Modeling spatial dependence in high spatial resolution hyperspectral data sets

 As either the spatial resolution or the spatial scale for a geographic landscape increases, both latent spatial dependence and spatial heterogeneity also will tend to increase. In addition, the amount of georeferenced data that results becomes massively large. These features of high spatial resolution hyperspectral data present several impediments to conducting a spatial statistical analysis of such data. Foremost is the requirement of popular spatial autoregressive models to compute eigenvalues for a row-standardized geographic weights matrix that depicts the geographic configuration of an image's pixels. A second drawback arises from a need to account for increased spatial heterogeneity. And a third concern stems from the usefulness of marrying geostatistical and spatial autoregressive models in order to employ their combined power in a spatial analysis. Research reported in this paper addresses all three of these topics, proposing successful ways to prevent them from hindering a spatial statistical analysis. For illustrative purposes, the proposed techniques are employed in a spatial analysis of a high spatial resolution hyperspectral image collected during research on riparian habitats in the Yellowstone ecosystem. Received: 25 February 2001 / Accepted: 2 August 2001     

Mapping of stream microhabitats with high spatial resolution hyperspectral imagery

 Maximum likelihood supervised classifications with 1-m 128 band hyperspectral data accurately map in-stream habitats in the Lamar River, Wyoming with producer's accuracies of 91% for pools, 87% for glides, 76% for riffles, and 85% for eddy drop zones. Coarser resolution 5-m hyperspectral data and 1-m simulated multiband imagery yield lower accuracies that are unacceptable for inventory and analysis. Both high spatial resolution and hyperspectral coverage are therefore necessary to map microhabitats in the study area. In many instances, the high spatial resolution hyperspectral (HSRH) imagery appears to map the stream habitats with greater accuracy than our ground-based surveys, thus challenging classical approaches used for accuracy assessment in remote sensing. Received: 9 April 2001 / Accepted: 8 October 2001     

Emerging and vector-borne diseases: Role of high spatial resolution and hyperspectral images in analyses and forecasts

 Many infectious diseases that are emerging or transmitted by arthropod vectors have a strong link to landscape features. Depending on the source of infection or ecology of the transmitting vector, micro-habitat characteristics at the spatial scale of square meters or less may be important. Recently, satellite images have been used to classify habitats in an attempt to understand associations with infectious diseases. Whether high spatial resolution and hyperspectral (HSRH) images can be useful in studies of such infectious diseases is addressed. The nature of questions that such studies address and the desired accuracy and precision of answers will determine the utility of HSRH data. Need for such data should be based on the goals of the effort. Examples of kinds of questions and applications are discussed. The research implications and public health applications may depend on available analytic tools as well as epidemiological observations. Received: 30 July 2001 / Accepted: 14 October 2001     

Geostatistical incorporation of spatial coordinates into supervised classification of hyperspectral data

 This paper presents a methodology to incorporate both hyperspectral properties and spatial coordinates of pixels in maximum likelihood classification. Indicator kriging of ground data is used to estimate, for each pixel, the prior probabilities of occurrence of classes which are then combined with spectral-based probabilities within a Bayesian framework. In the case study (mapping of in-stream habitats), accounting for spatial coordinates increases the overall producer's accuracy from 85.8% to 93.8%, while the Kappa statistic rises from 0.74 to 0.88. Best results are obtained using only indicator kriging-based probabilities, with a stunning overall accuracy of 97.2%. Significant improvements are observed for environmentally important units, such as pools (Kappa: 0.17 to 0.74) and eddy drop zones (Kappa: 0.65 to 0.87). The lack of benefit of using hyperspectral information in the present study can be explained by the dense network of ground observations and the high spatial continuity of field classification which might be spurious. Received: 12 April 2001 / Accepted: 7 September 2001     

Spatial analysis in a Markov random field framework: The case of burning oil wells in Kuwait

 This paper discusses a modeling approach for spatial-temporal prediction of environmental phenomena using classified satellite images. This research was prompted by the analysis of change and landscape redistribution of petroleum residues formed from the residue of the burning oil wells in Kuwait (1991). These surface residues have been termed “tarcrete” (El-Baz et al. 1994). The tarcrete forms a thick layer over sand and desert pavement covering a significant portion of south-central Kuwait. The purpose of this study is to develop a method that utilizes satellite images from different time steps to examine the rate-of-change of the oil residue deposits and determine where redistribution is are likely to occur. This problem exhibits general characteristics of environmental diffusion and dispersion phenomena so a theoretical framework for a general solution is sought. The use of a lagged-clique, Markov random field framework and entropy measures is deduced to be an effective solution to satisfy the criteria of determination of time-rate-of-change of the surface deposits and to forecast likely locations of redistribution of dispersed, aggraded residues. The method minimally requires image classification, the determination of time stationarity of classes and the measurement of the level of organization of the state-space information derived from the images. Analysis occurs at levels of both the individual pixels and the system to determine specific states and suites of states in space and time. Convergence of the observed landscape disorder with respect to an analytical maximum provide information on the total dispersion of the residual system. Received: 5 September 2000 / Accepted: 10 July 2001     

