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Fuzzy modelling of vegetation from remotely sensed imagery
ELSEVIER
Ecological Modelling 85 (1996) 3-12
Fuzzy modelling of vegetation from remotely sensed imagery G.M. Foody * Department of Geography, Universityof Wales, Swansea, Singleton Park, Swansea, SA2 8PP, UK Revised 21 October 1994; accepted 28 October 1994
Abstract
Remote sensing has considerable potential for vegetation mapping. The model of vegetation distribution represented in an image classification, however, may not alwaysbe appropriate as the algorithms typicallyused give a 'hard' class allocation. Here the output of three classification techniques, a maximum likelihood, artificial neural network and fuzzy sets classification, are softened and shown to be able to reflect the class composition of image pixels and so be able to provide a better representation of some vegetation from remotely sensed imagery.
Keywords: Classification; Fuzzy logic; Remote sensing
1. Introduction
Land cover maps which show the location and extent of vegetation types are fundamental to many ecological investigations. Despite the requirements for accurate and up-to-date maps of vegetative land cover, the maps that are available are often inaccurate or inappropriate (Townshend et al., 1991). Since mapping by traditional survey methods is fraught with difficulties and often impractical attention has increasingly turned to the derivation of land cover maps from remotely sensed data. Remote sensing offers the potential to map a wide variety of land covers at a range of spatial and temporal scales (Townshend, 1992; Foody and Curran, 1994). This enables the basic land cover maps to be derived but also facilitates
* Corresponding author. Fax: 44-1792 205556.
the investigations of scale effects on ecological patterns and processes (Wiens, 1989; Foody and Curran, 1994). It is hoped that this use of remote sensing will help raise awareness and encourage further use of remotely sensed imagery in ecology, where it has considerable unrealised potential (Allan, 1991; Roughgarden et al., 1991; Ustin et al., 1991; Wickland, 1991). Although remotely sensed imagery has been used to map land cover with considerable success in a range of environments there are, unfortunately, many examples of unsuccessful attempts to map land cover (Townshend, 1992). A range of factors may be responsible for this but key issues relate to the methods used to map and represent the desired land cover classes from the imagery. The basic aim in mapping vegetation is to model accurately the location and extent of the desired classes. Mapping from remotely sensed imagery is generally achieved through the appli-
0304-3800/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved
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G.M. Foody ~Ecological Modelling 85 (1996) 3-12
cation of a supervised image classification (Mather, 1987). With these techniques the analyst uses a training data set to provide a quantitative description of the appearance of each class and these are then used to allocate each pixel of the remotely sensed image to the land cover class with which it has the greatest similarity. These classification techniques are appropriate for the mapping of classes that lie in a mosaic of discrete mutually exclusive classes and assume that each pixel comprises one class only. Whilst this may be acceptable for the mapping of, for example, agricultural crops from relatively fine spatial resolution imagery, their use in mapping some ecologically significant vegetation classes may at times be questionable. This paper focuses on two situations where conventional classifications may be inappropriate. Firstly, for continuous vegetation classes which intergrade gradually, an image classification will model poorly the actual spatial distribution of the vegetation classes, especially near ecotones which may be of particular interest (Johnston and Bonde, 1989; Cornelius and Reynolds, 1991; Trodd, 1993), as only one class may be associated with each pixel in a classification. Furthermore, given the uncertainty of definition associated with ecosystems such a definite class allocation is generally inappropriate for many natural and seminatural vegetation classes. Secondly, even if the classes of interest may be considered to be discrete, a large number of pixels may contain two or more classes (Crapper, 1984). This can lead to significant errors in the apparent areal extent of a class over a region as well as provide a poor representation of class distribution. This problem is most acute with coarse spatial resolution satellite sensor imagery that is used for regional to global scale studies and may form an input to some ecosystem/environmental models. In both situations the common problem is that image pixels may contain a mix of classes and so cannot be unambiguously associated with a single class. In this paper approaches to better model vegetation distribution and extent are considered. The techniques discussed may all be considered as 'softened' versions of the 'hard' image classification routines. Their value will be illustrated with
reference to examples using remotely sensed data sets.
2. Non-classificatory modelling of vegetation from remotely sensed imagery As noted above a range of classification routines are available for the 'hard' classification of remotely sensed data. These vary from conventional statistical classifiers such as the maximum likelihood classifier (Mather, 1987) through nonparametric and fuzzy classifiers (Wang, 1990a) to artificial neural network based approaches (Benediktsson et al., 1990). Traditionally these classitiers are used to allocate each pixel to the class with which it has the greatest similarity. Often this is wasteful of the information generated in the classification process (Wang, 1990b). Here attention focuses on three major approaches to image classification which may be used to model vegetation; probabilistic classifiers, fuzzy classifiers and artificial neural networks. For the purpose of this paper the fuzzy classification output which may be derived from these techniques are considered to be fuzzy models of the vegetation analyzed. In remote sensing probabilistic classifiers such as the maximum likelihood classification are widely available and used. In essence this classification involves allocating each pixel to the class with which it displays the highest a posteriori probability of membership. This is extremely wasteful of information (Wang, 1990b, Foody et al., 1992). The classification is based on the probability density function from which the a posterior probability of class membership is derived from C
L( ilX) = PiP( gli) / ~ erP( SlJ) j=l
where L(iIX) is the posterior probability of pixel X belonging to class i, p(Xli) is the probability density function for pixel X as a member of class i, Pi the a priori probability for class i, and c the total number of classes. Each pixel is then allocated to the class with which it has the highest a
G.M. Foody / Ecological Modelling 85 (1996) 3-12
posteriori probability of membership. The actual magnitude of the class membership probabilities is ignored yet can provide useful information on the quality of the class allocation. Further valuable information may be derived from the typicality, which is derived from the Mahalanobis distance between a pixel and class centroid of interest derived in the calculation of the probability density function which indicates how typical the pixel is of the particular class. The magnitudes of the a posteriori probability and typicality are related to the strength of membership the pixel has to a class and hence to its class composition. The background and use of these variables are discussed more fully in the literature (Campbell, 1984; Foody et al., 1992) but the key issue is that a considerable amount of information is generated in the classification but not fully used. For some applications probabilistic classifiers may not always be appropriate. They should, for instance, only be used if the data for each class display a Gaussian normal distribution. Unfortunately, classes often display non-normal distributions which can be difficult to correct for. Additionally the size of the training set, used to characterise class appearance for the classification, is often too small to reliably characterise class appearance (Mather, 1987). A range of non-parametric classifiers are available which are therefore attractive if the requirements of the probabilistic methods cannot be satisfied. Fuzzy sets based methods are particularly attractive for use in ecology because the concept of a pixel possessing some degree of membership to each classes is fundamental to fuzzy classification techniques. Fuzzy sets techniques are also appropriate for use with ecological data which are often characterised by some degree of uncertainty and so are growing in use (Bosserman and Ragade, 1982; Dayong, 1988; Salski, 1992). Whilst fuzzy classification techniques may be used derive a hard classification, their value here is that they indicate the strength of class membership a pixel has to all classes. The fuzzy c-means algorithm (Bezdek et al., 1984) has been widely used for classification related applications, both in remote sensing (Foody, 1992) and ecological studies (Equihua, 1990).
