空间预测的地统计学框架(英文)

Geostatistics provides a coherent framework for spatial prediction and uncertainty assessment, whereby spatial dependence, as quantified by variograms, is utilized for best linear unbiased estimation of a regionalized variable at unsampied locations. Geostatistics for prediction of continuous regionalized variables is reviewed, with key methods underlying the derivation of major variants of uni-vafiate Kriging described in an easy-to-follow manner. This paper will contribute to demysti- fication and, hence, popularization of geostatistics in geoinformatics communities.     

The generic annular bucket histogram for estimating the selectivity of spatial selection and spatial join

Selectivity estimation is crucial for query optimizers choosing an optimal spatial execution plan in a spatial database management system.This paper presents an Annular Bucket spatial histogram(AB histogram)that can estimate the selectivity in finer spatial selection and spatial join operations even when the spatial query has more operators or more joins.The AB histogram is represented as a set of bucket-range,bucket-count value pairs.The bucket-range often covers an annular region like a sin-gle-cell-sized photo frame.The bucket-count is the number of objects whose Minimum Bounding Rectangles(MBRs)fall between outer rectangle and inner rectangle of the bucket-range.Assuming that all MBRs in each a bucket distribute evenly,for every buck-et,we can obtain serial probabilities that satisfy a certain spatial selection or join conditions from the operations’ semantics and the spatial relations between every bucket-range and query ranges.Thus,according to some probability theories,spatial selection or join selectivity can be estimated by the every bucket-count and its probabilities.This paper also shows a way to generate an updated AB histogram from an original AB histogram and those probabilities.Our tests show that the AB histogram not only supports the selectivity estimation of spatial selection or spatial join with "disjoint","intersect","within","contains",and "overlap" operators but also provides an approach to generate a reliable updated histogram whose spatial distribution is close to the distribution of ac-tual query result.     

Urban growth pattern modeling using logistic regression

Transformation of land use/land cover change occurs due to the numbers and activities of people.Urban growth mod-eling has attracted substantial attention because it helps to comprehend the mechanisms of land use change and thus helps relevant policies made.This paper tends to apply logistic regression to model urban growth in the Jiayu county of Hubei province,China.It is applied in a GIS environment to calculate variables and,then,in SPSS to discover the relationships between urban growth and the driving forces.The relative operating characteristic(ROC) shows the modeling accuracy with the curve 0.891 with standard er-ror 0.001.A probability map is generated finally to predict where urban growth will occur as a result of the computation.The result shows the model simulates urban growth well in the county scale.     

Bayesian and Geostatistical Approaches to Combining Categorical Data Derived from Visual and Digital Processing of Remotely Sensed Images

This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification. By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated. It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly. Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy. Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique.     

Image relaxation matching based on feature points for DSM generation

In photogrammetry and remote sensing, image matching is a basic and crucial process for automatic DEM generation. In this paper we presented a image relaxation matching method based on feature points. This method can be considered as an extention of regular grid point based matching. It avoids the shortcome of grid point based matching. For example, with this method, we can avoid low or even no texture area where errors frequently appear in cross correlaton matching. In the mean while, it makes full use of some mature techniques such as probability relaxation, image pyramid and the like which have already been successfully used in grid point matching process. Application of the technique to DEM generaton in different regions proved that it is more reasonable and reliable.     

Remote sensing image classification with GIS data based on spatial data mining techniques

Data mining techniques are used to discover knowledge from GIS database in order to improve remote sensing image classification.Two learning granularities are proposed for inductive learning from spatial data,one is spatial object granularity,the other is pixel granularity.We also present an approach to combine inductive learning with conventional image classification methods,which selects class probability of Bayes classification as learning attributes.A land use classification experiment is performed in the Beijing area using SPOT multi-spectral image and GIS data.Rules about spatial distribution patterns and shape features are discovered by C5.0 inductive learning algorithm and then the image is reclassified by deductive reasoning.Comparing with the result produced only by Bayes classification,the overall accuracy increased by 11% and the accuracy of some classes,such as garden and forest,increased by about 30%.The results indicate that inductive learning can resolve spectral confusion to a great extent.Combining Bayes method with inductive learning not only improves classification accuracy greatly,but also extends the classification by subdividing some classes with the discovered knowledge.     

Genetic feature selection for texture classification

This paper presents a novel approach to feature subset selection using genetic algorithms. This approach has the ability to accommodate multiple criteria such as the accuracy and cost of classification into the process of feature selection and finds the effective feature subset for texture classification. On the basis of the effective feature subset selected, a method is described to extract the objects which are higher than their surroundings, such as trees or forest, in the color aerial images. The methodology presented in this paper is illustrated by its application to the problem of trees extraction from aerial images.     

Multiresolution fusion of remote sensing images based on resolution degradation model

A new method based on resolution degradation model is proposed to improve both spatial and spectral quality of the synthetic images. Some ETM panchromatic and multispectral images are used to assess the new method. Its spatial and spectral effects are evaluated by qualitative and quantitative measures and the results are compared with those of IHS, PCA, Brovey, OWT(Orthogonal Wavelet Transform) and RWT (Redundant Wavelet Transform). The results show that the new method can keep almost the same spatial resolution as the panchromatic images, and the spectral effect of the new method is as good as those of waveletbased methods.     

