Computing Local Fractal Dimension Using Geographical Weighting Scheme

The fractal dimension (D) of a surface can be viewed as a summary or average statistic for characterizing the geometric complexity of that surface. The D values are useful for measuring the geometric complexity of various land cover types. Existing fractal methods only calculate a single D value for representing the whole surface. However, the geometric complexity of a surface varies across patches and a single D value is insufficient to capture these detailed variations. Previous studies have calculated local D values using a moving window technique. The main purpose of this study is to compute local D values using an alternative way by incorporating the geographical weighting scheme within the original global fractal methods. Three original fractal methods are selected in this study: the Triangular Prism method, the Differential Box Counting method and the Fourier Power Spectral Density method. A Gaussian density kernel function is used for the local adaption purpose and various bandwidths are tested. The first part of this dissertation research explores and compares both of the global and local D values of these three methods using test images. The D value is computed for every single pixel across the image to show the surface complexity variation. In the second part of the dissertation, the main goal is to study two major U.S. cities located in two regions. New York City and Houston are compared using D values for both of spatial and temporal comparison. The results show that the geographical weighting scheme is suitable for calculating local D values but very sensitive to small bandwidths. New York City and Houston show similar global D results for both year of 2000 and 2016 indicating there were not much land cover changes during the study period

A Genetic Bayesian Approach for Texture-Aided Urban Land-Use/Land-Cover Classification

Urban land-use/land-cover classification is entering a new era with the increased availability of high-resolution satellite imagery and new methods such as texture analysis and artificial intelligence classifiers. Recent research demonstrated exciting improvements of using fractal dimension, lacunarity, and Moran’s I in classification but the integration of these spatial metrics has seldom been investigated. Also, previous research focuses more on developing new classifiers than improving the robust, simple, and fast maximum likelihood classifier. The goal of this dissertation research is to develop a new approach that utilizes a texture vector (fractal dimension, lacunarity, and Moran’s I), combined with a new genetic Bayesian classifier, to improve urban land-use/land-cover classification accuracy. Examples of different land-use/land-covers using post-Katrina IKONOS imagery of New Orleans were demonstrated. Because previous geometric-step and arithmetic-step implementations of the triangular prism algorithm can result in significant unutilized pixels when measuring local fractal dimension, the divisor-step method was developed and found to yield more accurate estimation. In addition, a new lacunarity estimator based on the triangular prism method and the gliding-box algorithm was developed and found better than existing gray-scale estimators for classifying land-use/land-cover from IKONOS imagery. The accuracy of fractal dimension-aided classification was less sensitive to window size than lacunarity and Moran’s I. In general, the optimal window size for the texture vector-aided approach is 27x27 to 37x37 pixels (i.e., 108x108 to 148x148 meters). As expected, a texture vector-aided approach yielded 2-16% better accuracy than individual textural index-aided approach. Compared to the per-pixel maximum likelihood classification, the proposed genetic Bayesian classifier yielded 12% accuracy improvement by optimizing prior probabilities with the genetic algorithm; whereas the integrated approach with a texture vector and the genetic Bayesian classifier significantly improved classification accuracy by 17-21%. Compared to the neural network classifier and genetic algorithm-support vector machines, the genetic Bayesian classifier was slightly less accurate but more computationally efficient and required less human supervision. This research not only develops a new approach of integrating texture analysis with artificial intelligence for classification, but also reveals a promising avenue of using advanced texture analysis and classification methods to associate socioeconomic statuses with remote sensing image textures

Toward reduction of artifacts in fused images

Most fusion satellite image methodologies at pixel-level introduce false spatial details, i.e.artifacts, in the resulting fusedimages. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the à trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fusedimages and their classification results when compared with the original WAT metho

