Abstract: A fractal dimension is a useful feature parameter for texture analysis, segmentation and classification in many fields. The differential box-counting method is frequently used to estimate image fractal dimension because of its simplicity. However this method is flawed with lack of accuracy and stability. A new box-counting method is presented. First, more nodes are into the discrete intensity surface of a digital image to make it relatively more approximate to a continuous surface. This step makes it possible to distinguish different images at the smallest scale. Then, the fractal dimension of the digital image is estimated directly according to the box number at the smallest scale without the fitting step. Experimental results show that this method is more accurate and stable compared with some typical methods. For some special test images, such as pulse images, the proposed method outperormed unreasonable estimates. In addition, because there is no need to calculate the box numbers at other scales, the computational complexity of our method is lower.

Key words: fractal dimension, box-counting dimension, gray-level image