Peer-Reviewed Articles
41 Geostatistical Estimation of Resolution-Dependent Variance in Remotely
Sensed Images
John B. Collins and Curtis E. Woodcock
Abstract
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The variance of a remotely sensed image is determined by the interaction of
scene properties with the spatial characteristics of the sensor. Image variance
is related to information content, and therefore determines the ability to
extract useful information about scene conditions. We describe a technique
to estimate image variance at multiple spatial resolutions. The method is useful
for comparing the capabilities of sensors with differing spatial responses.
The point-spread function (PsF) and the variogram quantify the spatial characteristics of the sensor and image, respectively. A geostatistical model based on these two elements relates the punctual variogram of a scene with the regularized variogram of an image. This model forms the basis for a numerical approach to approximate the punctual variogram from regularized observations. The resulting estimate of the punctual variogram allows analytical determination of image variance at different spatial resolutions.
Analysis of simulated images confirms the utility of this algorithm. Variance of coarse-resolution images may be estimated reliably from fine-resolution data. Simulations of multiscale variability show that the method handles more complex types of scene variability as well. The geostatistical variance estimation algorithm better characterizes the relationship between variance and spatial resolution than do simpler methods, such as averaging blocks of pixels. Specifically, methods which do not account for overlap of adjacent placements of the sensor PSF tend to overestimate the variance of the resulting images. The algorithm presented here can be used to evaluate the utility of different sensors for particular applications, when the relationship between spatial resolution and image information content is important.
51 Multi-Scale Fractal Analysis of Image Texture and Patterns
Charles W. Emerson, Nina Siu-Ngan Lam, and Dale A. Quattrochi
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Analyses of the fractal dimension of Normalized Difference Vegetation Index
(NDVI) images of homogeneous land covers near Huntsville, Alabama revealed
that the fractal dimension of an image of an agricultural land cover indicates
greater complexity as pixel size increases, a forested land cover gradually
grows smoother, and an urban image remains roughly self-similar over the
range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat
Thematic Mapper images of the East Humboldt Range in Nevada taken four months
apart show a more complex relation between pixel size and fractal
dimension. The major visible difference between the spring and late summer
NDVI images is the absence of high elevation snow cover in the summer image.
This change significantly alters the relation between fractal dimension and
pixel size. The slope of the fractal dimension resolution relation provides
indications of how image classification or feature identification will be
affected by changes in sensor spatial resolution.
63 Fractal Characterization of Hyperspectral Imagery
Hong-lie Qiu, Nina Siu-Ngan Lam, Dale A. Quattrochi, and John A. Gamon
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Two AVIRIS hyperspectral images selected from the Los Angeles area, one representing
urban and the other rural, were used to examine their spatial complexity
across their entire spectrum of the remote sensing data. Using the ICAMS
(Image Characterization And Modeling System) software, we computed the fractal
dimension values using the isarithm and triangular prism methods for all
224 bands in the two AVIRIS scenes. The resultant fractal dimensions reflect
changes in image complexity across the spectral range of the hyperspectral
images. Both the isarithm and triangular prism methods detect unusually high
D values on the spectral bands that all within the atmospheric absorption
and scattering zones where signal-to-noise ratios are low. Fractal dimensions
for the urban area resulted in higher values than for the rural landscape,
and the differences between the resulting D values are more distinct in the
visible bands. The triangular rism method is sensitive to a few random speckles
in the mages, leading to a lower dimensionality. On the contrary, the isarithm
method will ignore the speckles and focus on the major variation dominating
the surface, thus resulting in higher dimension. It is seen where the fractal
curves plotted for the entire bandwidth range of the hyperspectral images
could be used to distinguish landscape types as well as or screening noisy
bands.
73 Comparing Effects of Aggregation Methods on Statistical and Spatial Properties
of Simulated Spatial Data
Ling Bian and Rachael Butler
Abstract
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Spatial data aggregation is widely practiced for "scaling-up" environmental
analyses and modeling from local to regional or global scales. Despite acknowledgments
of the general effects of aggregation, there is a lack of systematic comparison
between aggregation methods. The study evaluated three methods — averaging,
central-pixel resampling, and median — using simulated images. Both the
averaging and median methods can retain the mean and median values, respectively,
but alter significantly the standard deviation. The central-pixel method alters
both statistics. The statistical changes can be modified by the presence of
spatial autocorrelation for all three methods. Spatially, the averaging method
can reveal underlying spatial patterns at scales within the spatial autocorrelation
ranges. The median method produces almost identical results because of the
similarities between the averaged and median values of the simulated data.
To a limited extent, the central-pixel method retains contrast and spatial
patterns of the original images. At scales coarser than the autocorrelation
range, the averaged and median images become homogeneous and do not differ
significantly between these scales. The central-pixel method can induce severe
spatially biased errors at coarse scales. Understanding these trends can help
select appropriate aggregation methods and aggregation levels for particular
applications.
85 A Cartographic Modeling Approach for Surface Orientation-Related Applications
Michael E. Hodgson and Gary L. Gaile
Abstract
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Applications requiring the comparison of angular directions, descriptive angular
statistics, or spatial interpolation of directional data are problematic
to implement because accepted GIS modeling language constructs do not contain
the directional data types or operators. Embedded directional operators or
models may be developed with existing GIS functionality by reorganizing the
directions into unit vectors. Representation of directional observations,
such as surface orientation or solar rays, in a unit vector matrix form allows
for the development using linear algebra in cartographic modeling constructs.
This article presents fundamental directional opera tars and demonstrates
their development for several surface-oriented applications: mean and dispersion
in neighborhood surface orientation, comparison of surfaces, shaded relief
mapping, topographic normalization of remotely sensed imagery, and solar
radiation. Extension of the fundamental directional operators to spatial
interpolation is also discussed.
97 Scale-Dependent Relationships between Population and Environment in Northeastern
Thailand
Stephen J. Walsh, Tom. P. Evans, William F. Welsh, Barbara Entwisle, and Ronald
R. Rindfuss
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Social and biophysical data were collected, integrated, and analyzed to examine
scale-dependent relationships between selected population and environmental
variables for a study site in northeast Thailand. Data sets were generated
through the use of remote sensing to characterize land-use/land-cover and
plant biomass variation across the Nang Rong district GIS to derive elevation,
slope angle, and soil moisture potential; social survey data at the village
level to categorize dem ographic variables; and a population distribution
model to transform demographic data collected at discrete village locations
to spatially continuous surfaces stratified by agricultural land uses.
Statistical analysis employed multiple regression to estimate population
density in relation to social and biophysical variables, and canonical analysis
to relate pop ulation variables to environmental variables across a range
of spatial scales extending from 30 to 1050 m. Findings indicate the importance
of spatial scale in the study of population and the environment. Regression
models reflect the scale dependence of the selected variables through plots
of slope coefficients and R2 values across nine scale steps. The variation
in relationships among environment and population variables, evidenced through
factor loadings associated with canonical correlation, suggest that relationships
are not generalizeable across the sampled spatial scales.
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