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Spatial complexity of transport infrastructure in the Czech Republic
Abstract
The landscape of the Czech Republic is exceedingly varied. The country consists also river basins and low mountains and belongs to the small and midsize countries in Europe (78,866 km2). Transport of people and cargo is based mainly on roads, rails, air and inland waterways in the Czech Republic. Based on statistical evaluation, the most important type of transport (for both people and cargo) is road transport. The total length of road system in the Czech Republic is more than 55.000 km and is divided onto 5 main categories – motorways, highways, roads of type I, II and III. According to the annual report of Czech Ministry of Transport, yearly performance of road transport is 73.28 bn. passenger km and 66.17 bn. tkm of cargo. The coverage density is one of the densest in Europe. The aim of the presented paper is to show a mathematically based approach how to evaluate the complexity of roads and streets with respect to geographical location of the studied cities. Fractal geometry and statistical evaluation of hypothesis testing were used for this purpose. The paper shows also the general overview of the methodology for complexity evaluation of networks.
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The concept of entropy connected with GIS is relatively new. Its mathematical background was defined after World War II by Claude E. Shannon, well-known mathematician, electronic engineer and founder of information theory. Information theory deals with entropy as measure of information which every single message has. And thus entropy quantifies the amount of information in a message. The paper is based on entropy applications in cartography and demonstrates its usage as a measure of information in GIS. The authors provide an algorithm for setting number of intervals in thematic maps with using entropy calculations. Finally, the obtained knowledge is applied to sample datasets for creating climatic maps within GIS environment.
The conventional spectral-based classification techniques have often been criticized due to the lack of consideration of images’ spatial properties. This study evaluates and compares two lacunarity methods, fractal triangular prism, spatial autocorrelation, and original spectral band approaches in classifying urban images. Results from this study show that the traditional spectral-based classification approach is inappropriate in classifying urban categories from highresolution data. The fractal triangular prism approach was also found to be ineffective in classifying urban features. Spatial autocorrelation was more accurate than the fractal approach. The overall accuracies in this study for the fractal, conventional spectral, spatial autocorrelation, lacunarity binary, and lacunarity gray-scale approaches were 52 percent, 55 percent, 78 percent, 81 percent, and 92 percent, respectively. These findings suggest that the lacunarity approaches are far more effective than the other approaches tested and can be used to drastically improve urban classification accuracy.
There has been growing interest in the application of fractal geometry to observe spatial complexity of natural features at different scales. This study utilized three different fractal approaches—isarithm, triangular prism, and variogram—to characterize texture features of urban land-cover classes in high-resolution image data. For comparison purpose and to better evaluate the efficiency of fractal approaches in image classification, spatial autocorrelation techniques (Moran's I and Geary's C), simple standard deviation, and mean of the selected features were also examined in this study. The discriminant analysis was carried out to discriminate between classes of urban land cover on the basis of texture measures (variables). This study demonstrated that the spatial auto-correlation approach was superior to the fractal approaches. In some cases, simple standard deviation and mean value of the samples gave better accuracy than all or some of the fractal approaches. The results obtained from this analysis suggest that fractal-based textural discrimination methods are applicable but these methods alone may be ineffective in extracting texture features or identifying different land-use and land-cover classes in remotely sensed images.
Lacunarity analysis is a multi-scaled method of determining the texture associated with patterns of spatial dispersion (i.e., habitat types or species locations) for one-, two-, and three-dimensional data. Lacunarity provides a parsimonious analysis of the overall fraction of a map or transect covered by the attribute of interest, the degree of contagion, the presence of self-similarity, the presence and scale of randomness, and the existence of hierarchical structure. For self-similar patterns, it can be used to determine the fractal dimension. The method is easily implemented on the computer and provides readily interpretable graphic results. Differences in pattern can be detected even among very sparsely occupied maps.
The objective of this paper is to examine the development of the urban form of the city of Olomouc since the 1920s in terms of fractal dimension, and to link the observation with two other descriptors of shape - area and perimeter. The fractal dimension of built-up areas and fractal dimension of the boundary of the city are calculated employing the box-counting method; the possibilities of their interpretation and usage in urban planning are discussed. The process of urban growth is observed with respect to its fractality and perspectives of this approach are discussed. An interesting dependence between area and its fractal dimension is derived.
The fractal structure of streets in Seoul was studied through a scale-invariant length-area relation of the streets. Five zones of different residential types were selected, and their fractal dimensions, a coefficient of complexity, were calculated. The relation between the fractal dimensions and the abilities and distinctions of the zones was studied.
This paper discusses the concepts of fractal geometry in a cellular biological context. It defines the concept of the fractal dimension. D, as a measure of complexity and illustrates the two different general ways of quantitatively measuring D by length-related and mass-related methods. Then, these several Ds are compared and contrasted. A goal of the paper is to find methods other than length-related measures that can distinguish between two objects that have the same D but are structurally different. The mass-related D is shown potentially to be such a measure. The concept of lacunarity, L, is defined and methods of measuring L are illustrated. L is also shown to be a potentially distinguishing measure. Finally, the notion of multifracticality is defined and illustrated to exist in certain individual nerve and glial cells.
The notion of lacunarity makes it possible to distinguish sets that have the same fractal dimension but different textures. In this paper we define the lacunarity of a set from the fluctuations of the mass distribution function, which is found using an algorithm we call the gliding-box method. We apply this definition to characterize the geometry of random and deterministic fractal sets. In the case of self-similar sets, lacunarity follows particular scaling properties that are established and discussed in relation to other geometrical analyses.
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