An evaluation of fuzzy and texture-based ...

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An evaluation of fuzzy and texture-based classification approaches for mapping regenerating tropical forest classes from Landsat-TM data a

b

b

G. PALUBINSKAS , R. M. LUCAS , G. M. FOODY & P. J. CURRAN

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a

Department of Data Analysis, Institute of Mathematics and Informatics, Akademijos st. 4, Vilnius, 2600, Lithuania b

Department of Geography, University of Wales Swansea, Singleton Park, Swansea, Wales, SA2 8PP, U.K c

Department of Geography, University of Southampton, Highfield, Southampton, England, SOI7 1BJ, U.K Available online: 16 May 2007

To cite this article: G. PALUBINSKAS, R. M. LUCAS, G. M. FOODY & P. J. CURRAN (1995): An evaluation of fuzzy and texturebased classification approaches for mapping regenerating tropical forest classes from Landsat-TM data, International Journal of Remote Sensing, 16:4, 747-759 To link to this article: http://dx.doi.org/10.1080/01431169508954437

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INT.

J.

REMOTE SENSING, 1995, VOL. 16, No.4, 747-759

An evaluation of fuzzy and texture-based classification approaches for mapping regenerating tropical forest classes from Landsat-TM data G. PALUBINSKAS Department of Data Analysis, Institute of Mathematics and Informatics, Akadcmijos st. 4, 2600 Vilnius, Lithuania

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R. M. LUCAS and G. M. FOODY Department of Geography, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, Wales, U.K. and P. J. CURRAN Department of Geography, University of Southampton, Highfield, Southampton SOI7 IBJ, England, U.K. (Received 24 May 1994)

Abstract. Two classification approaches were investigated for the mapping of tropical forests from Landsat-TM data of a region north of Manaus in the Brazilian state of Amazonas. These incorporated textural information and made usc of fuzzy approaches to classification. In eleven class classifications the texture-based classifiers (based on a. Markov random field model) consistently provided higher classification accuracies than conventional per-pixel maximum likelihood and minimum distance classifications, indicating that they are more able to characterize accurately several regenerating forest classes. Measures of the strength of class memberships derived from three classification algorithms (based on the probability density function, a posteriori probability and the Mahalanobis distance) could be used to derive fuzzy image classifications and be used in postclassification processing. The latter, involving either the summation of class memberships over a local neighbourhood or the application of homogeneity measures, were found to increase classification accuracy by some 10 per cent in comparison with a conventional maximum likelihood classification, a result of comparable accuracy to that derived from the texture-based classifications.

t. Introduction Tropical forests are currently a focus of considerable attention. They represent, for instance, the world's largest bank of species diversity and play significant roles in global biogeochemical cycles. Despite their significance our knowledge of tropical forests is limited (Whitmore 1990). There is, for example, little information on basic forest properties such as age, composition and location. The role of tropical forests in a range of global environmental processes, most notably the global carbon cycle, requires information on the location and extent of regenerating tropical forests as these are major sinks for atmospheric carbon dioxide (Curran et al. 1992, 1995). Therefore land cover maps depicting relevant classes are required but such maps are not available and the only feasible means of deriving such maps is via remote sensing. 0143-1161/95 $10.00

© 1995 Taylor

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Land cover maps can be derived from remotely sensed data using a supervised image classification (Mather 1987). Of the range of classification techniques available the maximum likelihood classification is the most widely used. This approach allocates each case (typically a pixel) to the class with which it has the highest probability of membership. This classification is often applied on a per-pixel basis using information on image tone and other information, such as image texture, and the probability of class membership is not usually used. The lack of information on image texture may suppress class separability and the allocation of a pixel to a single class is wasteful of information on the strength of class membership that are generated in the classification (Wang 1990 a, Foody et 01. 1992). The aim of this paper is to investigate the potential of using simple measures of image texture and 'fuzzy' classification outputs to increase the accuracy with which regenerating tropical forest classes may be mapped. 2.

