Fractal Dimension Estimation Based on Mathematical Morphology
Yong Xia · 2004
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.