SAMPLING REMOTELY SENSED IMAGERY FOR STORAGE,RETRIEVAL, AND RECONSTRUCTION*

A major difficulty in remote sensing is handling the many data from sensors aboard aircraft and satellites. In this paper we identify an optimal procedure for sampling remotely sensed data before their storage or on their retrieval. The procedure depends on spatial correlation in the scene and uses kriging to estimate values that have been lost. An example in which data from an airborne multispectral scanner could be diminished to only about one tenth without serious loss of precision illustrates the method.     

On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

Histogram and variogram inference in the multigaussian model

Several iterative algorithms are proposed to improve the histogram and variogram inference in the framework of the multigaussian model. The starting point is the variogram obtained after a traditional normal score transform. The subsequent step consists in simulating many sets of gaussian values with this variogram at the data locations, so that the ranking of the original values is honored. The expected gaussian transformation and the expected variogram are computed by an averaging operation over the simulated datasets. The variogram model is then updated and the procedure is repeated until convergence. Such an iterative algorithm can adapt to the case of tied data and despike the histogram. Two additional issues are also examined, referred to the modeling of the empirical transformation function and to the optimal pair weighting when computing the sample variogram.     

Spatial variability in soil moisture as predicted from airborne thematic mapper (ATM) data

In the first part of this project, the extent to which moisture content of alluvial soils could be predicted from imagery derived from an airborne thematic mapper (ATM) was investigated. From sampling done on the same day as the flight, it was found that digital numbers derived from the thermal channel (waveband 11) were strongly correlated with gravimetric moisture content. From sampling three fields of contrasting land cover, the relationship between waveband 11 values and moisture content was found to be independent of land cover type. Spatial variation in waveband 11 values and thus moisture content were related to palaeochannel patterns on the alluvial land. This was investigated by deriving variograms for long transects from each of the three investigated fields. The range and sills of the variograms are shown to express the nature and pattern of palaeochannels. By the application of such geostatistical techniques, high resolution imagery can thus be used to quantify palaeochannel characteristics on alluvial land.     

The Linear Coregionalization Model and the Product–Sum Space–Time Variogram

The product covariance model, the product–sum covariance model, and the integrated product and integrated product–sum models have the advantage of being easily fitted by the use of marginal variograms. These models and the use of the marginals are described in a series of papers by De Iaco, Myers, and Posa. Such models allow not only estimating values at nondata locations but also prediction in future times, hence, they are useful for analyzing air pollution data, meteorological data, or ground water data. These three kinds of data are nearly always multivariate and because the processes determining the deposition or dynamics will affect all variates, a multivariate approach is desirable. It is shown that the use of marginal variograms for space–time modeling can be extended to the multivariate case and in particular to the use of the Linear Coregionalization Model (LCM) for cokriging in space–time. An application to an environmental data set is given.     

SOFTWARE REVIEWS

ATLAS*GIS , Version 1.0. ATLAS*MapMaker , Version 4.0. FIVFIV-SINSIN , Release 9.0. Geo-EAS , Version 1.2.1. Evan Englund Sim City , Version 1.0 Statistix , Version 3.1.     

二态序列变差函数的定理及初步地质应用

提出并证明了一个关于二态序列变差函数的定理,即二元平稳标准化正态序列的变差函数与其以零为水平的0—1二元序列变差函数的关系式。该定理为通过对定性地质变量的空间序列变异性研究以达到对原定量地质变量空间变异性的研究提供了可能与方便。文中进行了数字仿真分析,并提供了一个地质方面的初步应用。     

Mapping Curvilinear Structures with Local Anisotropy Kriging

Interpolating geo-data with curvilinear structures using geostatistics is often disappointing. Channels, for example, become disconnected sets of lakes when interpolated from point data. In order to improve the interpolation of geological structures (e.g., curvilinear structures), we present a new form of kriging, local anisotropy kriging (LAK). Local anisotropy kriging combines a gradient algorithm from image analysis with kriging in an iterative way. After an initial standard kriging interpolation, the gradient algorithm determines the local anisotropy for each cell in the grid using a search area around the cell. Subsequently, kriging is carried out with the spatially varying anisotropy. The anisotropy calculation and subsequent kriging steps will then succeed until the result is satisfactory in the way of reproducing the curvilinear structures. Depending on the size of the search area more or less detail in the geological structures can be reproduced with LAK. Using test examples we show that LAK interpolates data with curvilinear structures more realistically than standard kriging. In a real world case, using bathymetric data of the Oosterschelde estuary, LAK also proves to be quantitatively superior to standard kriging. Absolute interpolation errors are decreased by 23%. Local anisotropy kriging only uses information from point data, which makes the method very objective, it only presents “what the data can tell.”     

To be or not to be... stationary? That is the question

Stationarity in one form or another is an essential characteristic of the random function in the practice of geostatistics. Unfortunately it is a term that is both misunderstood and misused. While this presentation will not lay to rest all ambiguities or disagreements, it provides an overview and attempts to set a standard terminology so that all practitioners may communicate from a common basis. The importance of stationarity is reviewed and examples are given to illustrate the distinctions between the different forms of stationarity.     

Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping

Fractional Brownian surfaces have been widely discussed as an appropriate model for the statistical behavior of topographic surfaces. The fractals model proposes that topographic surfaces are statistically self-similar, and that a single parameter, the fractal dimension, applies at all scales. This paper presents the results of empirical examinations of 17 topographic samples. Only one of these samples shows the statistical behavior predicted by the fractals model; however, in 15 of the 17 samples, the surfaces' variograms could be adequately described by ranges of scales having constant fractal dimension, separated by distinct scale breaks. For scale ranges between adjacent breaks, surface behavior should be that predicted by the fractals model; the breaks represent characteristic horizontal scales, at which surface behavior changes substantially. These scale breaks are especially important for cartographic representations and digital elevation models, since they represent scales at which there is a distinct change in the relation between sampling interval and the associated error.