Effects of Landscape Fragmentation on Land Loss

Coastal Louisiana, the seventh largest delta on earth, is one of the most vulnerable coastal areas in the United States of America (USA) because of its land loss problem. Coastal land loss is usually caused by many complicated factors. With the rapid increase in human activities, more studies on land loss have focused on the anthropogenic elements, but less on the pattern of the landscape. It is expected that the type of spatial arrangement, such as high degree of fragmentation, would affect the degree of land erosion. A quantitative evaluation of coastal landscape fragmentation and its influences on land loss would help coastal protection. The purpose of this research is to study the effects of landscape fragmentation on land loss in the Lower Mississippi River Basin (LMRB) region. The main scientific question addressed in this study is: does the degree of fragmentation influence the degree of coastal land loss? This thesis applied fractal analysis and spatial autocorrelation statistics to calculate the degree of fragmentation, using Landsat-TM land cover data in 1996 and 2010 with a pixel size of 30m * 30m. First, 100 samples of a 50-percent land-water ratio for each of the three box sizes – 101*101, 51*51, and 31*31 pixels – were extracted from the study area. Linear regressions were conducted to compute the relationship between fragmentation and land loss. The hypothesis is that the higher the degree of spatial fragmentation, the greater the degree of land loss. The results show that boxes with a higher degree of fragmentation had more land loss for box sizes of 51*51 and 31*31 with p-values less than 0.001. The relationship is not significant for 101*101 with p-values greater than 0.05. Thus, land fragmentation is a worthy element to be considered as a land loss factor. These results should be useful to the development of better strategies to strengthen the protection of a highly fragmented coast

Multiscale Analysis for Characterization of Remotely Sensed Images.

In this study we addressed fundamental characteristics of image analysis in remote sensing, enumerated unavoidable problems in spectral analysis, and highlighted the spatial structure and features that increase information amount and measurement accuracy. We addressed the relationship between scale and spatial structure and the difficulties in characterizing them in complex remotely sensed images. We suggested that it is necessary to employ multiscale analysis techniques for analyzing and extracting information from remotely sensed images. We developed a multiscale characterization software system based on an existing software called ICAMS (Image Characterization And Modeling System), and applied the system to various test data sets including both simulated and real remote sensing data in order to evaluate the performance of these methods. In particular, we analyzed the fractal and wavelet methods. For the fractal methods, the results from using a set of simulated surfaces suggested that the triangular prism surface area method was the best technique for estimating the fractal dimension of remote sensing images. Through examining Landsat TM images of four different land covers, we found that fractal dimension and energy signatures derived from wavelets can measure some interesting aspects of the spatial content of remote sensing data, such as spatial complexity, spatial frequency, and textural orientation. Forest areas displayed the highest fractal dimension values, followed by coastal, urban, and agriculture respectively. However, fractal dimension by itself is insufficient for accurate classification of TM images. Wavelet analysis is more accurate for characterizing spatial structures. A longer wavelet was shown to be more accurate in the representation and discrimination of land-cover classes than a similar function of shorter length, and the combination of energy signatures from multiple decomposition levels and multispectral bands led to better characterization results than a single resolution and single band decomposition. Significant improvements in classification accuracy were achieved by using fractal dimensions in conjunction with the energy signature. This study has shown that multiscale analysis techniques are very useful to complement spectral classification techniques to extract information from remotely sensed images

Evaluation of the impacts of Hurricane Hugo on the land cover of Francis Marion National Forest, South Carolina using remote sensing

Hurricane Hugo struck the South Carolina coast on the night of September 21, 1989 at Sullivan’s Island, where it was considered a Category 4 on the Saffir-Simpson scale when the hurricane made landfall (Hook et al. 1991). It is probably amongst the most studied and documented hurricanes in the United States (USDA Southern Research Station Publication 1996). There has been a Landsat TM based Hugo damage assessment study conducted by Cablk et al. (1994) in the Hobcaw barony forest. This study attempted to assess for a different and smaller study area near the Wambaw and Coffee creek swamp. The main objective of this study was to compare the results of the traditional post-classification method and the triangular prism fractal method (TPSA hereafter, a spatial method) for change detection using Landsat TM data for the Francis Marion National Forest (FMNF hereafter) before and after Hurricane Hugo’s landfall (in 1987 and 1989). Additional methods considered for comparison were the principal component analysis (PCA hereafter), and tasseled cap transform (TCT hereafter). Classification accuracy was estimated at 81.44% and 85.71% for the hurricane images with 4 classes: water, woody wetland, forest and a combined cultivated row crops/transitional barren class. Post-classification was successful in identifying the Wambaw swamp, Coffee creek swamp, and the Little Wambaw wilderness as having a gain in homogeneity. It was the only method along with the local fractal method, which gave the percentage of changed land cover areas. Visual comparison of the PCA and TCT images show the dominant land cover changes in the study area with the TCT in general better able to identify the features in all their transformed three bands. The post-classification method, PCA, and the TCT brightness and greenness bands did not report increase in heterogeneity, but were successful in reporting gain in homogeneity. The local fractal TPSA method of a 17x17 moving window with five arithmetic steps was found to have the best visual representation of the textural patterns in the study area. The local fractal TPSA method was successful in identifying land cover areas as having the largest heterogeneity increase (a positive change in fractal dimension difference values) and largest homogeneity increase (a negative change in fractal dimension difference values). The woody wetland class was found to have the biggest increase in homogeneity and the forest class as having the biggest increase in heterogeneity, in addition to identifying the three swamp areas as having an overall increased homogeneity