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With this technique a fuzzy c-partition (Bezdek et al., 1984) is defined by: { n
M= U:Uik~[O,1]; ~_,Uik>O,i=l...C; k=l
~ Uik = 1, k-- 1 . . . n i~l where U is a fuzzy c-partition of n observations and c fuzzy groups or classes; Uik is an element of U and represents the membership of an observation, xk, to the ith fuzzy group where x k is a vector the length of which is p, the number of attributes used (e.g. wavebands). The optimal fuzzy c-partition is identified through the minimization of the generalised least-squared errors functional jm, n c
J (u,v)
=
E E k=l
i=1
'
where V is a c by p matrix, the elements, Vik, of which represent the mean of the kth of p attributes in the ith class, m is a weighting component, 1 < m < a , and (dik)2 is a measure of dissimilarity based on the distance between an observation and a class centroid which can be determined from ( dik) 2 = ( X k -- ui) T A ( x k -- Ui)
in which A is a weight matrix which determines the norm to be used. The algorithm was used in a supervised format and the Mahalanobis norm employed (Bezdek et al., 1984). A range of values were used for the parameter m, which is positively related to the degree of fuzziness; a value of m = 1 would produce a 'hard' classification. As with the probabilities derived from the maximum likelihood classification the magnitude of the fuzzy memberships (Uik) indicate the strength of class membership and so may be related to the class composition of a pixel. Another approach to classification that is increasingly popular in remote sensing is the use of artificial neural networks. These have a number of advantages over conventional probabilistic classifications, notably that they are distributionfree and computationally rapid once trained. An
6
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
artificial neural network is constructed from a set of simple processing units interconnected by weighted channels according to some architecture (Aleksander and Morton, 1990). Each unit consists of a number of input channels, an activation function and an output channel. Signals impinging on a unit's inputs are multiplied by the channel's weight and are summed to derive the unit's net input, net
=
~YiWi
where Yi is the magnitude of the ith input and w i the weight of the interconnection channel. This net input ( n e t ) is then transformed by the activation function to produce an output for the unit (Schalkoff, 1992). Typically a sigmoid activation function such as output = 1/(1 + e -xnet) where A is a gain parameter, often set to 1, is used. In this paper a fully-connected three-layered feedforward architecture with an external bias unit was used (Schalkoff, 1992). This network comprised one input, two hidden and two output units and the sigmoid activation function was used. The learning algorithm used was a variant of the backpropagation technique which has been widely used in pattern recognition applications. This iteratively minimizes an error function over the network outputs and a set of target outputs, taken from a training data set. The process continues until the error value converges to a (possibly local) minima. Conventionally the error function is given as g = 0.SE(T~ - 0,) 2
where T~ is the target output vector for the training set (T 1. . . . ,Tn) and 0 i is the output vector from the network for the given training set. On each iteration backpropagation recursively computes the gradient or change in error with respect to each weight in the network and these values are used to modify the weights between network units. Since standard backpropagation tends to be slow and does not scale up to larger problems well, faster variants of backpropagation are widely used. The algorithm employed here was the Quickprop algorithm which attempts to speed up
learning by using information on the current and previous error gradient and weight update to minimise error (Fahlman, 1988). The output of an artificial neural network classification for each pixel is conventionally the code of the class associated with the unit in the output layer with the highest level of activation. The magnitude of the activation level of an output unit, however, indicates the strength of class membership and so may be related to the class composition of a pixel. Information on the land cover class composition of a pixel could be derived from other techniques. For instance, land cover composition may be related to measures of support and plausibility derived from analyses based on the DempsterSharer evidential reasoning approach (Peddle, 1993) or from mixture modelling algorithms (Settle and Drake, 1993). These are, however, less available than the approaches described above and not considered further here.
3. Data and methods
Two data sets were used to evaluate the ability of the three techniques to provide measure of the strength of class membership that could be related to pixel land cover class composition. These were data from an airborne sensor for a region of lowland heath in the UK and spaceborne sensor data for a region of tropical vegetation in Ghana. Airborne thematic mapper (ATM) data were acquired by a Daedalus 1268 sensor in eleven wavebands for the lowland heath site at Ash Ranges in the UK in March 1989. These data had a spatial resolution of approximately 6.2 m and had been acquired along a pre-determined fiightline at a time that would minimize variations in the sun-target-sensor angular geometry (Foody, 1992). Ground data on heathland composition were acquired at 63 sites. Of these 31 were located in a region considered representative of the dry heath end point and 17 in a region representative of the wet heath end point. The remaining 15 samples were located along a transect that ran from one community into the other. These ground data comprised mainly a description of the canopy composition derived from 16 m 2 quadrats which
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
for the purpose of this study were degraded to show the percentage of dry heath species present. Furthermore, to simplify the investigation only data in one waveband, 2080-2350 nm, were used as this is a particularly moisture sensitive part of the electromagnetic spectrum and the vegetation types under investigation were thought to lie on a moisture gradient, and the image was preprocessed with a 3-by-3 low pass filter (Mather, 1987) to reduce possible mis-location errors. Relationships between pixel composition, as indicated by the percentage dry heath vegetation, and the measures of the strength of class membership derived from the maximum likelihood classification and fuzzy-c means algorithm were derived. The second data set was focused on tropical forest reserves in Ghana, West Africa. Within this region moist evergreen and moist semi-deciduous forest predominate (Hall and Swaine, 1981). These forests are bordered typically by savanna, much of which is used for agro-forestry and agriculture. The boundary between the forest and savanna is relatively abrupt and may be sharpened by fire within the savanna (Hall and Swaine, 1981). The abruptness of the forest boundary was evident in the remotely sensed data used in this investigation which was a relatively fine spatial resolution (79 m) Landsat MSS image. With this data set, therefore, the classes forest and non-forest could be considered as being discrete. As with the analysis of the ATM data set only data in one waveband were used to simplify the investigation. The near-infrared waveband, 800-1100 nm was selected since in this waveband the effects of atmospheric attenuation were minimized and the contrast between the forest and non-forest classes was high. The Landsat MSS image was resampled to 57-m pixel size with cubic convolution resampling, and was degraded to simulate imagery with a spatial resolution of 1.2 km, approximately that of NOAA AVHRR data, using a filtering approach similar to that described by Justice et al. (1989) which provides a set of co-registered imagery that may be considered identical in all aspects except spatial resolution. For each pixel in the simulated coarse spatial resolution image the percentage which was forest covered was derived from a
7
forest/non-forest classification of the original, undegraded spatially, Landsat MSS image. The use of a classification of fine spatial resolution data to evaluate the performance of classifications of coarse spatial resolution data has been used in other studies (e.g. Iverson et al., 1989) and this approach was necessary given the lack of accurate ground data. The percentage forest cover was estimated for a total of 89 pixels. Twelve pixels came from each end of the forest cover continuum and were used to train the analyses and the remaining 65 pixels contained a mixture of forest and non-forest vegetation. The measures of the strength of class membership derived from the fuzzy c-means algorithm and the artificial neural network for each sampled coarse spatial resolution pixel could then be related to the amount of forest cover within the pixel. An ability to derive such sub-pixel land cover composition data from imagery with a spatial resolution comparable to that of the NOAA AVHRR could substantially improve regional scale estimates of tropical forest extent from such data as part of a range of environmental programmes (Curran and Foody, 1994).
