Abstract: In order to improve the sawtooth gained by the traditional image zooming algorithm, this paper analyzes the statistical characteristics of the image pixels, and divides the image into smooth, texture and edge. Based on the local homogeneity in smoothing and texture area, the paper proposes image zooming algorithm based on local polynomial approximation. Firstly, it divides the image into several homomorphic image regions using the intersection of the confidence interval algorithm. Secondly, it figures the best polynomial fitting for each area, and then making oversampling of the fitting function to achieve regional amplification. Finally, it uses local smoothing to obliterate jagged edges. The experimental results show that the algorithm makes full use of the structural information of the image and improves the image visual effects and applicability compared with conventional interpolation zooming algorithm and the existing locally adaptive interpolation algorithm.

Key words: image zooming, polynomial approximation, adaptive area, function interpolation

摘要： 为了弥补传统图像放大算法的锯齿效应，统计分析了图像像素变化特点，将图像分成平滑、纹理和边缘，对平滑和纹理区根据其局部区域的同态性，提出了基于局部多项式逼近的图像放大：运用置信区间交集法则将图像分割为若干同态区域；对区域分别进行多项式拟合，并对拟合函数进行过采样实现区域放大；运用局部平滑消除边缘锯齿效应。实验结果表明，该算法充分利用了图像的结构信息，相比于传统的插值放大算法和已有局部自适应插值算法提高了图像的视觉效果与适用性。

关键词: 图像放大, 多项式逼近, 自适应区域, 函数插值