Improved Splitting-Integrating Methods for Image Geometric Transformations
摘要
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 paper 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, Poisson and blending
models which convert the original shape of images and patterns to other arbitrary shapes
by the PDE models. In this paper, the finite difference method(FDM), the finite element
method(FEM), and the finite volume method(FVM), are used to seek the appproximate
transformations of the harmonic, Poisson and blending models. The greyness of images
under geometric transformations by the splitting-integrating method has the error bounds,
O(H)+O(H/N2) by 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 N2 sub-pixels. Moreover, 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 paper to be
O(Hß)+O(Hß/N2), ß in (0,1] as u = 1. Some interesting examples for human face
transformations are also provided.
∼李子才教授演講摘要∼