The Design and Implementation of an Image Segmentation System for Forest Image Analysis

The United States Forest Service (USFS) is developing software systems to evaluate forest resources with respect to qualities such as scenic beauty and vegetation structure. Such evaluations usually involve a large amount of human labor. In this thesis, I will discuss the design and implementation of a digital image segmentation system, and how to apply it to analyze forest images so that automated forest resource evaluation can be achieved. The first major contribution of the thesis is the evaluation of various feature design schemes for segmenting forest images. The other major contribution of this thesis is the development of a pattern recognition-based image segmentation algorithm. The best system performance was a 61.4% block classification error rate, achieved by combining color histograms with entropy. This performance is better than that obtained by an ?intelligent? guess based on prior knowledge about the categories under study, which is 68.0%

Multi-Scale Modelling of Cold Regions Hydrology

Numerical computer simulations are increasingly important tools required to address both research and operational water resource issues related to the hydrological cycle. Cold region hydrological models have requirements to calculate phase change in water via consideration of the energy balance which has high spatial variability. This motivates the inclusion of explicit spatial heterogeneity and field-testable process representations in such models. However, standard techniques for spatial representation such as raster discretization can lead to prohibitively large computational costs and increased uncertainty due to increased degrees of freedom. As well, semi-distributed approaches may not sufficiently represent all the spatial variability. Further, there is uncertainty regarding which process conceptualizations are used and the degree of required complexity, motivating modelling approaches that allow testing multiple working hypotheses. This thesis considers two themes. In the first, the development of improved modelling techniques to efficiently include spatial heterogeneity, investigate warranted model complexity, and appropriate process representation in cold region models is addressed. In the second, the issues of non-linear process cascades, emergence, and compensatory behaviours in cold regions hydrological process representations is addressed. To address these themes, a new modelling framework, the Canadian Hydrological Model (CHM), is presented. Key design goals for CHM include the ability to: capture spatial heterogeneity in an efficient manner, include multiple process representations, be able to change, remove, and decouple hydrological process algorithms, work both at point and spatially distributed scales, reduce computational overhead to facilitate uncertainty analysis, scale over multiple spatial extents, and utilize a variety of boundary and initial conditions. To enable multi-scale modelling in CHM, a novel multi-objective unstructured mesh generation software *mesher* is presented. Mesher represents the landscape using a multi-scale, variable resolution surface mesh. It was found that this explicitly captured the spatial heterogeneity important for emergent behaviours and cold regions processes, and reduced the total number of computational elements by 50\% to 90\% from that of a uniform mesh. Four energy balance snowpack models of varying complexity and degree of coupling of the energy and mass budget were used to simulate SWE in a forest clearing in the Canadian Rocky Mountains. It was found that 1) a compensatory response was present in the fully coupled models’ energy and mass balance that reduced their sensitivity to errors in meteorology and albedo and 2) the weakly coupled models produced less accurate simulations and were more sensitive to errors in forcing meteorology and albedo. The results suggest that the inclusion of a fully coupled mass and energy budget improves prediction of snow accumulation and ablation, but there was little advantage by introducing a multi-layered snowpack scheme. This helps define warranted complexity model decisions for this region. Lastly, a 3-D advection-diffusion blowing snow transport and sublimation model using a finite volume method discretization via a variable resolution unstructured mesh was developed. This found that the blowing snow calculation was able to represent the spatial redistribution of SWE over a sub-arctic mountain basin when compared to detailed snow surveys and the use of the unstructured mesh provided a 62\% reduction in computational elements. Without the inclusion of blowing snow, unrealistic homogeneous snow covers were simulated which would lead to incorrect melt rates and runoff contributions. This thesis shows that there is a need to: use fully coupled energy and mass balance models in mountains terrain, capture snow-drift resolving scales in next-generation hydrological models, employ variable resolution unstructured meshes as a way to reduce computational time, and consider cascading process interactions