Classifiers Two groups of classifiers were used; texture-based classifiers and fuzzy classifiers.

2.1. Texture-based classifiers Texture was, for the purposes of this investigation, expressed by the variations in image tone (ON) within an n x n pixel window (where n is an odd number). The texture-based classifiers classified the central pixel of the window using both the ON of all neighbouring pixels and a texture variable derived from autocorrelation coefficients in horizontal and vertical directions (Palubinskas 1993 a). In total eight texture-based classifiers were investigated. These consisted of six texture-based maximum likelihood classifiers and two texture-based minimum distance classifiers (table I). Four classifiers OMARKI, OINOI, OMEANINOI, OMEANI are for cross-shaped windows and OMARK3, OlN03, OM EANIN03, OMEAN3 are for square-shaped windows. OMARKI and OMARK3 incorporate the spatial characteristics of an image directly through a causal Markov random field model of the first and third order respectively. OINO I and OlN03 classify the central pixel on the assumption that the pixels inside the window are independent whereas OMEANINOI and OMEANIN03 classify the mean of the window under the assumption that the pixels inside the window arc independent. OMEAN I and

Table I. Thc classifiers used in the evaluation of texture-based approaches to classification. Classifier MDIST PIX OMARKI OINDI OMEANINDI OMEANI OMARK3 OlND3 OMEANIND3 OMEAN3

Usc of spatial character

Window shape

ciassifier

None None

Single pixel Single pixel Cross Cross Cross Cross Square Square Square Square

Minimum distance Maximum likelihood Maximum likelihood Maximum likelihood Maximum likelihood Minimum distance Maximum likelihood Maximum likelihood Maximum likelihood Minimum distance

Directly Indirectly

Indirectly Indirectly Dircetly Indirectly Indirectly Indirectly

Nature of

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OMEAN3 classify the mean of the window under the assumption that the pixels inside the window are independent and with the covariance matrix equal to the identity matrix. The results from these eight texture-based approaches to classification were evaluated relative to a conventional per-pixel maximum likelihood classification (PIX) and a minimum distance classification (MOIST). For further details of the classifiers see Palubinskas (1988, 1993 a-1993 f) or for preliminary results of their application in remote sensing see Foody and Palubinskas (1993) and Palubinskas (1992, 1993 f). 2.2. Fuzzy classifiers The maximum likelihood classification is used generally to derive a 'hard' classification output; with the output consisting of only the code of the most likely class of membership for each pixel. Tn calculating the most likely class of membership, however, a number of measures of the strength of class membership are derived which may be used to increase the value of the classification. For instance, the measures of the strength of class membership may be used to indicate sub-pixel land cover composition, show the presence of 'untrained' classes or represent the spatial distribution of continuous land cover classes (Foody et al. 1992). By outputting these class memberships therefore more of the information generated in the classification may be made available. This form of output may be considered to be fuzzy rather than hard, with strength of class membership a case has to each class displayed and may allow further investigation with fuzzy set theory (Zenzo et al. 1987, Kent and Mardia 1988, Klir and Folger 1988, Wang 1990a, 1990 b). The measures of the strength of class membership that may be derived from conventional maximum likelihood or Mahalanobis distance classifiers can be used for postprocessing of the classification output in order to increase the accuracy of the final map (Foody et al. 1988, 1992). Three measures of the strength of class membership were derived, each of which could be used to achieve a hard classification if desired. Firstly, the probability density function; p(xli)

I

= (2 n)k/2IK.l1/2 exp ( -

1/2(x- m,)' K,- I(X_ m);))

(I)

where n is the number of classes, k is the number of bands, x is the pixel vector, , is the sign of transposition, m, is the mean vector of class i, K, is covariance matrix of class i, p(xli) is the probability density function of a pixel as a member of class i. The probability density function may be used to achieve a hard classification, with each pixel allocated to the class with which it has the highest probability density function value. This type of classification will be referred to later as CLASS I. Secondly, the a posteriori probability; n

