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在传统的基于表面积的图像分形维数计算中,不同尺度下的表面积计算均在原图像中进行。这与图像细节随空间尺度的变化而变化的事实不符,据此计算的同类地物的分数维变化范围较大,对基于分形的图像分割、分类产生不利影响。针对这一问题,提出一种基于面积加权的快速插值算法来模拟不同尺度下的遥感图像,进而计算图像的分数维。实验结果表明,对于大小为512pixel×512pixel的标准Lena图像来说,新算法的插值速度提高10倍以上,且得到的分数维具有更小的类内方差以及更好的抗噪性,因而更适用于基于分形的遥感图像分割、分类。
In the traditional calculation of surface fractal dimension based on surface area, the calculation of surface area under different scales is carried out in the original image. This is inconsistent with the fact that the detail of the image changes with the change of the spatial scale. The calculated fractal dimension of the same kind of object has a large variation range, which adversely affects the image segmentation and classification based on fractal. In response to this problem, a fast interpolation algorithm based on area weight is proposed to simulate remote sensing images at different scales and calculate the fractal dimension of the image. The experimental results show that the proposed algorithm is more suitable for standard Lena images of size 512 pixels × 512 pixels and the interpolation speed of the new algorithm is more than 10 times higher and the resulting fractal has smaller intra-class variance and better noise immunity Segmentation and classification of remote sensing images based on fractal.