4. Results and discussion
The sensitivity of the measures of the strength of class membership to variations in class composition along the dry to wet heath continuum was assessed with the sample of 15 pixels located along the transect at the Ash Ranges site. The 48 pixels located at sites that were considered to be at the ends of the continuum were used to train the analyses. A maximum likelihood classification was performed, with each pixel allocated to the class with which it displayed the highest a posteriori probability of membership. The magnitude of the a posteriori probability and typicality were, however, also output from the analysis. These two measures of the strength of class membership were found to be significantly correlated, at the 99% level of confidence, with the percentage cover of dry heath vegetation within the pixels sampled; rank order correlations of 0.88 and 0.87 between the percentage dry heath vegetation and
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G.M. Foody/Ecological Modelling 85 (1996) 3-12
the typicality and a posteriori probability respectively. These measure of class membership could therefore be used to portray the gradual transition of canopy composition along the continuum and so offer a more realistic model of the vegetation from the remotely sensed imagery than the classification in which they were calculated. This could be represented by, for instance, modulating
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the coloration of pixel in the classified image in relation to its composition. Thus if the end points of the dry-wet heath continuum were represented by red and blue respectively, the zone where the classes intergraded would appear in a magenta colour (Wood and Foody, 1989). Furthermore, as these measures of the strength of class membership can be derived from a conven-
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Fig. 1. Relationships between the fuzzy membership function value associated with dry heath and the percentage dry heath vegetation for the 15 samples acquired along the transect along the dry-wet heath continuum at Ash Ranges at different values of the weighting parameter m.
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
tional hard image classification techniques they are potentially widely available. Using the same ground data the sensitivity of the fuzzy memberships derived from the fuzzy c-means algorithm to the variations in canopy composition was assessed. In the analyses the value of the parameter m was varied to alter the hardness of the analysis, and the fuzzy memberships derived were related to the percentage dry heath vegetation in a manner similar to that used with the probabilistic measures above. The resuits of four analysis ranging from a fairly hard analysis, with m = 1.25, to a very soft analysis, with m = 8.00 are given in Fig. 1. Slightly stronger
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correlations were observed with the fuzzy membership function values than with the probabilistic measures; all the correlation coefficients were 0.90 or higher. The results from the analysis with m = 1.25 were most similar to those from the probabilistic measures. The distinction between dry heath and wet heath became fuzzier as the parameter m was increased, and the value for each pixel would tend to 1/c with further increases in m (Bezdek et al., 1984). The results indicated that both approaches have a considerable potential for modelling the variations in canopy composition along the continuum more appropriately than a conventional
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Fig. 2. Relationships between the fuzzy membership function value associated with forest and the percentage forest cover for the 65 samples acquired from the imagery of Ghana at different values of the weighting parameter m.
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G.M. Foody ~Ecological Modelling 85 (1996) 3-12
classification. Whilst the probabilistic measures are potentially widely available the freedom from distributional constraints is a considerable advantage of the fuzzy c-means approach. The value of the latter technique was further assessed, along with the outputs from the artificial neural network, for a larger sample derived from the satellite sensor data set for Ghana. In the analyses the end member spectra were defined by the 12 pixels sampled from each end of the forest cover continuum. The analyses were run with the same values for the weighting parameter rn used in the study of the heathland vegetation at Ash Ranges. The relationship between the fuzzy membership function associated with the forest class and percentage forest cover is shown in Fig. 2. As before the difference between the end points of the forest cover continuum became fuzzier as m was increased. With m = 1.25 there was a sharp distinction, in terms of the magnitude of the fuzzy membership function, between predominantly forested and predominantly non-forested pixels. As m was increased this distinction was decreased and a strong relationship between the fuzzy membership function associated with forest and the percentage forest observed (Fig. 2); linear correlations for the analyses with m = 2, 3 and 8 were r = 0.93, 0.93 and 0.89 respectively, all significant at the 99% level of confidence. This indicated a considerable potential for the accurate estimation of the extent of sub-pixel forest cover, which should improve knowledge on forest extent and dynamics as well as environmental/ ecosystem models that use information on forest location and extent. The 12 pixels sampled from each end of the forest cover continuum were also used to train the artificial neural network. The remaining 65 pixels were then entered into the network and classified. Rather than use the conventional class allocation, the activation level of the unit associated with the forest class in the output layer of the network was derived. This was then related to the percentage forest cover (Fig. 3a). The relationship obtained showed some similarity to that from the fuzzy c-means algorithm with m = 1.25, with a sharp distinction between the predominantly forest covered and predominantly non-
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Fig. 3. Relationships between measures of class membership derived from the artificial neural network and the percentage forest cover for the 65 samples acquired from the imageryof Ghana. The measures of class membership shown are in (a) the activation level of the output unit associated with the forest class and in (b) the magnitude of the net input to the output unit associated with forest. forest covered pixels. However, the activation function used in the artificial neural network was a conventional sigrnoid function which encourages hard allocation. If a different, perhaps more linear, function had been used, the output unit activation level may have been more sensitive to the percentage forest composition. This potential is illustrated in Fig. 3b which shows the relationship between the net input into the output unit associated with forest and the percentage forest cover. This relationship was significant (r -- 0.94,
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
significant at the 99% level of confidence). Note also that although the analysis was based on a single waveband of data the relationship observed was stronger than if the raw image tone data were used; the correlation between percentage forest cover and image tone was r = - 0.91. These preliminary analyses of a simple data set indicate that the technique may provide accurate estimates of pixel composition and further research is in progress.
