A Fractal Approach to the Classification of Land Cover in Radar imagery
Randy John N. Vinluan, Mark J. Encarnacion, Epifanio D. Lopez, Guillermo Q. Tabios
College of Engineering, University of the Philippines
Dliman, Quezon City 1101 Metro Manila, The Philippines
Tel : (63 2 ) 434-3633; Fax (63 2) 922-4714
Email :rjnv@engg.upd.edu.ph,
edl@engg.upd.edu.ph
Abstract
Fractals are useful in remote sensing image analysis because of the self-similarity and scaling properties inherent in satellite imagery. This stud sought to determine whether fractal analysis is a useful means for characterizing land cover in radar imagery. It also sough to determine how speckle filtering affects the computed fractal dimension and whether this will enhance classification. Thirty ERS-1 synthetic aperture radar images of seven land cover types present in Central Luzon (bay areas, forested areas, mountainous terrain, rice fields, river areas, urban areas, and wetlands) were represented as a three-dimensional backscatter surface with the pixel and line coordinates of the image serving as the x- and y- coordinates of the backscatter surface and the backscatter intensity as the z-coordinate. Using two methods for computing the fractal dimension - the triangular prism surface area method and the box-counting method- four fractal parameters are computed : the Fract3D dimension, capacity dimension, information dimension, information dimension, and correlation dimension. A multivariate statistical method called multiple discriminant analysis is applied to these parameters, as well as to two other statistical measures - the image mean and standard deviation - to determine the separation between the different land cover types. Results show that all six parameters significantly separate the seven land cover types. Including all fractal and statistical measures in the multiple discriminant analysis yields an observed classification accuracy of 70.95%, or a kappea coefficient of about 0.66.Speckle-filtering results in an image set with totally different fractal and statistical properties from the original, with the exception of the capacity dimension for bay areas and the information dimension for urban areas. This resulted in an improvement of the classification to 80.48%, or a kappa coefficient of 0.77.
Introduction:
Fractals are mathematical models for very irregular and very detailed characterized by the so-called fractal dimension (Stoyan and Stoyan, 1994). Just as a Euclidean curve has a topological dimension of 1, and a Euclidean plane has a topological dimension of 2, a fractal curve has a dimension between 1 and 2, and a fractal surface has a dimension between 2 and 3, depending on the degree of complexity (Lam, 1990). Furthermore, fractals are characterized by self-similarity and scaling (Peitgen, et al., 1992), which means that the characteristics of fractals can be identified at all scales of observation, although our ability to visualize them is limited by the resolution of the computer screen (Shibli, 1996).
Remote sensing digital image analysis is an appropriate field for the application of fractals because of the inherent significance of self-similarity, both strictly and statistically (Quattrochi and Lam, 1991; Goodchild and Mark, 1987); scale, both spatial and temporal (Ridd, 1991; Goodchild and Mark, 1987); and patterns and processes (Davis, 1991) in geographic entities.
Fractal analysis of remotely-sensed images, although relatively new, seems to have great potential (Quattrochi and Lam, 1991). The research direction is clearly toward the further exploration on the use of fractals to characterize, measure, and even simulate (Carr, 1995) earth patterns and processes over space and time.
Objectives:
The general objective of this study is to determine whether fractal analysis is a useful means for characterizing different tropical land cover types. In particular, the study seeks to find most effectively between the different land cover types?; and 2) Does speckle filtering enhance classification?
Methods:
Three ERS-1 SAR scenes of Central Luzon dated July 25, August 29, and October 3, 1993 were used in the study. For easier manipulation, each pixel in the images was requantizd to 8-bit, without significant loss of information, from an original radiometric resolution of 16 bit per pixel. Using as reference recent aerial photographs, ground truth data, and existing topographic and land cover maps, seven tropical land cover types were identified - bay areas, forested areas mountainous terrain, rice fields, river areas, urban areas, and wetlands. Thirty 129 pixel by 129 line subsets for each land cover type, or a total of 210 image subsets, were extracted from the three ERS-1 SAR scenes. The image subsets were represented as a radar backscatter surface with the x- and y- coordinates corresponding to the pixel and the coordinates respectively, and the z-coordinate corresponding to the radar backscatter intensity . Figure 1 shows the ERS- SAR scene of Central Luzon dated July 25, 1993 and sample regions where the different land cover types were extracted.
Four representations of the fractal dimension- the Fract3D dimension (Fract3D), derived using the triangular prism surface area method (Clarke, 1986), and the capacity (CapDim), information (InfDim) and correlation (CorrDim) dimensions, derived using the box-counting method (Rasband, 1990)-as well as two first-order statistical measures, the image mean and standard deviation, were computed for each of the image subsets representing different land cover types. The fractal dimensions are interpreted as measures of radar backscatter surface complexity.
A multivariate statistical method called multiple discriminant analysis, which exhibits some similarity with principal component analysis, was applied to the computed fractal and statistical measures. This method aims to compute a set of linear or discriminant functions which best separate a set of , in this case, 7 groups. These discriminant functions represent coordinate axes in the p-dimensional space defined by the p (in this case, 6: the four fractal dimensions, the image mean, and the standard deviation) spectral bands making up the data (Mather, 1987).
Figure 1, ERS-1 SAR Scene of Central Luzon dated July 25, 1993
A 5 x 5 Lee filter, which is an adaptive speckle-reduction filter, was applied to the same set of images. The four fractal and two first-order statistical measures were computed for the new set of image subsets. Student's test was applied to the original and speckle-filtered data in order to determine whether there were significant differences between the two sets of data. Finally, multiple discriminant analysis was also applied to the speckle-filtered datasets in order to determine whether speckle-reduction filtering enhances fractal-based classification.
