Abstract: 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 ratio-nal fractal functions were investigated,and the box-counting dimension of fractal surfaces was obtained.Finally,a super-resolution 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 a proper 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. 〖BHDWG1,WK32,WK44,WK42W〗第3期 刘甜甜 ,等:有理分形曲面造型及其在图像超分辨中的应用

Key words: Iterated function system,Rational fractal interpolation,Dimension,Super-resolution reconstruction