5. Conclusions
The output of a conventional 'hard' image classification often provides a poor model of the location and distribution of vegetation. Hard classification is inappropriate for some ecological applications since it runs contrary to the continuum concept and can make no allowance for uncertainty characteristic in much ecological data. Softer or fuzzier techniques, by indicating the composition of pixels could model more realistically the spatial distribution of some vegetation types and improve estimates of class areal extent. The results of the research above has shown, however, that the output of hard classifications such as the maximum likelihood classification and artificial neural network can be 'softened' to provide information which may model the vegetation more appropriately than the classification itself. Furthermore fuzzy sets techniques, such as the fuzzy c-means algorithm enable the degree of fuzziness to be modulated as required.
Acknowledgements
I am grateful to the NERC for the ATM data acquired during its 1989 airborne campaign and Nigel Trodd for assistance and provision of ground data for the Ash Ranges site.
References Aleksander, I. and Morton, H., 1990. An Introduction to Neural Computing. Chapman and Hall, London.
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Allan, J.A., 1991. Global ecology: who is responsible? J. Biogeogr., 18: 121-122. Benediktsson, J.A., Swain, P.H. and Ersoy, O.K., 1990. Neural network approaches versus statistical methods on classification of multisource remote sensing data. IEEE Trans. Geosci. Remote Sens., 28: 540-551. Bezdek, J.C., Ehrlich, R. and Full, W., 1984. FCM: the fuzzy c-means clustering algorithm. Comp. Geosci., 10: 191-203. Bosserman, R.W. and Ragade, R.K., 1982. Ecosystem analysis using fuzzy set theory. Ecol. Model., 16: 191-208. Campbell, N.A., 1984. Some aspects of allocation and discrimination. In: G.N. van Vark and W.W. HoweUs (Editors), Multivariate Statistical Methods in Physical Anthropology. Reidel, Dordrecht, pp. 177-192. Cornelius, J.M. and Reynolds, J.F., 1991. On determining the statistical significance of discontinuities within ordered ecological data. Ecology, 72: 2057-2070. Crapper, P.F., 1984. An estimate of the number of boundary cells in a mapped landscape coded to grid cells. Photogramm. Eng. Remote Sensing, 50: 1497-1503. Curran, P.J. and Foody, G.M., 1994. The use of remote sensing to characterise the regenerative states of tropical forests. In: G.M. Foody and P.J. Curran (Editors), Environmental Remote Sensing from Regional to Global Scales. Wiley, Chichester, pp. 44-83. Dayong, Z., 1988. An index to measure the strength of relationship between community and site. Ecol. Model., 40: 145-153. Equihua, M., 1990. Fuzzy clustering of ecological data. J. Ecol., 78: 519-534. Fahlman, S.E., 1988. Faster-learning variations of backpropagation: an empirical study. Proceedings of the 1988 Connectionist Models Summer School, Morgan Kaufman, San Mateo, pp. 38-51. Foody, G.M., 1992. A fuzzy sets approach to the representation of vegetation continua from remotely sensed data: an example from lowland heath. Photogramm. Eng. Remote Sensing, 58: 221-225. Foody, G.M. and Curran, P.J. (Editors), 1994. Environmental Remote Sensing from Regional to Global Scales. Wiley, Chichester. Foody, G.M., Campbell, N.A., Trodd, N.M. and Wood, T.F., 1992. Derivation and applications of probabilistic measures of class membership from the maximum likelihood classification. Photogramm. Eng. Remote Sensing, 58: 1335-1341. Hall, J.B. and Swaine, M.D., 1981. Distribution and Ecology of Vascular Plants in a Tropical Rain Forest. Forest Vegetation in Ghana. Dr Junk, The Hague. Iverson, L.R., Cook, E.A. and Graham, R.L., 1989. A technique for extrapolating and validating forest cover across large regions. Calibrating AVHRR data with TM data. Int. J. Remote Sensing, 10: 1805-1812. Johnston, C.A. and Bonde, J., 1989. Quantitative analysis of ecotones using a geographic information system. Photogramm. Eng. Remote Sensing, 55: 1643-1647.
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Justice, C.O., Markham, B.L., Townshend, J.R.G. and Kennard, R.L., 1989. Spatial degradation of satellite data. Int. J. Remote Sensing, 10: 1539-1561. Mather, P.M., 1987. Computer Processing of Remotely-Sensed Images. Wiley, Chichester. Peddle, D.R., 1993. An empirical comparison of evidential reasoning, linear discriminant analysis and maximum likelihood algorithms for alpine land cover classification. Can. J. Remote Sensing, 19: 31-44. Roughgarden, J., Running, S.W. and Matson, P.A., 1991. What does remote sensing do for ecology? Ecology, 72: 1918-1922. Salski, A., 1992. Fuzzy knowledge-based models in ecological research. Ecol. Model., 63: 103-112. Schalkoff, R., 1992. Pattern Recognition: Statistical, Structural and Neural. Wiley, New York. Settle, J.J. and Drake, N.A., 1993. Linear mixing and the estimation of ground cover proportions. Int. J. Remote Sensing, 14: 1159-1177. Townshend, J.R.G., 1992. Land cover. Int. J. Remote Sensing, 13: 1319-1328. Townshend, J., Justice, C., Li, W., Gurney, C. and McManus, J., 1991. Global land cover classification by remote sens-
ing: present capabilities and future possibilities. Remote Sensing Environ., 35: 243-255. Trodd, N.M., 1993. Characterising semi-natural vegetation: continua and ecotone. Towards Operational Applications. Remote Sensing Society, Nottingham, pp. 191-198. Ustin, S.L., Wessman, C.A., Curtiss, B., Kasischke, E., Way, J. and Vanderbilt, V.C., 1991. Opportunities for using the EOS imaging spectrometers and synthetic aperture radar in ecological models. Ecology, 72: 1934-1945. Wang, F., 1990a. Fuzzy supervised classification of remote sensing images. IEEE Trans. Geosci. Remote Sensing, 28: 194-201. Wang, F., 1990b. Improving remote sensing image analysis through fuzzy information representation. Photogramm. Eng. Remote Sensing, 56: 1163-1169. Wicldand, D.E., 1991. Mission to planet Earth: the ecological perspective. Ecology, 72: 1923-1933. Wiens, J.A., 1989. Spatial scaling in ecology. Funct. Ecol., 3: 385-397. Wood, T.F. and Foody, G.M., 1989. Analysis and representation of vegetation continua from Landsat Thematic Mapper data for lowland heaths. Int. J. Remote Sensing, 10: 181-191.
