中文摘要：

目的图像插值是图像处理中的重要问题，为了提高纹理图像的放大质量，结合以往的有理函数的捅仇算法，提出一种新的基于有理分形函数的图像插值算法。方法对于输入图像，首先，运用中值滤波和直方图均衡化对输入图像预处理；其次，通过毯子覆盖法求出图像的多尺度分形特征值，进行纹理区域和平滑区域的划分；最后，在纹理区域采用有理分形插值函数，在平滑区域采用有理插值函数。结果对于一般图像，本文算法与NARM（nonlocalautoregressivemodel），NEDI（newedge-directedinterpolation）相当，在纹理区域较多的图像中，本文算法在峰值信噪比（PSNR）和结构相似性（SSIM）数值上较对比算法进一步提高，在视觉效果上，图像对比发明显增强，往Barbara，Truck等的对比图像中，峰值信噪比均提高了0．5～1dB。结论本文插值算法利用多尺度分形特征将图像划分区域，在不同区域采用不同的插值模型。优化模型参数使得插值质量进一步提高。实验表明本文算法能够对纹理和非纹理区域有效划分对纹理的信息保持优于传统算法，获得了较好的主客观效果。

英文摘要：

Objective Image interpolation plays a vital role in image processing. A new image interpolation algorithm based on a rational fraetal funetion is proposed to improve the quality of texture image magnification, This method is combined with a previous rational function inteqmlation algorithm. Method For input image prepraeessing, a median fiher and histo- gram equalization are utilized. The texture and smooth areas in the image are classified through the blanket method and the muhi-scale fraetal characteristic value of the image. Finally, a rational fractal interpolation function is employed for the tex- ture region, and a rational interpolation function is adopted for the smooth area. An optimization technique is then utilized to further modify the interpolation model, which is proven to be effective. Result A rational factal interpnlalion algorithm is proposed in this article. For common images, the quality of interpnlation approximates that of NEDI anti NARM. For lex- ture images, the proposed method is highly competitive not only in PSNR and SSIM but also in visual effeet. ConclusionThis article presents a novel image interpolation method based on a rational fractal function. Experimental results demon- strate that the proposed method exhibits competitive performance, especially in terms of image details and texture features.