Fractal Surface Dimension for Classification of Remotely Sensed Data
H. T. Ewe1, H. K. Low2 and H. T. Chuah1
1Faculty of Engineering,
Universiti Telekom,
Bukit Beruang,
75450 Melaka, Malaysia
Tel : (60)-6-252-3507 Fax : (60)-6-231-6552
Email :htewe@unitele.com.my
2Department of Electrical Engineering
University of Malaya,
50603 Kuala Lumpur, Malaysia
Abstract
It is generally found that natural objects possess self-similarity and self-affinity in their structures. Fractal analysis, a technique based on these properties, has been widely used in various research applications [1]. In the active remote sensing of the earth terrain, it is possible to extract this fractal information from the images obtained. In this application, fractal surface dimension, an important parameter in fractal analysis, can be employed as an additional feature to classify different landuse areas. This fractal surface dimension is generally related to the roughness of the surface. By keeping the x and y coordinates of the pixels of the image, and taking the grey level of each pixel as its z coordinate, a three-dimensional surface can be constructed. The calculation of fractal surface dimension can then be carried out on that surface. However, in order to obtain a good ensembled average of fractal surface dimension, a proper window size must be selected to capture the real textural information of that area. This process is normally lengthy and repetitive. In this paper, a modified fractal surface dimension based on dimension normalization technique is proposed. A study is made to compare the conventional and the modified fractal surface dimensions with different window sizes. It is found that the values of modified fractal surface dimension are more stable than those of the conventional one across different window sizes. In addition, the distribution of the modified fractal surface dimensions for six land use classes is more distinctly separable from that of the conventional fractal surface dimensions. This indicates that the modified fractal surface dimension is a useful input feature for landuse classification in remote sensing images such as SAR and Landsat TM data [2].
Introduction
For centuries, people have been using simple ideal forms such as spheres, cylinders and cubes to model the real world. It is believed that complex structures can be broken down into smaller and more regular basic forms, this will not only simplify the structure but also make the problem easy to deal with. However, since the 19th century, through the work of Koch, Hausdroff, Cantor, Sierpinski and lately Mandelbrot [1], scientific community has been exposed to a new field of science called fractal analysis. It is found that natural objects, though complex in structure, generally possess self-similarity and self affinity ( a more general relationship). This property of the natural objects is also scale invariant. Recently, there has been a great number of findings in applying fractal analysis in various scientific and engineering fields such as acoustics, clustering of galaxies, Brownian statistics, aggregation of molecules, mathematics and image compression [3]. In earth terrain image processing, a number of research activities have also been carried out to exploit the close relationship between the natural surface and the earth images [4-5]. Fractal surface dimension [6], the basic quantity in characterizing fractals, is also widely used in the image classification process [5-7]. However, the calculated fractal surface dimension is usually affected by the window size of the surface image selected. In this paper, a modified surface fractal dimension which gives stable values across multiple window sizes is proposed. This attempt is based on the dimension normalization technique. The SAR image used in this study was taken in Sungai Petani Area in Kedah state, Malaysia under the GlobeSAR program in 1993. Six landuse classes are chosen from the data set and both the modified and the conventional fractal surface dimensions of the pixels in respective classes are calculated. The study shows that the six landuse classes are more clearly separated out in the distribution graph of the modified fractal surface dimension compared to that of the conventional fractal surface dimension. Thus, the modified fractal surface dimension will be a good input candidate for further classification processes.