Ecological Modelling 85 (1996) 3-12
Fuzzy modelling of vegetation from remotely sensed imagery G.M. Foody * Department of Geography, Universityof Wales, Swansea, Singleton Park, Swansea, SA2 8PP, UK Revised 21 October 1994; accepted 28 October 1994
Abstract
Remote sensing has considerable potential for vegetation mapping. The model of vegetation distribution represented in an image classification, however, may not alwaysbe appropriate as the algorithms typicallyused give a 'hard' class allocation. Here the output of three classification techniques, a maximum likelihood, artificial neural network and fuzzy sets classification, are softened and shown to be able to reflect the class composition of image pixels and so be able to provide a better representation of some vegetation from remotely sensed imagery.
Keywords: Classification; Fuzzy logic; Remote sensing
1. Introduction
Land cover maps which show the location and extent of vegetation types are fundamental to many ecological investigations. Despite the requirements for accurate and up-to-date maps of vegetative land cover, the maps that are available are often inaccurate or inappropriate (Townshend et al., 1991). Since mapping by traditional survey methods is fraught with difficulties and often impractical attention has increasingly turned to the derivation of land cover maps from remotely sensed data. Remote sensing offers the potential to map a wide variety of land covers at a range of spatial and temporal scales (Townshend, 1992; Foody and Curran, 1994). This enables the basic land cover maps to be derived but also facilitates
* Corresponding author. Fax: 44-1792 205556.
the investigations of scale effects on ecological patterns and processes (Wiens, 1989; Foody and Curran, 1994). It is hoped that this use of remote sensing will help raise awareness and encourage further use of remotely sensed imagery in ecology, where it has considerable unrealised potential (Allan, 1991; Roughgarden et al., 1991; Ustin et al., 1991; Wickland, 1991). Although remotely sensed imagery has been used to map land cover with considerable success in a range of environments there are, unfortunately, many examples of unsuccessful attempts to map land cover (Townshend, 1992). A range of factors may be responsible for this but key issues relate to the methods used to map and represent the desired land cover classes from the imagery. The basic aim in mapping vegetation is to model accurately the location and extent of the desired classes. Mapping from remotely sensed imagery is generally achieved through the appli-
0304-3800/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved
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G.M. Foody ~Ecological Modelling 85 (1996) 3-12
cation of a supervised image classification (Mather, 1987). With these techniques the analyst uses a training data set to provide a quantitative description of the appearance of each class and these are then used to allocate each pixel of the remotely sensed image to the land cover class with which it has the greatest similarity. These classification techniques are appropriate for the mapping of classes that lie in a mosaic of discrete mutually exclusive classes and assume that each pixel comprises one class only. Whilst this may be acceptable for the mapping of, for example, agricultural crops from relatively fine spatial resolution imagery, their use in mapping some ecologically significant vegetation classes may at times be questionable. This paper focuses on two situations where conventional classifications may be inappropriate. Firstly, for continuous vegetation classes which intergrade gradually, an image classification will model poorly the actual spatial distribution of the vegetation classes, especially near ecotones which may be of particular interest (Johnston and Bonde, 1989; Cornelius and Reynolds, 1991; Trodd, 1993), as only one class may be associated with each pixel in a classification. Furthermore, given the uncertainty of definition associated with ecosystems such a definite class allocation is generally inappropriate for many natural and seminatural vegetation classes. Secondly, even if the classes of interest may be considered to be discrete, a large number of pixels may contain two or more classes (Crapper, 1984). This can lead to significant errors in the apparent areal extent of a class over a region as well as provide a poor representation of class distribution. This problem is most acute with coarse spatial resolution satellite sensor imagery that is used for regional to global scale studies and may form an input to some ecosystem/environmental models. In both situations the common problem is that image pixels may contain a mix of classes and so cannot be unambiguously associated with a single class. In this paper approaches to better model vegetation distribution and extent are considered. The techniques discussed may all be considered as 'softened' versions of the 'hard' image classification routines. Their value will be illustrated with
reference to examples using remotely sensed data sets.
2. Non-classificatory modelling of vegetation from remotely sensed imagery As noted above a range of classification routines are available for the 'hard' classification of remotely sensed data. These vary from conventional statistical classifiers such as the maximum likelihood classifier (Mather, 1987) through nonparametric and fuzzy classifiers (Wang, 1990a) to artificial neural network based approaches (Benediktsson et al., 1990). Traditionally these classitiers are used to allocate each pixel to the class with which it has the greatest similarity. Often this is wasteful of the information generated in the classification process (Wang, 1990b). Here attention focuses on three major approaches to image classification which may be used to model vegetation; probabilistic classifiers, fuzzy classifiers and artificial neural networks. For the purpose of this paper the fuzzy classification output which may be derived from these techniques are considered to be fuzzy models of the vegetation analyzed. In remote sensing probabilistic classifiers such as the maximum likelihood classification are widely available and used. In essence this classification involves allocating each pixel to the class with which it displays the highest a posteriori probability of membership. This is extremely wasteful of information (Wang, 1990b, Foody et al., 1992). The classification is based on the probability density function from which the a posterior probability of class membership is derived from C
L( ilX) = PiP( gli) / ~ erP( SlJ) j=l
where L(iIX) is the posterior probability of pixel X belonging to class i, p(Xli) is the probability density function for pixel X as a member of class i, Pi the a priori probability for class i, and c the total number of classes. Each pixel is then allocated to the class with which it has the highest a
G.M. Foody / Ecological Modelling 85 (1996) 3-12
posteriori probability of membership. The actual magnitude of the class membership probabilities is ignored yet can provide useful information on the quality of the class allocation. Further valuable information may be derived from the typicality, which is derived from the Mahalanobis distance between a pixel and class centroid of interest derived in the calculation of the probability density function which indicates how typical the pixel is of the particular class. The magnitudes of the a posteriori probability and typicality are related to the strength of membership the pixel has to a class and hence to its class composition. The background and use of these variables are discussed more fully in the literature (Campbell, 1984; Foody et al., 1992) but the key issue is that a considerable amount of information is generated in the classification but not fully used. For some applications probabilistic classifiers may not always be appropriate. They should, for instance, only be used if the data for each class display a Gaussian normal distribution. Unfortunately, classes often display non-normal distributions which can be difficult to correct for. Additionally the size of the training set, used to characterise class appearance for the classification, is often too small to reliably characterise class appearance (Mather, 1987). A range of non-parametric classifiers are available which are therefore attractive if the requirements of the probabilistic methods cannot be satisfied. Fuzzy sets based methods are particularly attractive for use in ecology because the concept of a pixel possessing some degree of membership to each classes is fundamental to fuzzy classification techniques. Fuzzy sets techniques are also appropriate for use with ecological data which are often characterised by some degree of uncertainty and so are growing in use (Bosserman and Ragade, 1982; Dayong, 1988; Salski, 1992). Whilst fuzzy classification techniques may be used derive a hard classification, their value here is that they indicate the strength of class membership a pixel has to all classes. The fuzzy c-means algorithm (Bezdek et al., 1984) has been widely used for classification related applications, both in remote sensing (Foody, 1992) and ecological studies (Equihua, 1990).
