有理分形曲面造型及其在图像超分辨中的应用

Rational Fractal Surface Modeling and Its Application in Image Super-resolution

曲面构造是计算机辅助几何设计的一个关键问题。为了使建模曲面在实际应用中更加灵活、有效,提出一种有理分形曲面的构造方法,并基于该模型给出一种单幅图像超分辨率重建算法。首先,将分形插值函数视为高度函数的分形扰动,给出了一种双变量有理样条迭代函数系统,由此生成有理分形曲面;其次,研究了有理分形函数的一些分析性质,给出了有理分形曲面的计盒维数;最后,将该模型及其理论结果应用于单幅图像的超分辨率重建,提出一种重建算法。该算法先通过非下采样轮廓波变换将图像划分为边缘区域和非边缘区域;然后借助于维数公式精确计算尺度因子,利用模型的多样性对不同区域采用不同的模型进行插值,非边缘区域采用有理函数模型,边缘区域采用有理分形插值函数模型;最后通过适当的变换得到目标图像。实验结果表明了所提模型和算法的有效性,其在处理图像纹理细节和边缘方面优于对比算法,特别是在保持图像的结构信息上具有较强的竞争力,同时获得了较好的客观评价数据和主观视觉效果。

The construction of surfaces is a key issue in computer aided geometric design.In order to make the constructed surfaces more flexible and effective in practical application,this paper proposed a constructive method of rational fractal surfaces and a single image super-resolution reconstruction algorithm based on this model.Firstly,a bivariate rational spline iterated function system was presented in which the fractal interpolation functions are regarded as the fractal perturbation of height functions,generating rational fractal surfaces.Secondly,some analytical properties of the rational fractal functions were investigated,and the box-counting dimension of fractal surfaces was obtained.Finally,a superresolution reconstruction algorithm of single image was proposed based on the model and its theoretical results.In this algorithm,the image is divided into edge region and non-edge region by using the Non-subsampled Contourlet Transform(NSCT).And then,the scaling factors are accurately calculated by the dimension formula,the shape parameters are determined based on maintaining the structure similarity of the image,and different models are selected in different regions to interpolate the image data.Rational fractal interpolation and rational interpolation are used in edge region and non-edge region respectively.Next,the target image is obtained by aproper transformation.The experimental results show the effectiveness of the model and algorithm.The presented method is better in maintaining texture details and edge information than the compared algorithms,especially,it achieves competitive performance for preserving the structure information of image,and obtains good objective evaluation data and subjective visual effects.