基于三角区域有理函数的图像自适应插值

Adaptive Weighted Interpolation Based on Rational Function over Triangular Domain

基于有理函数模型提出了一种新的图像插值算法。此类有理函数基于三角区域构造并且具有简洁且灵活的表达式,同时含有一个可调节参数,在不改变插值曲面输入数据的前提下,可以通过调整参数来微调曲面弯曲程度从而达到更加理想的插值效果。首先将图像区域进行三角剖分,将有理函数模型定义域转化到其特殊域(等腰直角三角形域),通过区域变换使插值曲面达到更好的连续性和光滑性,有效提升了插值精度;然后利用一种基于边缘走向的权值确定方法分别确定各个三角域的权值;最后通过等值线分析将图像划分为不同区域,在平滑区域上随机选择或者固定参数进行插值即可,在非平滑区域上则进行参数的最优化选取,使当前的插值曲面块达到最优,进一步提升了插值精度。本文算法在边缘区域和纹理信息保持方面相对于传统插值算法具有一定的优势,有效地消除了常见的振铃、走样等现象,并且具有良好的视觉效果。

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.