5
With this technique a fuzzy c-partition (Bezdek et al., 1984) is defined by: { n
M= U:Uik~[O,1]; ~_,Uik>O,i=l...C; k=l
~ Uik = 1, k-- 1 . . . n i~l where U is a fuzzy c-partition of n observations and c fuzzy groups or classes; Uik is an element of U and represents the membership of an observation, xk, to the ith fuzzy group where x k is a vector the length of which is p, the number of attributes used (e.g. wavebands). The optimal fuzzy c-partition is identified through the minimization of the generalised least-squared errors functional jm, n c
J (u,v)
=
E E k=l
i=1
'
where V is a c by p matrix, the elements, Vik, of which represent the mean of the kth of p attributes in the ith class, m is a weighting component, 1 < m < a , and (dik)2 is a measure of dissimilarity based on the distance between an observation and a class centroid which can be determined from ( dik) 2 = ( X k -- ui) T A ( x k -- Ui)
in which A is a weight matrix which determines the norm to be used. The algorithm was used in a supervised format and the Mahalanobis norm employed (Bezdek et al., 1984). A range of values were used for the parameter m, which is positively related to the degree of fuzziness; a value of m = 1 would produce a 'hard' classification. As with the probabilities derived from the maximum likelihood classification the magnitude of the fuzzy memberships (Uik) indicate the strength of class membership and so may be related to the class composition of a pixel. Another approach to classification that is increasingly popular in remote sensing is the use of artificial neural networks. These have a number of advantages over conventional probabilistic classifications, notably that they are distributionfree and computationally rapid once trained. An
6
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
artificial neural network is constructed from a set of simple processing units interconnected by weighted channels according to some architecture (Aleksander and Morton, 1990). Each unit consists of a number of input channels, an activation function and an output channel. Signals impinging on a unit's inputs are multiplied by the channel's weight and are summed to derive the unit's net input, net
=
~YiWi
where Yi is the magnitude of the ith input and w i the weight of the interconnection channel. This net input ( n e t ) is then transformed by the activation function to produce an output for the unit (Schalkoff, 1992). Typically a sigmoid activation function such as output = 1/(1 + e -xnet) where A is a gain parameter, often set to 1, is used. In this paper a fully-connected three-layered feedforward architecture with an external bias unit was used (Schalkoff, 1992). This network comprised one input, two hidden and two output units and the sigmoid activation function was used. The learning algorithm used was a variant of the backpropagation technique which has been widely used in pattern recognition applications. This iteratively minimizes an error function over the network outputs and a set of target outputs, taken from a training data set. The process continues until the error value converges to a (possibly local) minima. Conventionally the error function is given as g = 0.SE(T~ - 0,) 2
where T~ is the target output vector for the training set (T 1. . . . ,Tn) and 0 i is the output vector from the network for the given training set. On each iteration backpropagation recursively computes the gradient or change in error with respect to each weight in the network and these values are used to modify the weights between network units. Since standard backpropagation tends to be slow and does not scale up to larger problems well, faster variants of backpropagation are widely used. The algorithm employed here was the Quickprop algorithm which attempts to speed up
learning by using information on the current and previous error gradient and weight update to minimise error (Fahlman, 1988). The output of an artificial neural network classification for each pixel is conventionally the code of the class associated with the unit in the output layer with the highest level of activation. The magnitude of the activation level of an output unit, however, indicates the strength of class membership and so may be related to the class composition of a pixel. Information on the land cover class composition of a pixel could be derived from other techniques. For instance, land cover composition may be related to measures of support and plausibility derived from analyses based on the DempsterSharer evidential reasoning approach (Peddle, 1993) or from mixture modelling algorithms (Settle and Drake, 1993). These are, however, less available than the approaches described above and not considered further here.
3. Data and methods
Two data sets were used to evaluate the ability of the three techniques to provide measure of the strength of class membership that could be related to pixel land cover class composition. These were data from an airborne sensor for a region of lowland heath in the UK and spaceborne sensor data for a region of tropical vegetation in Ghana. Airborne thematic mapper (ATM) data were acquired by a Daedalus 1268 sensor in eleven wavebands for the lowland heath site at Ash Ranges in the UK in March 1989. These data had a spatial resolution of approximately 6.2 m and had been acquired along a pre-determined fiightline at a time that would minimize variations in the sun-target-sensor angular geometry (Foody, 1992). Ground data on heathland composition were acquired at 63 sites. Of these 31 were located in a region considered representative of the dry heath end point and 17 in a region representative of the wet heath end point. The remaining 15 samples were located along a transect that ran from one community into the other. These ground data comprised mainly a description of the canopy composition derived from 16 m 2 quadrats which
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
for the purpose of this study were degraded to show the percentage of dry heath species present. Furthermore, to simplify the investigation only data in one waveband, 2080-2350 nm, were used as this is a particularly moisture sensitive part of the electromagnetic spectrum and the vegetation types under investigation were thought to lie on a moisture gradient, and the image was preprocessed with a 3-by-3 low pass filter (Mather, 1987) to reduce possible mis-location errors. Relationships between pixel composition, as indicated by the percentage dry heath vegetation, and the measures of the strength of class membership derived from the maximum likelihood classification and fuzzy-c means algorithm were derived. The second data set was focused on tropical forest reserves in Ghana, West Africa. Within this region moist evergreen and moist semi-deciduous forest predominate (Hall and Swaine, 1981). These forests are bordered typically by savanna, much of which is used for agro-forestry and agriculture. The boundary between the forest and savanna is relatively abrupt and may be sharpened by fire within the savanna (Hall and Swaine, 1981). The abruptness of the forest boundary was evident in the remotely sensed data used in this investigation which was a relatively fine spatial resolution (79 m) Landsat MSS image. With this data set, therefore, the classes forest and non-forest could be considered as being discrete. As with the analysis of the ATM data set only data in one waveband were used to simplify the investigation. The near-infrared waveband, 800-1100 nm was selected since in this waveband the effects of atmospheric attenuation were minimized and the contrast between the forest and non-forest classes was high. The Landsat MSS image was resampled to 57-m pixel size with cubic convolution resampling, and was degraded to simulate imagery with a spatial resolution of 1.2 km, approximately that of NOAA AVHRR data, using a filtering approach similar to that described by Justice et al. (1989) which provides a set of co-registered imagery that may be considered identical in all aspects except spatial resolution. For each pixel in the simulated coarse spatial resolution image the percentage which was forest covered was derived from a
7
forest/non-forest classification of the original, undegraded spatially, Landsat MSS image. The use of a classification of fine spatial resolution data to evaluate the performance of classifications of coarse spatial resolution data has been used in other studies (e.g. Iverson et al., 1989) and this approach was necessary given the lack of accurate ground data. The percentage forest cover was estimated for a total of 89 pixels. Twelve pixels came from each end of the forest cover continuum and were used to train the analyses and the remaining 65 pixels contained a mixture of forest and non-forest vegetation. The measures of the strength of class membership derived from the fuzzy c-means algorithm and the artificial neural network for each sampled coarse spatial resolution pixel could then be related to the amount of forest cover within the pixel. An ability to derive such sub-pixel land cover composition data from imagery with a spatial resolution comparable to that of the NOAA AVHRR could substantially improve regional scale estimates of tropical forest extent from such data as part of a range of environmental programmes (Curran and Foody, 1994).
