Fractals and fuzzy sets for modelling the heterogenity and spatial complexity of urban landscapes using multiscale remote sensing data

Abstract

This research presents models for the analysis of textural and contextual information content of multiscale remote sensing to select an appropriate scale for the correct interpretation and mapping of heterogeneous urban land cover types. Spatial complexity measures such as the fractal model and the Moran’s I index of spatial autocorrelation were applied for addressing the issue of scale, while fuzzy set theory was applied for mapping heterogeneous urban land cover types. Three local government areas (e.g. the City of Perth, the City of Melville and the City of Armadale) of the Perth metropolitan area were selected, as the dominant land covers of these areas are representative to the whole metropolitan area, for the analysis of spatial complexity and the mapping of complex land covers. Characterisation of spatial complexity of the study areas computed from SPOT, Landsat-7 ETM+, and Landsat MSS was used for assessing the appropriateness of a scale for urban analysis. Associated with this outcome, the effect of spectral resolution and land cover heterogeneity on spatial complexity, the performance of fractal measurement algorithms and the relationship between the fractal dimension and Moran’s I were identified. A fuzzy supervised approach of the fuzzy c-means algorithm was used to generate fuzzy memberships of the selected bands of a Landsat-7 ETM+ scene based on the highest spectral separability among different urban land covers (e.g. forest, grassland, urban and dense urban) as determined by a transformed divergence analysis. Fuzzy land cover maps resulting from the application of fuzzy operators (e.g. maximum, minimum, algebraic sum, algebraic product and gamma operators) were evaluated against fuzzy memberships derived from the virtual field reference database (VFRDB).The performance of fuzzy operators in generating fuzzy categorical maps along with the effect of land cover heterogeneity on fuzzy accuracy measures and sources of classification error were assessed. The analysis of spatial complexity computed from remote sensing images using a fractal model indicated that the various urban land cover types of the Perth metropolitan area are best represented at a resolution of 20 m (SPOT) as the fractal dimension (D) was found higher, as compared to the 25 m and 50 m resolutions of the Landsat-7 ETM+ and Landsat MSS, respectively, demonstrated the ability of the fractal model in distinguishing variations in the composition of built-up areas in the green and red bands of the satellite data, while forested areas typical of the urban fringe appear better characterised in the NIR band. Moran’s I of spatial autocorrelation was found useful in describing the spatial pattern of urban land cover types. A comparison between the D and Moran’s I of the study areas revealed a negative correlation, indicating that the higher the Moran’s I, the lesser the fractal dimension indicating a lower spatial complexity. Likewise, the results The accuracy of the fuzzy categorical maps associated with multiple spectral bands of a Landsat-7 ETM+ scene using various fuzzy operators reveals that the fuzzy gamma operator (y = 0.90) outperformed the categorical accuracy measures obtained by applying the fuzzy algebraic sum and other fuzzy operators for the City of Perth, while the accuracy measures of y value of 0.95 were found highest for the City of Melville and the City of Armadale.A comparison of the accuracy measures of the fuzzy land cover maps of the study areas indicated that the overall accuracy of the City of Perth was up to 13% higher than the overall accuracy of the City of Melville and the City of Armadale which was found 69% and 71%, respectively. The lower accuracy measures of the City of Melville and the City of Armadale was attributed to highly mixed land cover classes resulting in mixed pixels in Landsat-7 ETM+ scene. In addition, the spectral similarity among the class forest and grassland, urban and dense urban were identified as sources of classification errors. The analysis of spatial complexity using multiscale and multisource remote sensing data and the application of fuzzy set theory provided a viable methodology for assessing the appropriateness of scale selection for an urban analysis and generating fuzzy urban land cover maps from a multispectral image. It also illustrated the longstanding issue of carrying out the accuracy of the fuzzy land cover map considering the fuzzy memberships of the classified data and the reference data using a fuzzy error matrix.