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Institute for Water and Environmental Problems, SB RAS 105 Papanintsev St., 656099 Barnaul, Russia
* Corresponding author (knm{at}iwep.ab.ru, knm{at}santafe.edu)
Received for publication January 17, 2001.
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ABSTRACT |
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 TOPNOTES ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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Abbreviations: GPD, Gibbs probability distribution • MRF, Markov random field
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INTRODUCTION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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A leading German biogeographer, Troll (1971), defined landscape as "the total spatial and visual–perceptual entity" of human living space, integrating the geosphere with the biosphere and its man-made artifacts.
In his comprehensive textbook of photo interpretation, Zonneveld (1972) proposed the following hierarchical levels for the distribution of landscape units in space:
Landforms, through their effects on climate, hydrology, soils, and vegetation, include much of the spatial variability in real-time physical and chemical processes and the functioning of the biosphere (Hobbs and Mooney, 1990, p. 291–305). One of the major tools for the holistic approach to landscape evaluation is remote sensing in its various forms, including aerial photography and satellite imagery. It should be noted that remote sensing satellites provide a combination of two types of information that can be used to assess landscape behavior—the radiance of the earth's surface on a pixel-by-pixel basis and the spatial variability of radiance due to spatial patterns that can be detected. Spatial data contain information that can greatly increase the potential of remote sensing in landform study. Spatial variability allows us to derive information on vegetation cover, water body morphology, and surface roughness inhomogeneity, as well as a method to describe the surface properties of landforms and the state of landscapes in terms of an evolutionary process.
Existing methods of classification of lakes consider neither the distribution of water bodies by their physical–chemical, electrical, and radiophysical properties, nor the amount of suspended material nor kinds and production of hydrological bionts (Kondratyev and Filatov, 1999). Existing spectral sensors make it difficult to study these properties and water quality of water bodies: the indicated parameters of water masses are non-uniformly distributed over the basin and require a volumetric expression of the point where the water was sampled and the properties measured. In principle, the use of spectral sensors solves the problem of representativity of in situ point-to-point measurements. Statistical spatial measures describing landscape characteristics and water bodies have not been widely adapted to remote sensing data and to collecting data, information, and knowledge for reports on the state of the environment.
Looking at environmental monitoring, the major tasks are either to update existing geo-information (observing changes at t1 in regard to conditions recorded at t0) or to delineate land cover features in areas that have not been mapped before (baseline data at t0) (Blaschke et al., 2000). Multiple schemes of image classification used in environmental mapping are either traditionally statistical (nonparametric rule of parallelepipeds; parametric rules of Maximum Likelihood, Mahalanobis Distance, Minimum Distance; Isodata, etc.) or still heuristic (region growing, labeling relaxation, fuzzy classification, etc.). While the former methods do not take account of spatial variability of space and aerial data, the latter ones cannot produce an optimal decision (Gimel'farb, 1993).
Although segmentation of an image into a given number of regions is not new, available methods for environmental mapping do not allow taking into account local interactions and spatial variability within the framework of the unified Bayesian approach. Among the most important characteristics of the segmentation procedure is the homogeneity of objects. Human vision generally tends to divide images into homogeneous areas first, and characterizes those areas more carefully later (Blaschke et al., 2000). The goal of this research was to use the general supervised scheme of image processing that can use both multiband piecewise-constant images and piecewise-textured images for landscape characterization. In contrast to usual schemes, the new method is based upon features of spatial homogeneity and Bayesian decision rules (in particular, compound rules), simultaneously.
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MATERIALS AND METHODS |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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For Bayesian segmentation, a prior MRF–GPD model of regional maps is combined, usually, with separate prior models of homogeneous regions in the multiband images. This leads sometimes to a non-Gibbs posterior distribution of the desired maps under the given initial image. Here, a new model of multiband (noisy piecewise-constant) images and regional maps is introduced. Any "image–map" pair is considered as a sample of this joint model. The resulting posterior distributions of images or maps are necessarily the GPDs. The model parameters can be estimated, from a given learning pair, by stochastic approximation.