Spatial statistical techniques for aggregating point objects extracted from high spatial resolution remotely sensed imagery

 Using a local maximum filter, individual trees were extracted from a 1 m spatial resolution IKONOS image and represented as points. The spatial pattern of individual trees was determined to represent forest age (a surrogate for forest structure). Point attributes, based on the spatial pattern of trees, were generated via nearest neighbour statistics and used as the basis for aggregating points into forest structure units. The forest structure units allowed for the mapping of a forested area into one of three age categories: young (1–20 years), intermediate (21–120 years), and mature (>120 years). This research indicates a new approach to image processing, where objects generated from the processing of image data (rather than pixels or spectral values) are subjected to spatial statistical analysis to estimate an attribute relating an aspect of forest structure. Received: 22 April 2002 / Accepted: 23 November 2002     

Use of Markov Random Fields for automatic cloud/shadow detection on high resolution optical images

In this study, we propose an automatic detection algorithm for cloud/shadow on remote sensing optical images. It is based on physical properties of clouds and shadows, namely for a cloud and its associated shadow: both are connex objects of similar shape and area, and they are related by their relative locations. We show that these properties can be formalized using Markov Random Field (MRF) framework at two levels: one MRF over the pixel graph for connexity modelling, and one MRF over the graph of objects (clouds and shadows) for their relationship modelling. Then, we show that, practically, having performed an image pre-processing step (channel inter-calibration) specific to cloud detection, the local optimization of the proposed MRF models leads to a rather simple image processing algorithm involving only six parameters. Using a 39 image database, performance is shown and discussed, in particular in comparison with the Marked Point Process approach.     

Area-based tests for association between spatial patterns

 Edge effects pervade natural systems, and the processes that determine spatial heterogeneity (e.g. physical, geochemical, biological, ecological factors) occur on diverse spatial scales. Hence, tests for association between spatial patterns should be unbiased by edge effects and be based on null spatial models that incorporate the spatial heterogeneity characteristic of real-world systems. This paper develops probabilistic pattern association tests that are appropriate when edge effects are present, polygon size is heterogeneous, and the number of polygons varies from one classification to another. The tests are based on the amount of overlap between polygons in each of two partitions. Unweighted and area-weighted versions of the statistics are developed and verified using scenarios representing both polygon overlap and avoidance at different spatial scales and for different distributions of polygon sizes. These statistics were applied to Soda Butte Creek, Wyoming, to determine whether stream microhabitats, such as riffles, pools and glides, can be identified remotely using high spatial resolution hyperspectral imagery. These new “spatially explicit” techniques provide information and insights that cannot be obtained from the spectral information alone. Received 1 June 2001 / Accepted 25 October 2001     

Solution and econometric estimation of spatial dynamic models in continuous space and continuous time

 This paper presents and demonstrates a general approach to solving spatial dynamic models in continuous space and continuous time that characterize the behaviour of intertemporally and interspatially optimizing agents and estimating from discrete data the parameters of such models. The approach involves the use of a projection method to solve the models and a quasi-Newton algorithm to update quasi-FIML parameter estimates. Received: 26 July 2000 / Accepted: 31 January 2001     

Change detection thresholds for remotely sensed images

 The detection of change in remotely sensed images is often carried out by designating a threshold to distinguish between areas of change and areas of no change. The choice of threshold is often arbitrary however. The purpose of this paper is to offer a statistical framework for the selection of thresholds. The framework accounts for the facts that one carries out multiple tests of the null hypothesis of no change, when searching for regions of change over an image with a large number of pixels. Special attention is given to global spatial autocorrelation, which can affect the selection of appropriate threshold values. Received: 8 March 2001 / Accepted: 12 October 2001     

The Bayesian approach applied to GPS ambiguity resolution. A mixture model for the discrete–real ambiguities alternative

