT, we show that column-oriented iterations better suppress the range and rate of growth of ghost image values. After N row-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.8N . After N column-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.7N . The slower rate of expansion of pixel values for column iteration comes at the expense of fragmenting the compactness of the set of FRT projection angles that are chosen to sum to zero.

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    Svalbe I, Chandra S. Growth of discrete projection ghosts created by iteration. In Debled-Rennesson I, Domenjoud E, Kerautret B, Even P, editors, Discrete Geometry for Computer Imagery. Vol. 6607. Germany: Springer. 2011. p. 406 - 416 https://doi.org/10.1007/978-3-642-19867-0_34