4. Results and discussion
The sensitivity of the measures of the strength of class membership to variations in class composition along the dry to wet heath continuum was assessed with the sample of 15 pixels located along the transect at the Ash Ranges site. The 48 pixels located at sites that were considered to be at the ends of the continuum were used to train the analyses. A maximum likelihood classification was performed, with each pixel allocated to the class with which it displayed the highest a posteriori probability of membership. The magnitude of the a posteriori probability and typicality were, however, also output from the analysis. These two measures of the strength of class membership were found to be significantly correlated, at the 99% level of confidence, with the percentage cover of dry heath vegetation within the pixels sampled; rank order correlations of 0.88 and 0.87 between the percentage dry heath vegetation and
8
G.M. Foody/Ecological Modelling 85 (1996) 3-12
the typicality and a posteriori probability respectively. These measure of class membership could therefore be used to portray the gradual transition of canopy composition along the continuum and so offer a more realistic model of the vegetation from the remotely sensed imagery than the classification in which they were calculated. This could be represented by, for instance, modulating
1.0
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the coloration of pixel in the classified image in relation to its composition. Thus if the end points of the dry-wet heath continuum were represented by red and blue respectively, the zone where the classes intergraded would appear in a magenta colour (Wood and Foody, 1989). Furthermore, as these measures of the strength of class membership can be derived from a conven-
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Fig. 1. Relationships between the fuzzy membership function value associated with dry heath and the percentage dry heath vegetation for the 15 samples acquired along the transect along the dry-wet heath continuum at Ash Ranges at different values of the weighting parameter m.
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
tional hard image classification techniques they are potentially widely available. Using the same ground data the sensitivity of the fuzzy memberships derived from the fuzzy c-means algorithm to the variations in canopy composition was assessed. In the analyses the value of the parameter m was varied to alter the hardness of the analysis, and the fuzzy memberships derived were related to the percentage dry heath vegetation in a manner similar to that used with the probabilistic measures above. The resuits of four analysis ranging from a fairly hard analysis, with m = 1.25, to a very soft analysis, with m = 8.00 are given in Fig. 1. Slightly stronger
9
correlations were observed with the fuzzy membership function values than with the probabilistic measures; all the correlation coefficients were 0.90 or higher. The results from the analysis with m = 1.25 were most similar to those from the probabilistic measures. The distinction between dry heath and wet heath became fuzzier as the parameter m was increased, and the value for each pixel would tend to 1/c with further increases in m (Bezdek et al., 1984). The results indicated that both approaches have a considerable potential for modelling the variations in canopy composition along the continuum more appropriately than a conventional
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Fig. 2. Relationships between the fuzzy membership function value associated with forest and the percentage forest cover for the 65 samples acquired from the imagery of Ghana at different values of the weighting parameter m.
10
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
classification. Whilst the probabilistic measures are potentially widely available the freedom from distributional constraints is a considerable advantage of the fuzzy c-means approach. The value of the latter technique was further assessed, along with the outputs from the artificial neural network, for a larger sample derived from the satellite sensor data set for Ghana. In the analyses the end member spectra were defined by the 12 pixels sampled from each end of the forest cover continuum. The analyses were run with the same values for the weighting parameter rn used in the study of the heathland vegetation at Ash Ranges. The relationship between the fuzzy membership function associated with the forest class and percentage forest cover is shown in Fig. 2. As before the difference between the end points of the forest cover continuum became fuzzier as m was increased. With m = 1.25 there was a sharp distinction, in terms of the magnitude of the fuzzy membership function, between predominantly forested and predominantly non-forested pixels. As m was increased this distinction was decreased and a strong relationship between the fuzzy membership function associated with forest and the percentage forest observed (Fig. 2); linear correlations for the analyses with m = 2, 3 and 8 were r = 0.93, 0.93 and 0.89 respectively, all significant at the 99% level of confidence. This indicated a considerable potential for the accurate estimation of the extent of sub-pixel forest cover, which should improve knowledge on forest extent and dynamics as well as environmental/ ecosystem models that use information on forest location and extent. The 12 pixels sampled from each end of the forest cover continuum were also used to train the artificial neural network. The remaining 65 pixels were then entered into the network and classified. Rather than use the conventional class allocation, the activation level of the unit associated with the forest class in the output layer of the network was derived. This was then related to the percentage forest cover (Fig. 3a). The relationship obtained showed some similarity to that from the fuzzy c-means algorithm with m = 1.25, with a sharp distinction between the predominantly forest covered and predominantly non-
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Fig. 3. Relationships between measures of class membership derived from the artificial neural network and the percentage forest cover for the 65 samples acquired from the imageryof Ghana. The measures of class membership shown are in (a) the activation level of the output unit associated with the forest class and in (b) the magnitude of the net input to the output unit associated with forest. forest covered pixels. However, the activation function used in the artificial neural network was a conventional sigrnoid function which encourages hard allocation. If a different, perhaps more linear, function had been used, the output unit activation level may have been more sensitive to the percentage forest composition. This potential is illustrated in Fig. 3b which shows the relationship between the net input into the output unit associated with forest and the percentage forest cover. This relationship was significant (r -- 0.94,
G.M. Foody ~Ecological Modelling 85 (1996) 3-12
significant at the 99% level of confidence). Note also that although the analysis was based on a single waveband of data the relationship observed was stronger than if the raw image tone data were used; the correlation between percentage forest cover and image tone was r = - 0.91. These preliminary analyses of a simple data set indicate that the technique may provide accurate estimates of pixel composition and further research is in progress.