Assessment of regression kriging for spatial interpolation – comparisons of seven GIS interpolation methods

As an important GIS function, spatial interpolation is one of the most often used geographic techniques for spatial query, spatial data visualization, and spatial decision-making processes in GIS and environmental science. However, less attention has been paid on the comparisons of available spatial interpolation methods, although a number of GIS models including inverse distance weighting, spline, radial basis functions, and the typical geostatistical models (i.e. ordinary kriging, universal kriging, and cokriging) are already incorporated in GIS software packages. In this research, the conceptual and methodological aspects of regression kriging and GIS built-in interpolation models and their interpolation performance are compared and evaluated. Regression kriging is the combination of multivariate regression and kriging. It takes into consideration the spatial autocorrelation of the variable of interest, the correlation between the variable of interest and auxiliary variables (e.g., remotely sensed images are often relatively easy to obtain as auxiliary variables), and the unbiased spatial estimation with minimized variance. To assess the efficiency of regression kriging and the difference between stochastic and deterministic interpolation methods, three case studies with strong, medium, and weak correlation between the response and auxiliary variables are compared to assess interpolation performances. Results indicate that regression kriging has the potential to significantly improve spatial prediction accuracy even when using a weakly correlated auxiliary variable.     

Comparison of Geographically Weighted Regression and Regression Kriging for Estimating the Spatial Distribution of Soil Organic Matter

Soil organic matter (SOM) is an important component of soils, and knowing the spatial distribution and variation of SOM is the premise for sustainably utilizing soils. The objective of this study was to compare geographically weighted regression (GWR) with regression kriging (RK) for estimating the spatial distribution of SOM using field-sample data in SOM and auxiliary data in correlated environmental variables (e.g., elevation, slope, ferrous minerals index, and Normalized Difference Vegetation Index). Results showed that GWR was a relatively better method and could provide promising results for SOM prediction in comparison with RK. The map interpolated by GWR showed similar spatial patterns influenced by environmental variables and the nonapparent effect of data outliers, but with higher accuracies, compared to that interpolated by RK.     

Downscaling in remote sensing

Downscaling has an important role to play in remote sensing. It allows prediction at a finer spatial resolution than that of the input imagery, based on either (i) assumptions or prior knowledge about the character of the target spatial variation coupled with spatial optimisation, (ii) spatial prediction through interpolation or (iii) direct information on the relation between spatial resolutions in the form of a regression model. Two classes of goal can be distinguished based on whether continua are predicted (through downscaling or area-to-point prediction) or categories are predicted (super-resolution mapping), in both cases from continuous input data. This paper reviews a range of techniques for both goals, focusing on area-to-point kriging and downscaling cokriging in the former case and spatial optimisation techniques and multiple point geostatistics in the latter case. Several issues are discussed including the information content of training data, including training images, the need for model-based uncertainty information to accompany downscaling predictions, and the fundamental limits on the representativeness of downscaling predictions. The paper ends with a look towards the grand challenge of downscaling in the context of time-series image stacks. The challenge here is to use all the available information to produce a downscaled series of images that is coherent between images and, thus, which helps to distinguish real changes (signal) from noise.     

Increased accuracy of geostatistical prediction of nitrogen dioxide in the United Kingdom with secondary data

Five techniques were used to map nitrogen dioxide (NO₂) concentrations in the United Kingdom. The methods used to predict from point data, collected as part of the UK NO₂ diffusion tube network, were local linear regression (LR), inverse distance weighting (IDW), ordinary kriging (OK), simple kriging with a locally varying mean (SKlm) and kriging with an external drift (KED). These techniques may be divided into two groups: (i) those that use only a single variable in the prediction process (IDW, OK) and (ii) those that make use of additional variables as a part of prediction (LR, SKlm and KED). Nitrous oxides emission data were used as secondary data with LR, SKlm and KED. It was concluded that SKlm provided the most accurate predictions based on the summary statistics of prediction errors from cross-validation.     

Mapping of Soil Micronutrients in Kashmir Agricultural Landscape Using Ordinary Kriging and Indicator Approach

Soil nutrient maps based on intensive soil sampling are useful to adopt site-specific management practices. Geostatistical methods have been widely used to determine the spatial correlation and the range of spatial dependence at different sampling scales. If spatial dependence is detected, the modeled semivariograms can then be used to map the interested variable by kriging, an interpolation method that produces unbiased estimates with minimal estimation variance. The objectives of this paper were to examine and map the spatial distribution of the soil micronutrients Cu, Zn, Fe and Mn on an agricultural area in Kupwara, J&K, under temperate climatic conditions. The ordinary kriging was first used to determine the values for the non-sampled locations, and then the indicator approach was used to transform the micronutrient content values into binary values having the mean values of each nutrient as the threshold content. All four elements analyzed showed spatial dependence using the indicator semivariograms. The strength of spatial dependence was assessed using the values of nugget effect and range from the semivariogram, the fitted range values decreased in the order Zn > Cu > Mn > Fe. The spatial dependence of the combination of two or more of the studied micronutrients was also examined using indicator semivariograms. In opposition to spatial analysis of individual microelements, indicator semivariograms obtained for the binary coding of the variables showed a great nugget effect value or a low proportion of sill. The maps for each nutrient obtained using indicator kriging showed some similarity in the spatial distribution, suggesting the delimitation of uniform management areas.     