PUlx) = P(i)*p(xIO/

2: P(j)*p(xU)

(2)

j= 1

whereP(ilx}-a posteriori probability of a pixel belonging to class i, P(i)-prior probability of the class i. To achieve a hard classification each pixel would be allocated to the class with which it had the highest a posteriori probability of membership. This type of classification will be referred to below as CLASS2. Thirdly, a measure of class membership based on the Mahalanobis distance;

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memb= 1/(1 + (MAHDIST/A(k,Q)))

(3)

where MAH DIST -(x-m i )' K i- 1 (x-m i ) is Mahalanobis distance, A(k,Q)-quintile of chi-square distribution Q=probability (confidence value), which means that (I - Q) x 100 per cent of pixels of this class will be outside hyperellipsoid defined by Mahalanobis distance (Beyer 1981). A hard classification may be achieved by allocating each pixel to the class with which it has the highest membership value, or smallest Mahalanobis distance. This type of classification is referred to as CLASSM. By deriving these measures of the strength of class membership and outputting a fuzzy image classification, which shows the measures of the strength of class membership a pixel has to each class, additional information is made available relative to that contained in the conventional classification output. The fuzzy classification output, for example, enables post-classification processing to be performed on the class memberships. For instance, post-processing operations such as summation in a local neighbourhood and more complicated context-sensitive reclassification method based on homogeneity of a class (Schumacher 1992) allows the incorporation of spatial information into the classification result both simply and efficiently (Palubinskas 19931', 1994, Palubinskas et al. 1994). Fuzzy logic operations, such as or and and can be used to derive a new measure of the strength of class membership from two such class memberships derived from different fuzzy classification outputs. This new measure of the strength of class membership may provide a more accurate classification than either of the two sets of class memberships from which it was derived. The algorithms for calculating class memberships, fuzzy operations on memberships, post-classification algorithms, including summation of memberships in a local neighbourhood and homogeneity used in this study were derived with the Fuzzy Image Classification software, FVZIC (Palubinskas 1993 e).

2.3. Fuzzy post-classification Three post-classification techniques were applied to the fuzzy classification outputs. These were the summation of class memberships in a local neighbourhood, fuzzy operations on the class memberships derived from two classifications, and the application of homogeneity measures for post-classification processing. Whilst the former approach is straightforward the latter two require further elaboration.

2.3.1. Fuzzy operations on memberships Fuzzy logic operations, such as or and and can be used to derive a new class membership from two such memberships derived from different fuzzy classification outputs (e.g., outputs from classifiers CLASS2 and CLASSM, or results of classifications from images acquired on different dates). Two fuzzy logic operations or and and were investigated. The classical implementation of the operation or is to take the maximum of the two values (MAX). With this approach, however, the magnitude of the differences between the class memberships is unimportant and the same result would, for example, be obtained for the following pairs of memberships 0·9, 0·1 and 0·9.0·8. The YAGER function (Klir and Folger 1988, Schumacher 1992) makes use of the magnitude of both class memberships. The formula for the ~GER function of or is, (4)

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where IV = 2 and a and b are the class memberships from the two fuzzy classification images. Two functions of and were used, minimum (MIN) and lJIGER function. The formula for the lJIGER function for and is,

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(5)

