King (1991) presented an upscaling method in which it is assumed interest
variables will be random variables, their outputs will vary spatially across a landscape,
and the spatial heterogeneity of the landscape will be defined by a joint probability
distribution of the variables. The expected values of the variables at any locations are
then estimated by Monte Carlo simulation and are weighted with corresponding areas.
This method simulates window means as realizations of random variables from a joint
probability distribution and provides the potential to capture dominant features within
windows.
Hay et al. (1997) developed an object-specific resampling method. In this method,
it is assumed that the closer the locations, the more similar the data. Furthermore, each
ground object can be represented with a corresponding image object and consists of
pixels that have similar spectral features. When the values of pixels are aggregated
using different window sizes such as 3 ´ 3 pixels, 5 ´ 5 pixels, 7 ´ 7 pixels, and so
on, window variances can be calculated. As the window size increases, the window
variance varies and a distinct threshold of area in the variance of pixel values will thus
be observed. If the spatial resolution is fine enough, the area within the neighborhood
of the threshold can then be determined for each pixel and used to determine the
pixel’s weight to calculate the window value. This method is similar to the window
averaging mentioned previously and cannot be used to aggregate the sampling plot
data that are not available everywhere.
Wang et al. (2004a) developed and assessed five upscaling methods in a study for
aggregating and using Landsat Thematic Mapper (TM) images for mapping vegetation covers and inferring a topographic factor related to soil erosion from finer to
coarser spatial resolutions. These methods included three spatial variability-weighted
methods and two simulation methods. The idea behind the methods is that the spatial
autocorrelation of variables measured as the square difference of two data values that
are separated by a distance h can be used to derive weights of pixels within a window.
The larger the square difference, the less the weight for this pixel is. The weight is thus
defined as the reciprocal of the square difference. Based on the different definitions of
the square difference, Wang et al. (2004a) obtained (i) the center-pixel variabilityweighted method in which the square difference is quantified based on the differences
of spectral values between the central pixel and each pixel within the window; (ii) the
dominant-class variability-weighted method in which the square difference between
the window dominant-class value and each pixel value is used; and (iii) the arithmeticaverage variability-weighted method in which the square difference between the
window arithmetic average and each pixel value is defined.
Moreover, Wang et al. (2004a) assumed a window dominant feature be the
expectation of a random variable and be determined by a set of realizations by
randomly drawing from its distribution at the location. The local distribution can be
obtained by calculating a conditional mean and a conditional variance of the pixel
values within the window or neighborhood. In addition, the spatial autocorrelation
between the pixel values can also be incorporated into the conditional variance. From
the obtained distribution, a value can be randomly drawn and used as a realization
of the window average. This process is repeated many times, which results in more
than one value. These values are used to calculate a window mean. The obtained
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UPSCALING WITH CONDITIONAL COSIMULATION FOR MAPPING
variables will be random variables, their outputs will vary spatially across a landscape,
and the spatial heterogeneity of the landscape will be defined by a joint probability
distribution of the variables. The expected values of the variables at any locations are
then estimated by Monte Carlo simulation and are weighted with corresponding areas.
This method simulates window means as realizations of random variables from a joint
probability distribution and provides the potential to capture dominant features within
windows.
Hay et al. (1997) developed an object-specific resampling method. In this method,
it is assumed that the closer the locations, the more similar the data. Furthermore, each
ground object can be represented with a corresponding image object and consists of
pixels that have similar spectral features. When the values of pixels are aggregated
using different window sizes such as 3 ´ 3 pixels, 5 ´ 5 pixels, 7 ´ 7 pixels, and so
on, window variances can be calculated. As the window size increases, the window
variance varies and a distinct threshold of area in the variance of pixel values will thus
be observed. If the spatial resolution is fine enough, the area within the neighborhood
of the threshold can then be determined for each pixel and used to determine the
pixel’s weight to calculate the window value. This method is similar to the window
averaging mentioned previously and cannot be used to aggregate the sampling plot
data that are not available everywhere.
Wang et al. (2004a) developed and assessed five upscaling methods in a study for
aggregating and using Landsat Thematic Mapper (TM) images for mapping vegetation covers and inferring a topographic factor related to soil erosion from finer to
coarser spatial resolutions. These methods included three spatial variability-weighted
methods and two simulation methods. The idea behind the methods is that the spatial
autocorrelation of variables measured as the square difference of two data values that
are separated by a distance h can be used to derive weights of pixels within a window.
The larger the square difference, the less the weight for this pixel is. The weight is thus
defined as the reciprocal of the square difference. Based on the different definitions of
the square difference, Wang et al. (2004a) obtained (i) the center-pixel variabilityweighted method in which the square difference is quantified based on the differences
of spectral values between the central pixel and each pixel within the window; (ii) the
dominant-class variability-weighted method in which the square difference between
the window dominant-class value and each pixel value is used; and (iii) the arithmeticaverage variability-weighted method in which the square difference between the
window arithmetic average and each pixel value is defined.
Moreover, Wang et al. (2004a) assumed a window dominant feature be the
expectation of a random variable and be determined by a set of realizations by
randomly drawing from its distribution at the location. The local distribution can be
obtained by calculating a conditional mean and a conditional variance of the pixel
values within the window or neighborhood. In addition, the spatial autocorrelation
between the pixel values can also be incorporated into the conditional variance. From
the obtained distribution, a value can be randomly drawn and used as a realization
of the window average. This process is repeated many times, which results in more
than one value. These values are used to calculate a window mean. The obtained
110
UPSCALING WITH CONDITIONAL COSIMULATION FOR MAPPING