The compound Bayesian rule is based on maximal marginal posterior probabilities of the region labels (Gimel'farb, 1993). In this study, two possible estimates of these marginals are proposed and compared experimentally: (i) the traditional sample frequencies of the labels in the generated chain of the maps and (ii) averaging of transition probabilities of the labels at all steps of generating the chain. Both approaches can be implemented by generating either a single chain of C maps or S independent subchains (S > 1) each containing CS = C/S maps and having each a different starting sample of the map (Fig. 1) . Both estimates are computed from one or more Markov chains of the maps generated, under the given GPD and initial grayscale image, by stochastic relaxation.
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(xi,yi); IM = {IM(i): i
R; q = IM(i)Q} denote an image with a finite set of gray levels Q; and MP = {MP(i): iR; l = MP(i)L} be a region (land cover) map with a finite set of region labels L. Any pair (IM, MP), containing the grayscale image and corresponding regional map is considered as a sample of spatial homogeneity, except for borders of the lattice, MRF. This MRF is assumed to have only multiple pairwise pixel interactions defined on two identical superposed lattices RIM RMP R (Fig. 2)
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: = (i,j); i,jR; xi - xj = 
x; yi - yj = y; (x,y)
}, with clique types = {(-1,0), (-1,1), (0,1), (1,1)}, specifies pairwise interactions of the region labels. 
= {
a: a = 1,2} are control parameters to be learned. Potential functions V1(qi,li) and V2(li,lj) on the cliques, assumed to be known in advance, characterize the relative strength of intraclique interactions between the corresponding gray levels q and/or region labels l.
The following potential functions are used in Eq. [1]: V1(qi,li) = |qi - µ(li)| and V2(li,lj) = 0 if li = lj and V2(li,lj) = 1 otherwise. Here, µ(l) is a noiseless gray level for the region l. The parameter 1 defines the noise variance assumed to be the same for all the regions. The features of the regions are specified by the parameter 2: the higher its positive value, the more regular the regional shapes.
Experiments with Simulated Images and Region Maps
The Markov chain of the sample pairs having the GPD of Eq. [1] can be generated by the stochastic relaxation. Each step of the generation involves two successive passes (iterations) over the superposed lattices to form (i) the current map under the fixed previous grayscale image and (ii) the current grayscale image under the fixed current regional map. In experiments, these chains reach the quasi-equilibrium state after a rather small number of iterations.
Four examples of the final pairs are shown in Fig. 3 . It should be stressed that the simulated images are especially useful since polygon boundaries are unambiguous. The similar noisy piecewise-constant images can be found in practical environmental studies, for instance, using some of the earth's surface images obtained from multiband scanning radiometers or aerial images.
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= (IM1,...,IMB) is a multiband image, and B denotes number of bands.
The following potential function is used in Eq. [2]:
 | [3] |
Here qib is the gray level in the pixel iR and µb(k) is the noiseless gray level for the region k in the band b.
It is assumed that every type of land cover gives a distinguishable "signature" of electromagnetic radiation so that hue, saturation, and intensity appear to be constant for multispectral imagery of each specific land cover type (Kovalevskaya, 1996).
Let number of bands B = 3 (red–green–blue [RGB] model) and qir, qig, and qib denote relative colors in the pixel i:
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Then the model described by Eq. [2] with the following potential function takes into account changes of intensity, hue, and saturation of different regions:
Here, 
denotes level of hue and saturation changes, and r(l) and g(l) are relative colors for region l:
In the model described by Eq. [2] and [3] we assume that relative colors of regions are constant, but the regions' intensities may take different values. In the model described by Eq. [2] and [4] every region is assumed to have strong changes of intensity and weak changes of hue and saturation.
To perform textural analysis of images, spatial attributes of piecewise-textured images should be added in the MRF–GPD model (Kovalevskaya, 1999).
Texture Model of Multiple Pair-Wise Interactions
For most uses, the segmentation process should include both tone and texture attribute schemes to ensure the greatest accuracy. It is apparent that the addition of texture can improve the accuracy in areas where the features of interest exhibit differences in local variance. For a human, the visual features of a textured area relate mostly to specific spatially homogeneous or piecewise-homogeneous patterns created by "weaving" specific primitive elements, or micropatterns. Many natural and artificial patterns appear to be modeled adequately by the proposed Gibbs model with multiple pair-wise interactions (Kovalevskaya, 2000). We propose to take into account only second-order statistics or multiple pairwise interactions between the gray levels in the pixels:
 | [5] |
Here, K = {R2
(i,j): i - j = (µ ,
)} is the pairwise clique family given by the shifts (µ,) between both pixels in a clique, and A denotes a set of indices.
