为了准确地研究图像奇异性以及各部分的属性及特征，采用一种基于亚像素边缘测度的多重分形算法，该算法根据方形孔径采样定理计算亚像素位置的梯度面密度函数值和图像任意子集(半径可以达到亚像素精度)的边缘测度，进而利用多重分形理论将实际图像分割成一系列具有不同奇异性指数的分形集合。并利用含有不同信息含量的分形集合重建原图像算法，实现了图像从纹理到边缘各层面内容的精确划分。对该算法进行了理论分析和实验验证，得到3×3亚像素方法提取的边缘信息重构原图像，其峰值信噪比达到14．76dB。结果表明，重建图像峰值信噪比主要依赖于所提取的边缘信息质量以及重构系数比，提取的各层面信息与人类的视觉系统所捕获的重要信息相吻合。

In order to analyze image singularity and the features of the different sections,a new multifractal algorithm based on sub-pixel edge measure is proposed. The greylevel gradient area density function and edge-measure of random subsets(radii can reach the precision of sub-pixel)were obtained by the square aperture sampling law on the position of sub-pixel. Utilized the multifractal frame,the image could be segmented into a series of fractal sets of the different singularity exponents. At the same time,the reconstruction algorithm was presented by using the different information content of multifractal subset. So the image could be divided from texture to edge precisely. At last,the algorithm was analyzed and examined. The data showed that the reconstruction PSNR was 14.76dB from the edge extracted by 3 × 3 sub-pixels method. The results show that the peak signal-tonoise ratio of the reconstruction image depends on the extracted image edge quality and the coefficient ratio of the reconstruction and the information of the different layers of the image are identical with the important information from the human visual reception.