Wavelet Analysis and Classification of Urban Environment Using High -Resolution Multispectral Image Data.

Attempts to analyze urban features and classify land use and land cover directly from high-resolution satellite data with traditional computer classification techniques have proven to be inefficient. The fundamental problem usually found in identifying urban land cover types from high-resolution satellite imagery is that urban areas are composed of diverse materials (metal, glass, concrete, asphalt, plastic, trees, soil, etc.). These materials, each of which may have completely different spectral characteristics, are combined in complex ways by human beings. Hence, each urban land cover type may contain several different objects with different reflectance values. Noisy appearance with lots of edges, and the complex nature of these images, inhibit accurate interpretation of urban features. Traditional classifiers employ spectral information based on single pixel value and ignore a great amount of spatial information. Texture features play an important role in image segmentation and object recognition, as well as interpretation of images in a variety of applications ranging from medical imaging to remote sensing. This study analyzed urban texture features in multi-spectral image data. Recent development in the mathematical theory of wavelet transform has received overwhelming attention by the image analysts. An evaluation of the ability of wavelet transform and other texture analysis algorithms in urban feature extraction and classification was performed in this study. Advanced Thermal Land Application Sensor (ATLAS) image data at 2.5 m spatial resolution acquired with 15 channel (0.45 mum--12.2 mum) were used for this research. The data were collected by a NASA Stennis LearJet 23 flying at 6600 feet over Baton Rouge, Louisiana, on May 7, 1999. The algorithms examined were the wavelet transforms, spatial co-occurrence matrix, fractal analysis, and spatial autocorrelation. The performance of the above approaches with the use of different window sizes, different channels, and different feature measures were investigated. Six types of urban land cover features were evaluated. Wavelet transform was found to be far more efficient than other advanced spatial methods. The results of this research indicate that the accuracy of texture analysis in classifying urban features in fine resolution image data could be significantly improved with the use of wavelet transform approach

Land -Cover Change Detection for the Tropics Using Remote Sensing and Geographic Information Systems.

Changing land-cover in the tropics is a central issue in global change research. This dissertation used Landsat-TM data to examine processes of land-use and land-cover changes for a lowland tropical site in Sarapiqui, Costa Rica. Performances of selected image-processing methods to detect and identify land-cover changes were evaluated. A land-cover time-series from 1960 to 1996 for the site was generated using maps derived from aerial photographs and Landsat-TM classifications. Changes in land-cover from 1986 to 1996 were evaluated using standard landscape indices, and interpreted in terms of their historical context. Dominant changes in the site during this decade included the breakup of extensive cattle ranches for large-scale plantation enterprises and small-scale farming. Colonization processes, improvements in access, and changes in export markets were identified as the major driving forces of change. Evaluation of change-detection methods revealed that postclassification comparison performed significantly better than image differencing algorithms. Image differencing using mid- infrared bonds performed the best of the differencing algorithms tested. Selection of a suitable change-detection method can be aided through examination of the individual bond statistics for the specific area and problem in question. The univariate bond differencing technique has potential for identification of \u27hot spots\u27 of change using Landsat-TM data. Spatial pattern-recognition techniques to characterize complexity of Landsat-TM data were evaluated. Fractal dimension calculated using the triangular prism surface area method, and Moran\u27s I index of spatial autocorrelation, clearly distinguished different land-cover types. Shannon\u27s diversity index and the contagion metric were not found to be useful in characterizing the images. The use of fractal dimension, in conjunction with standard non-spatial descriptive band statistics, are seen as having great potential in characterizing unclassified remotely sensed data based on differences in land-cover types. These statistics could be further developed for rapid environmental monitoring