| Fractal geometry has led to new understanding of many natural objects and phenomena. As a scale-dependent measure, lacunarity can be used to discriminate different textures that may not be differentiated by fractal dimension. Based on a differential box counting method and a gliding-box algorithm, a new lacunarity estimation method is developed for texture analysis of digital images, and a "Lacunarity Analysis" extension built for ArcView (ESRI) geographical information system software. To reveal the directional properties of textures, the directionality of lacunarity is also defined. The new lacunarity measure is evaluated through quantitative comparison with the Voss lacunarity, the binary lacunarity, the grey level cooccurrence matrix (GLCM) based texture measures (homogeneity, contrast, dissimilarity, entropy), the fractal dimension, and the min-max operator using Brodatz textures. The results from Brodatz textures suggest that the new lacunarity estimation method for grey-scale images provides more accurate texture measurements than the above-mentioned fractal-based and statistical texture measures. In comparison with the Voss lacunarity, the fractal dimension, and the GLCM-based texture measures, the new lacunarity measure is then applied to dual-band (L and C) and dual-polarization (HH and HV) Shuttle Imaging Radar (SIR-C), and C-band HH polarization Radarsat images of two imaging modes for rock unit discrimination in a study area between California and Arizona, USA. Using textural analysis of 36 SIR-C and Radarsat sub-images and classification accuracy assessment of the combined Landsat Thematic Mapper (TM) images and spaceborne radar textural feature images, it has been demonstrated that the new lacunarity measure outperformed other texture measures in comparison, and the L-band HH polarization SIR-C image provides more textural information of the rock units compared with the Radarsat and other SIR-C radar images used in this study. The study shows that the anisotropic properties of textures can be characterized by directionality of lacunarity, and the texture classification accuracy can be improved by combining lacunarity measures at different scales and indifferent directions. Finally, to assess the mapping accuracy of the rock units efficiently, a new calculation method is developed for measuring boundary displacement error, which can be used in any geographical information system that supports geometrical and logical operators. |
