关键词: 有理函数插值, 等值线分析, 图像自适应, 参数最优化

Abstract: This paper proposed a novel image interpolation algorithm based on the rational function
model. The interpolation function is carried out by a simple and explicit mathematical representation
through a parameter and the shape of the interpolation surface can be modified by using the parameter
for the unchanged interpolation data. Firstly, we change the domain of definition of the interpolation
function into a special domain (the domain of the isosceles right triangle), then the interpolation surface
will be smoother and the interpolation precision will be improved effectively. Secondly, we have given
more consideration to the directional information of the image. Finally, the image is divided into
smooth area and non-smooth area by drawing contour lines. Then we select a random or a fixed
parameter in smooth area and choose the optimal parameter in non-smooth area. The experimental
results show that the algorithms proposed by this paper achieve comparatively good effects and the
common interpolation artifacts (ringing, aliasing, etc) are greatly reduced.

Key words: rational function interpolation, contour lines, adaptive, parameter optimization