5. Conclusions
The output of a conventional 'hard' image classification often provides a poor model of the location and distribution of vegetation. Hard classification is inappropriate for some ecological applications since it runs contrary to the continuum concept and can make no allowance for uncertainty characteristic in much ecological data. Softer or fuzzier techniques, by indicating the composition of pixels could model more realistically the spatial distribution of some vegetation types and improve estimates of class areal extent. The results of the research above has shown, however, that the output of hard classifications such as the maximum likelihood classification and artificial neural network can be 'softened' to provide information which may model the vegetation more appropriately than the classification itself. Furthermore fuzzy sets techniques, such as the fuzzy c-means algorithm enable the degree of fuzziness to be modulated as required.
Acknowledgements
I am grateful to the NERC for the ATM data acquired during its 1989 airborne campaign and Nigel Trodd for assistance and provision of ground data for the Ash Ranges site.
References Aleksander, I. and Morton, H., 1990. An Introduction to Neural Computing. Chapman and Hall, London.
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Allan, J.A., 1991. Global ecology: who is responsible? J. Biogeogr., 18: 121-122. Benediktsson, J.A., Swain, P.H. and Ersoy, O.K., 1990. Neural network approaches versus statistical methods on classification of multisource remote sensing data. IEEE Trans. Geosci. Remote Sens., 28: 540-551. Bezdek, J.C., Ehrlich, R. and Full, W., 1984. FCM: the fuzzy c-means clustering algorithm. Comp. Geosci., 10: 191-203. Bosserman, R.W. and Ragade, R.K., 1982. Ecosystem analysis using fuzzy set theory. Ecol. Model., 16: 191-208. Campbell, N.A., 1984. Some aspects of allocation and discrimination. In: G.N. van Vark and W.W. HoweUs (Editors), Multivariate Statistical Methods in Physical Anthropology. Reidel, Dordrecht, pp. 177-192. Cornelius, J.M. and Reynolds, J.F., 1991. On determining the statistical significance of discontinuities within ordered ecological data. Ecology, 72: 2057-2070. Crapper, P.F., 1984. An estimate of the number of boundary cells in a mapped landscape coded to grid cells. Photogramm. Eng. Remote Sensing, 50: 1497-1503. Curran, P.J. and Foody, G.M., 1994. The use of remote sensing to characterise the regenerative states of tropical forests. In: G.M. Foody and P.J. Curran (Editors), Environmental Remote Sensing from Regional to Global Scales. Wiley, Chichester, pp. 44-83. Dayong, Z., 1988. An index to measure the strength of relationship between community and site. Ecol. Model., 40: 145-153. Equihua, M., 1990. Fuzzy clustering of ecological data. J. Ecol., 78: 519-534. Fahlman, S.E., 1988. Faster-learning variations of backpropagation: an empirical study. Proceedings of the 1988 Connectionist Models Summer School, Morgan Kaufman, San Mateo, pp. 38-51. Foody, G.M., 1992. A fuzzy sets approach to the representation of vegetation continua from remotely sensed data: an example from lowland heath. Photogramm. Eng. Remote Sensing, 58: 221-225. Foody, G.M. and Curran, P.J. (Editors), 1994. Environmental Remote Sensing from Regional to Global Scales. Wiley, Chichester. Foody, G.M., Campbell, N.A., Trodd, N.M. and Wood, T.F., 1992. Derivation and applications of probabilistic measures of class membership from the maximum likelihood classification. Photogramm. Eng. Remote Sensing, 58: 1335-1341. Hall, J.B. and Swaine, M.D., 1981. Distribution and Ecology of Vascular Plants in a Tropical Rain Forest. Forest Vegetation in Ghana. Dr Junk, The Hague. Iverson, L.R., Cook, E.A. and Graham, R.L., 1989. A technique for extrapolating and validating forest cover across large regions. Calibrating AVHRR data with TM data. Int. J. Remote Sensing, 10: 1805-1812. Johnston, C.A. and Bonde, J., 1989. Quantitative analysis of ecotones using a geographic information system. Photogramm. Eng. Remote Sensing, 55: 1643-1647.
12
G.M. Food),~Ecological Modelling 85 (1996) 3-12
Justice, C.O., Markham, B.L., Townshend, J.R.G. and Kennard, R.L., 1989. Spatial degradation of satellite data. Int. J. Remote Sensing, 10: 1539-1561. Mather, P.M., 1987. Computer Processing of Remotely-Sensed Images. Wiley, Chichester. Peddle, D.R., 1993. An empirical comparison of evidential reasoning, linear discriminant analysis and maximum likelihood algorithms for alpine land cover classification. Can. J. Remote Sensing, 19: 31-44. Roughgarden, J., Running, S.W. and Matson, P.A., 1991. What does remote sensing do for ecology? Ecology, 72: 1918-1922. Salski, A., 1992. Fuzzy knowledge-based models in ecological research. Ecol. Model., 63: 103-112. Schalkoff, R., 1992. Pattern Recognition: Statistical, Structural and Neural. Wiley, New York. Settle, J.J. and Drake, N.A., 1993. Linear mixing and the estimation of ground cover proportions. Int. J. Remote Sensing, 14: 1159-1177. Townshend, J.R.G., 1992. Land cover. Int. J. Remote Sensing, 13: 1319-1328. Townshend, J., Justice, C., Li, W., Gurney, C. and McManus, J., 1991. Global land cover classification by remote sens-
ing: present capabilities and future possibilities. Remote Sensing Environ., 35: 243-255. Trodd, N.M., 1993. Characterising semi-natural vegetation: continua and ecotone. Towards Operational Applications. Remote Sensing Society, Nottingham, pp. 191-198. Ustin, S.L., Wessman, C.A., Curtiss, B., Kasischke, E., Way, J. and Vanderbilt, V.C., 1991. Opportunities for using the EOS imaging spectrometers and synthetic aperture radar in ecological models. Ecology, 72: 1934-1945. Wang, F., 1990a. Fuzzy supervised classification of remote sensing images. IEEE Trans. Geosci. Remote Sensing, 28: 194-201. Wang, F., 1990b. Improving remote sensing image analysis through fuzzy information representation. Photogramm. Eng. Remote Sensing, 56: 1163-1169. Wicldand, D.E., 1991. Mission to planet Earth: the ecological perspective. Ecology, 72: 1923-1933. Wiens, J.A., 1989. Spatial scaling in ecology. Funct. Ecol., 3: 385-397. Wood, T.F. and Foody, G.M., 1989. Analysis and representation of vegetation continua from Landsat Thematic Mapper data for lowland heaths. Int. J. Remote Sensing, 10: 181-191.