2.3.2. Homogeneity Local and global homogeneity measures calculated from the fuzzy classification output can be used in post-classification to produce an increase in classification accuracy (Schumacher 1992). The degree of post-classification for a class depends on the value of the global homogeneity of that class. Thus, for homogeneous classes the post-classification processing will remove isolated pixels inside the area of this class (the degree of smoothing of the image is high) whereas for more heterogeneous classes a larger number of isolated pixels may be left inside the areas of these classes (the degree of smoothing of the image is low). Local homogeneity was calculated for the central pixel in the neighbourhood defined by a 3 by 3 pixel window for each class. If the local homogeneity is calculated for all eight neighbours of the central pixel it is called all-side local homogeneity. But for the boundary pixels this type of local homogeneity can give inexact estimates. For this reason the half-side local homogeneity (Schumacher 1992) which is based on the five sequent neighbours of the central pixel may be used. Further details are given in the Appendix. 2.3.2.1. Global homogeneity Global homogeneity is calculated from the whole fuzzy classification image for each class. It is used as a criterion for the application of local homogeneity to recalculate the membership to a given class. It may be derived from,

Mh=(~mjm7)/~mj

(6)

where m7 is the membership of local homogeneity for the central pixel of the neighbourhood, and mj the spectral membership of the pixel j.

2.3.2.2. Derivation of resultant class membership with homogeneity information The resultant strength of class membership for a pixel is calculated on the basis of spectral membership of the pixel, local homogeneity of the pixel and global homogeneity of the class (figure I). The resultant strength of class membership is equal to 0, when the local homogeneity membership and spectral membership are equal to 0, and equal to I when the local homogeneity membership and spectral membership are equal to I. All points with resultant membership equal to 0·5 are on the line passing through the point (0'5, 0'5). All points which are on the line parallel to this line have the same resultant membership. The resultant membership changes linearly from the point (0, 0) to the point (1, I) as shown in the figure I. The angle between these lines and the horizontal axis is defined from the global homogeneity. This angle is equal to 90° for heterogeneous classes and equal to 28° (defined heuristically in Schumacher (1992)) for very homogeneous classes. When the global homogeneity is high (near I), then the local homogeneity has the main influence on the resultant membership and when the global homogeneity is low (less than 0'4),

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O'--

o

----l_-'--'------'----J....

__

rn-.I

Figure I. Calculation of the resultant membership from the spectral membership mj of the pixel and local homogeneity mJ if the pixeldepending on the global homogeneity of the class.

then the spectral membership has the main influence on the resultant membership. For more details see Schumacher (1992). 3.

Data For the classifications, Landsat-TM data acquired in August 1991 for an approximately 1000km 2 area north of Manaus in the Brazilian Amazon (2 0 2 0 ' S , 60°00' W) were used (figure 2). Since Landsat-TM data are generally three dimensional in character, with the dimensions relating to reflectance in visible, near- and middle-infrared wavelengths (Townshend 1984, Weaver 1987), only three such wavebands were used. These were TM bands, 3, 4 and 5. Although much of the area was originally covered by primary forest large areas were cleared for cattle pastures and plantations in the late 1970s and 1980s. By 1991 many of these clearances had been abandoned allowing secondary forest vegetation to establish. These secondary forests were identified and aged using a time-series of Landsat-MSS and TM data from 1976 from which a map depicting forest regenerative age classes had been produced (Lucas et al. 1993). This map was refined by fieldwork performed in August 1993 and used as the ground data for this investigation. The field investigation also involved the collection of data on species which allowed the differentiation of two classes of forest within each regenerative age class that were following different successional pathways. Forest Type I was dominated by Cecropiaceae species and occurred mainly on pasture land that had been abandoned shortly after clearance. Forest Type 1\ was dominated by Clusiaceae, Melastomataceae and Flacourtiaceae species with some Cecropiaceae species and was typically found on sites which had, prior to abandonment, been cleared by fire and used for many years as pasture. In total eleven classes were identified. The location of the training sites for the classification was based on the forest regenerative age class map and the sites visited in the field. The performance of the classifications was evaluated by their accuracy. In the absence of a universally

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N

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t 40 km

Figure 2. Location of the test site (dashed box) in Amazonas, Brazil; the shaded area within the box indicates regions of regenerating forest at the tcst site.

