对于分形维数的估计是基于分形理论的纹理图像分割算法中最重要的环节。由于使用固定划分的规则网格，常用的基于盒计数的分形维数估计算法及其各种改进方法的误差较大；而传统的形态学维数估计算法虽然在准确性上有一定提高．但其时间复杂度偏高。为此提出了一种基于可变结构元的数学形态学分形维数估计方法(VSEM)。该方法将灰度图像视为一个三维空间中的曲面，使用一组不同尺度的结构元分别度量该曲面．根据度量结果与尺度之间满足的指数率来估计图像表面的分形维数。通过恰当的选择结构元和使用递推技术得到不同尺度下的膨胀结果，新方法成功地弥补了现有算法的不足。本文使用了一组合成纹理和一组自然纹理来评估几种常见的分形维数估计算法。结果显示，本文提出的新方法能够在较小的时间复杂度下，得到更为精确的估计结果。最后，将该方法应用于遥感图像的分割。与其他常用的分形分割算法相比，使用该方法估计的分形维数和图像的临域均值作为特征能够得到更好的分割结果。在对比分析和分割实验中表现出的良好性能说明本文提出的分形维数估计算法可以有效地应用于纹理图像分割。

The estimation of fractal dimension is essential in fractal-based image segmentation. The most popular estimation algorithm is based on box-counting. However, the regular partition and counting methods used in this scheme produces less accurate results. Though morphological fractal estimation is more accurate, the traditional method is very time consuming. In this paper, a new morphological fractal dimension estimation algorithm based on variable structure elements (SE) is proposed. The digitized gray level image is treated as a three-dimensional surface, which is measured under different scales by performing dilations by a series of structuring elements with different sizes on it. And the fractal dimension of it can be estimated from the power law followed by the metrics of the surface and the size of the structuring elements. By properly choosing the structure elements and constructing iterative dilations, the new method achieves better accuracy as well as efficiency. Comparative experiments on both synthetic textures and natural textures show that the proposed approach gives better results than five other commonly used estimation methods. Finally, the estimated fractal dimension and local average gray level are used as characters to segment remote sensing images, comparing with other fractal-based methods, it provides more meaningful segmentation. All these satisfied experimental results demonstrate that the proposed estimation can be successfully applied to texture segmentation.