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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0617102-105736 |
| Date | 17 June 2002 |
| Creators | Lin, Yi-Chiung |
| Contributors | Tzon-Tzer Lu, Yung-Nien Sun, Y. W. Chiang, Chien-Sen Huang, Zi-Cai Li |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0617102-105736 |
| Rights | not_available, Copyright information available at source archive |
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