The validity of this model can be visually and quantitatively checked by comparing simulated samples with the training one. The spatial homogeneity or piecewise homogeneity of a training sample can also be quantitatively verified by matching sample relative frequency distributions of gray level combinations collected over different patches within the sample.
Experiments with Real Images
Experiments were carried out with the images of two unique Siberian lakes: Lake Baikal and Lake Teletskoye. Baikal is one of the largest lakes of the world that has been in existence for 25 million years. It contains about one-fifth of the world reserves of fresh water. Lake Baikal is the deepest lake in the world (1641 m). This lake is considered to be a reservoir and factory of high-quality pure water.
The Baikal coastline is constantly changing due to water level fluctuations. A diversity of sediments enters the lake in different years. On average, it constitutes one-third of all solutes received by the lake from its tributaries during a year. However, the years of high precipitation are distinguished by sediment increase; for example, Selenga River (Fig. 5f) contributes up to 10 million tons (Galazy, 1988). National Oceanic and Atmospheric Administration (NOAA) imagery (resolution 1000 m) has been used to obtain the length of coastline as well as the total area of shallow regions and the regions with suspended matter.
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1,2) = (0.17, 1.20) and = 0.1 (Gimel'farb and Kovalevskaya, 1995; Kovalevskaya, 1999). The results of our Gibbs model–based environmental mapping were compared with traditional techniques such as clustering. Lake Teletskoye is the largest and the deepest freshwater reservoir in the south of western Siberia. Among all freshwater lakes in Russia it ranks next to Lake Baikal for storage of fresh pure water. Lake Teletskoye is placed in the Teletsk Metamorphic Complex, which forms a part of an accretionary prism between the West Sayany and Altai Mountains. Lake Teletskoye occupies an elongated and narrow depression along the Central Asian intracontinental dislocation zone.
Extensional features suggest that it represents a local basin connected with stress fields. The Teletskoye depression is about 80 km long and 3 to 5 km wide, and in a north–south orientation. It is bordered by steep mountains, which reach up to 2000 m above Lake Teletskoye. The lake is dimictic and oligotrophic. Its hydrophysical characteristics are poorly understood. The majority of ecological system peculiarities are caused by the stretched form of the lake valley. The lake's hollow is of trapezium form with slopes of 100 to 300 m high passing into valley slopes of 600 to 1300 m high.
Since Lake Teletskoye is situated in highlands (434 m above sea level), the surrounding regions are presented on Systeme Probatoire d'Observation de la Terre (SPOT, French earth observation satellite) imagery by different textures of mountain surface. Therefore, to identify the coastline (or, in other words, to outline both the tone regions of the lake and texture regions of mountains) some extra experiments on Gibbs modeling of stochastic textured patterns in accord with the model described by Eq. [5] were required.
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RESULTS AND DISCUSSION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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2), a smaller number of iterations is necessary for obtaining a quasi-equilibrium result: 30 iterations for 2 = 0.4 and 25 iterations for 2 = 1.2.
The joint model of Eq. [1] allows us to estimate marginal posterior probabilities of the regional labels (for the compound Bayesian segmentation) by generating regional maps under the given grayscale image. Two possible estimates are compared: (i) sample frequencies and (ii) average transition probabilities for the labels. The segmentation results of the images simulated under the GPD of Eq. [1] gave the following results with C = 36 and a different number of subchains S{1\4\9} in terms of fit to the true region maps (Tables 1 and 2):
2 
1.2). 1 1), single-chain and multichain estimates are equally effective. 1 0), the efficiency of multichain estimation increases. 1 1), estimates based on sample frequencies and on averaging of transition probabilities are equally effective. 1 0), the efficiency of estimation by averaging transition probabilities becomes higher than the efficiency of frequency estimation. 1 1), multichain estimation is more effective than single-chain estimation. 1 0), the efficiency of multichain estimation increases. 1 1), the efficiency of estimation by sample frequencies almost coincides with efficiency of estimation by averaging transition probabilities. 1 0), the efficiency of estimation by averaging transition probabilities increases as compared with proficiency of frequency estimates.