Geostatistical modeling using LiDAR-derived prior knowledge with SPOT-6 data to estimate temperate forest canopy cover and above-ground biomass via stratified random sampling

Forest canopy cover (CC) and above-ground biomass (AGB) are important ecological indicators for forest monitoring and geoscience applications. This study aimed to estimate temperate forest CC and AGB by integrating airborne LiDAR data with wall-to-wall space-borne SPOT-6 data through geostatistical modeling. Our study involved the following approach: (1) reference maps of CC and AGB were derived from wall-to-wall LiDAR data and calibrated by field measurements; (2) twelve discrete LiDAR flights were simulated by assuming that LiDAR data were only available beneath these flights; (3) training/testing samples of CC and AGB were extracted from the reference maps inside and outside the simulated flights using stratified random sampling; (4) The simple linear regression, ordinary kriging and regression kriging model were used to extend the sparsely sampled CC/AGB data to the entire study area by incorporating a selection of SPOT-6 variables, including vegetation indices and texture variables. The regression kriging model was superior at estimating and mapping the spatial distribution of CC and AGB, as it featured the lowest mean absolute error (MAE; 11.295% and 18.929 t/ha for CC and AGB, respectively) and root mean squared error (RMSE; 17.361% and 21.351 t/ha for CC and AGB, respectively). The predicted and reference values of both CC and AGB were highly correlated for the entire study area based on the estimation histograms and error maps. Finally, we concluded that the regression kriging model was superior and more effective at estimating LiDAR-derived CC and AGB values using the spatially-reduced samples and the SPOT-6 variables. The presented modeling workflow will greatly facilitate future forest growth monitoring and carbon stock assessments for large areas of temperate forest in northeast China. It also provides guidance on how to take full advantage of future sparsely collected LiDAR data in cases where wall-to-wall LiDAR coverage is not available from the perspective of geostatistics.     

Geostatistical techniques for incorporating spatial correlation into land use change models

Land use modeling requires large amounts of data that are typically spatially correlated. This study applies two geostatistical techniques to account for spatial correlation in residential land use change modeling. In the first approach, we combined generalized linear model (GLM) with indicator kriging to estimate the posterior probability of residential development. In the second approach, generalized linear mixed model (GLMM) was used to simultaneously model spatial correlation and regression fixed effects. Spatial agreement between actual and modeled land use change was higher for the GLM incorporating indicator kriging. The GLMM produced more reliable estimates and could be more useful in analyzing the effects of driving factors of land use change for land use planning.     

The hierarchical tessellation model and its use in spatial analysis

The hierarchid tessellation model belongs to a class of spatial data models based on the recursive decomposition of space. The quadtree is one such tessellation and is characterized by square cells and a 1:4 decomposition ratio. To relax these constraints in the tessellation, a generalized hierarchical tessellation data model, called Adaptive Recursive Tessellations (ART), has been proposed. ART increases flexibility in the tessellation by the use of rectangular cells and variable decomposition ratios. In ART, users can specify cell sizes which are intuitively meaningful to their applications, or which can reflect the scales of data. ART is implemented in a data structure called Adaptive Recursive Run-Encoding (ARRE), which is a variant of two-dimensional run-encoding whose running path can vary with the different tessellation structures incorporated in an ART model. Given the recognition of the benefits of implementing statistical spatial analysis in GIS, the use of hierarchical tessellation models such as ART in spatial analysis is discussed. Three examples are introduced to show how ART can: (1) be applied to solve the quadrat size problem in quadrat analysis of point patterns; (2) act as the data model in the variable resolution block kriging technique for geostatistical data to reduce variation in kriging error; and (3) facilitate the evaluation of spatial autocorrelation for area data at multiple map resolutions via the construction of a connectivity matrix for calculating spatial autocorrelation indices based on ARRE.     

Interpolation Methods for Scattered Sample Data: Accuracy,Spatial Patterns,Processing Time

Interpolation routines based on polynomials, splines, linear triangulation, proximation, distance weighting, and kriging are tested on their efficacy to visualize spatial patterns. Implementations in commonly available software packages are used in order to yield practical recommendations on the application of current information technology. Two data sets of physical variables containing irregularly distributed sample point values are used as input data. Accuracy of predicted values at unvisited points, preservation of distinct spatial patterns (established from map use tasks), and processing time, are used as criteria to determine the merits of the various interpolation methods. It was found that highly accurate interpolations do not always produce realistic spatial patterns. Effectiveness of distance weighting and kriging methods was found to be largely dependent on the number of neighbors used. For both gradually and abruptly changing data, geographic reality was visualized most satisfactorily with the squared inverse distance weighting (w=d^-2 ) method using respectively few (four to eight) and many (16 to 24) neighbors.