 The problem of phase ambiguity resolution in global positioning system (GPS) theory is considered. The Bayesian approach is applied to this problem and, using Monte Carlo simulation to search over the integer candidates, a practical expression for the Bayesian estimator is obtained. The analysis of the integer grid points inside the search ellipsoid and their evolution with time, while measurements are accumulated, leads to the development of a Bayesian theory based on a mathematical mixture model for the ambiguity. Received: 29 March 2001 / Accepted: 3 September 2001     

Determining the size of spatial clusters in focused tests: Comparing two methods by means of simulation in a GIS

 Based on a four-point evaluation system consisting of accuracy, consistency, power, and chance to commit type I errors, this study compares Tango's minimum p (MinP) and Stone's maximum relative risk (MaxRR) methods for detecting focused cluster size through simulations in GIS. It reveals that the MinP method is more effective than the MaxRR method. The MinP method exhibits higher levels of accuracy and consistency; and its power and chance to commit type I errors are similar to the MinP method. The MaxRR method has a tendency to underestimate the cluster size, while the MinP method tends to overestimate the cluster size, particularly when the clusters are relatively big and have high relative risk levels. In addition, the MinP method seems to be most effective in revealing the size of clusters when clusters are neither too strong nor too weak. The lowest detection rates for clustering occur when the clustering signal is relatively weak, which is easily understandable. In practice, it might be useful to use both the methods to estimate a range of possible cluster sizes, where the MaxRR method indicates the lower estimate, while the MinP method gives the higher estimate of the cluster size. Received: 24 August 2002 / Accepted: 20 December 2002     

Testing spatial patterns and growth spillover effects in clusters of cities

 This paper analyzes the spatial patterns of households' distribution in clusters of cities and the effects on regional growth using spatial exploratory techniques and a model of growth that incorporates spatial location. Our empirical analysis shows that, over the 1980–1990 period, in Southern New England, patterns of spatial clustering of households did create heterogeneous growth rates in the region. Also, there is evidence that clusters of cities and isolated cities created spillover growth effects in bordering towns. Received: 5 September 2001 / Accepted: 2 August 2002     

The role of spatial effects in the empirical analysis of regional concentration

 Economists have recently devoted an increasing attention to the issue of spatial concentration of economic activities. However, surprisingly enough, most of the empirical work is still based on the computation of very basic statistical measures in which the geographical characteristics of data play no role. By making use of a series of empirical examples we show that spatial concentration consists of two different features that are rarely kept as separate in the statistical analysis: an a-spatial concept of variability which is invariant to permutations, and the concept of polarization that refers to the geographical position of observations. Received: 8 August 2000 / Accepted: 20 June 2001     

Misspecifications in interaction model distance decay relations: A spatial structure effect

 An exclusively statistical approach is proposed to address the spatial structure effects of general interaction models. It is shown that the spatial heterogeneity in the estimated region-specific distance decay parameters may in part be due to the combination of two factors: (a) a functional mis-specification of the global distance decay relationship; and (b) the heterogeneity in the region-specific conditional distance distributions. A properly specified global distance decay function allows controlling for these spatially induced biases in the local distance decay parameters. However, inherent multicollinearities between the set of region specific distance decay parameters and other estimated model parameters prevent an unambiguous interpretation. A key conclusion is that a proper model specification, in particular, the specification of the global distance decay relationship, is of paramount importance in interaction modeling and for accessibility studies. Received: September 2002 / Accepted: January 2003     

A computational approach for the analysis of changes in polygon distributions

 This paper develops a computational method for analyzing changes in polygon distributions. Unmovable polygons that change discontinuously without explicit functional linkage information are discussed. Six types of primitive events are used to describe the change: 1) generation, 2) disappearance, 3) expansion, 4) shrinkage, 5) union, and 6) division. The change of polygon distributions is decomposed into a combination of these events. A computational procedure for deducing a set of events from polygon distributions of two times is proposed. The method is applied to the analysis of the spatial competition between the major and small chains of convenience stores in Tokyo, Japan. Some empirical findings are shown. Received: 3 August 2000 / Accepted: 6 February 2001     

Spatial econometrics functions in R: Classes and methods

 Placing spatial econometrics and more generally spatial statistics in the context of an extensible data analysis environment such as R exposes similarities and differences between traditions of analysis. This can be fruitful, and is explored here in relation to prediction and other methods usually applied to fitted models in R. Objects in R may be assigned a class attribute, including fitted model objects. Such fitted model objects may be provided with methods allowing them to be displayed, compared, and used for prediction, and it is of interest to see whether fitted spatial models can be treated in the same way. Received: 26 August 2002 / Revised version: 15 January 2003