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1,2) = (0.17, 1.20)], this approach gives 88% of coincidence of the obtained map with the true one (Fig. 4g).
Lake Baikal
Figure 5
shows some results of the space image segmentation (Lake Baikal, eastern Siberia, Russia; NOAA advanced very-high-resolution radiometer, 1000 m). Comparisons with geographical maps and visual experts' interpretation showed that the result of Gibbs-model segmentation is rather effective for identifying and enhancement of the shore outline as well as for shoals and suspended matter detection. Taking into account all folds formed by the bays, the Lake Baikal shoreline makes up 2000 km. Width of coastal shoals in different regions of Baikal is of several tens up to several hundreds meters while in delta regions of the Selenga, Barguzin, and Upper Angara Rivers it contributes tens of kilometers. Total area of shoal and suspended matter regions is 16.8% of the water surface, or 5040 km2.
It is interesting to compare the results of our Gibbs model–based environmental mapping in Fig. 5e with traditional pixel-wise thematic mapping by clustering multiband signatures using the ISODATA method, which is the most popular in the practice of environmental mapping (see Fig. 5d). It is evident that the clustering-based mapping involves too many unessential and even superfluous details, whereas the Gibbs models provide generalized and consistent environmental maps.
Lake Teletskoye
Figures 6 and 7
show some results of Altai Mountains image analysis. Different fragments of the image were used to analyze how the proposed model described by Eq. [5] reflects the self-similarity within the patterns. The analysis showed that visual patterns of the mountains' images belong to the class of stochastic textured patterns. In such cases, the natural and simulated patterns possess good visual resemblance and high proximity of the characteristic clique's families. That is why in the following experiments on segmentation of Lake Teletskoye by Eq. [2] noisy tone regions were described by Eq. [4] while homogeneous textured regions by Eq. [5].
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CONCLUSION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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The proposed "image–map" model takes into account the local interactions between pixels assumed to represent the properties of environmental objects. The unified approach overcomes the principal difficulties in automatic environmental mapping by using the remotely sensed imagery.
Also, experimental investigations allow us to make conclusions on the possibilities of multichain estimation of a posteriori marginal probabilities, whereby exchange of single-chain length for chain plurality under equal total computational costs takes place. Use of pixelwise stochastic relaxation in processing of images described by MRF–GPD models lead to a new scheme of environmental mapping (i.e., multiple processing from different initial maps with results combined at the last stage).
Comparisons with geographic maps and visual interpretation showed that the computed images are encouraging. The predicted region maps are appropriate for a subsequent subject-matter treatment in the studies of environmental properties. The model described by Eq. [2] and [4] appears to be very useful for analysis of qualitative and quantitative changes to inland waters, pure and eutrophic water, coastal dynamics, and humid biotopes. Sparsely vegetated areas, human-generated areas (urban–suburban interface), and erosion terraces (terrace valleys of rivers in mountains) seem to be highly textured. In such textured cases, the model described by Eq. [5] is more appropriate for environmental mapping.
Experiments show that natural image textures, including the textured objects of remotely sensed imagery typical for environmental studies, can be adequately described with the model described by Eq. [5]. Thus, these textures can in principal supply specific quantitative features to facilitate more objective thematic mapping.
Segmentation of the grayscale images shows the abilities of environmental mapping based on the proposed joint model to produce meaningful regions of spatially homogeneous objects. This environmental mapping suggests a viable application model for landscape structure (shallow and deep lakes, saline lands, forests, steppes, bogs) and water bodies (fresh water, algal blooms, transparent saline water, turbid silty water, etc.).
There are many theoretical issues and applied problems to be resolved for this approach. In particular, it is necessary to develop efficient searching routines for characteristic clique families, and to implement basic elements of the unsupervised learning. A practical problem is to create comprehensive environment-oriented prototype sets of natural objects of the earth's surface to be used for the applied environmental mapping.
The knowledge-based interpretation of environment states by remotely sensed imagery is still more art than a formal theory. It is mostly descriptive, uses fuzzy terms, and is not systematically equated with the measurable attributes. The next step should be to gain more insight into the processes of knowledge capture connected with changes in environmental patterns and reformulate this knowledge into quantitative terms.
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NOTES |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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