Title page for etd-0617102-105736


[Back to Results | New Search]

URN etd-0617102-105736
Author Yi-Chiung Lin
Author's Email Address No Public.
Statistics This thesis had been viewed 5081 times. Download 0 times.
Department Applied Mathematics
Year 2001
Semester 2
Degree Master
Type of Document
Language English
Title Image Transformation by Numerical Methods
Date of Defense 2002-06-07
Page Count 65
Keyword
  • image
  • transformation
  • Abstract The splitting-integrating method(SIM) is well suited to the
    inverse transformations of digital images and patterns in 2D, but
    it encounters some difficulties involving nonlinear solutions for
    the forward transformation. New techniques are explored in this
    thesis to bypass the nonlinear solution process completely, to
    save CPU time, and to be more flexible for general and complicated
    transformations T, such as the harmonic model which convert the
    original shape of images and patterns to other arbitrary shapes.
    In this thesis, the finite element method (FEM) are used to seek
    the approximate transformation of the harmonic model. The new
    methods of image transformation are applied to human face. To
    describe the face boundary, we use the method combining
    Lagrange polynomial and Hermite interpolation seeking for the
    corresponding grid points besides the fixed ones. The greyness of
    images under geometric transformations by the
    splitting-integrating method has the error bounds,
    O(H)+O(H/N^2) as using the piecewise bilinear interpolations
    (u =1), for smooth images, where H(<<1) is mesh resolution
    of an optical scanner, and N is the division number of a pixel
    split into N^2 sub-pixels. Furthermore, there often occur in
    practical applications the discontinuity images whose greyness
    jump is a minor portion of the entire image, e.g., the piecewise
    continuous images but with the interior and exterior boundary of
    greyness jumps, or the continuous pictures accompanied with a
    finite number of isolated pixels. For this kind of discontinuous
    images, the error bounds are also derived in this thesis to be
    $O(H^{eta})+O(H^{eta}/N^2), ~ eta
    in (0,1]$ as $mu =1$. The image greyness made before was always assumed
    to be smooth enough, this error analysis is significant for
    geometric image transformations.
    Advisory Committee
  • Tzon-Tzer Lu - chair
  • Yung-Nien Sun - co-chair
  • Y. W. Chiang - co-chair
  • Chien-Sen Huang - co-chair
  • Zi-Cai Li - advisor
  • Files
  • etd-0617102-105736.pdf
  • indicate not accessible
    Date of Submission 2002-06-17

    [Back to Results | New Search]


    Browse | Search All Available ETDs

    If you have more questions or technical problems, please contact eThesys