A Study On Fractal Dimension And Orientation Angle Calculation Methods For Gray Level Images

The fractal theory is a very active branch of modern mathematics and non-lineal science. In the last years, it has played an increasingly important role in image processing and analysis. Fractal dimension is a very important feature in fractal geometry research.Among the existing research on the fractal dimension estimation, there are very little on the gray level images directly in previous papers. Most of them use strict fractal curves or graphic images or threshold images as examples for experiments. The popular method for fractal dimension estimation is box-counting method, but as to gray level images, the results are so coarse that they could hardly be used as the feature for image analysis.Because of accuracy and relatively simplicity in area measurement, a new fractal dimension estimating method is proposed by taking area covering instead of the volume covering in box-counting method. In order to testify the validity of the proposed method, there is a complex digital image to be applied to the experiment. The results show that the calculated fractal dimensions are almost continuous for a gray level image. Compared with box-counting method, the proposed method avoids jumpiness of calculated fractal dimensions. It provides a good foundation for image analysis that uses fractal dimension as the feature.Because fractal dimension can not respond to the orientation of the gray level images, an image orientation angle estimating method is proposed by basic knowledge of vector algebra. The experimental results show that the proposed algorithm can respond to similarities and differences of digital image orientation and make up the shortage of fractal dimension. The methods would have new applying prospects in taking fractal dimension and the orientation angle as the feature for image analysis.