acceptable measure of classification accuracy (Congalton 1991) attention focused here on one simple measure, the producer's accuracy (Story and Congalton 1986). This is derived from the ratio of the number of correctly allocated pixels to this class and the total number of pixels in this class and expressed as a percentage. The accuracy was assessed for classification of both the training and testing data. Whilst the former may be used for guidance on the likely performance of a classifier attention is focused mainly on the latter as a tool for classification evaluation. 4. Results and discussion 4.1. Fuzzy classification For each of the eleven classes a sample of pixels was obtained to train and test the classifications (table 2). Using the CLASS2 and CLASSM algorithms the class memberships for each pixel were derived. These were used to derive hard classifications for which the producer's accuracy for each class was calculated (table 3).

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Number of pixels sampled for training and testing the fuzzy approaches to classification for each of the eleven classes.

Table 2.

Abbreviation

Class

Train

Test

A B C

Forest Type I, age 4-6 years Forest Type I, age 7-10 years Forest Type I, age> 14 years Forest Type II, age < 3 years Forest Type II, age 4-10 years Fallow (herbaceous vegetation) Riverine vegetation Mature closed forest Pasture Burnt pasture Plantation

160 136 108 35 324 54 51 2402 337 91 254

94 253 125 37 220 272

D E F

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G H I J K

77 1140 219 252 254*

*As there was little plantation at the site the same data for this class were used for both training and testing the classification.

Table 3. Classification accuracies for each class and the overall average (Av.) accuracy derived from the CLASS2 and CLASSM algorithms and from fuzzy post-processing of the CLASSM output for both classifications of the training and testing data sets. CLASS2 and CLASSM were per-pixel classifiers (i.e., I by I) whereas post-processing operations were undertaken with respect to a 3 by 3 pixel window. The testing sites of the burnt pasture class (class J) were spectrally closer to the pasture class (class I) than to the burnt pasture class, possibly indicating a problem in class definition, particularly in relation to the period since burning. This may account for the poor accuracy with which class J is classified. Classifier CLASS2 (I x I)

Class

Train

A B C D E F G H I

86·3 73'4 64·7 43-9 89·8 86·4 57·1 54·1 75·9 82·7 96·3 90-4 100·0 97-4 98·3 99·7 100·0 100·0 96·7 00-4 87-4 87·4 86·6 74·2

J K

Av.

Test

CLASSM (I x I)

CLASSM (3 x 3) summation

CLASSM (3 x 3) homogeneity

CLASSM (3 x 3) global homogeneity = 1

Train

Test

Train

Test

Train

Test

Train

Test

80·6 nI 89·8 71-4 65-4 96·3 100·0 98·7 100·0 94·5 83· I 86·5

70·2 50·2 86·4 70·3 77·7 90-4 94·8 99·8 100·0 00·0 83·1 74·8

90·0 98·5 100·0 85·7 71·3 100·0 100·0 100·0 100·0 100·0 99·2 95·0

92·6 64·8 99·2 86·5 88·2 100·0 100·0 100·0 100·0 00·0 99·2 84·6

85-6 89·7 96·3 71·4 71·0 98·2 100·0 99·3 100·0 97·8 93·7 91·2

77-7 56·1 92-8 83-8 85·0 92·3 97·4 99·8 100·0 00·0 93·7 79·9

88,) 97·8 100·0 82·9 71·0 100·0 100·0 99·8 100·0 97-8 98·4 94·2

87·2 66·0 98-4 83-8 886 94·1 97-4 100·0 100·0 00·8 98-4 83·2

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Table 4. Average classification accuracy for the fuzzy operations or and and for classifiers CLASS2 and CLASSM. CLASS2 and CLASSM combined CLASS2

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Train Test

86·59 74·16

CLASSM 86·54 74·18

OR

OR

MAX

YAGER

AND MIN

YAGER

AND

86·60 74-47

86·40 74·13

86·56 74·11

86·60 74·36

Whilst the average producer's accuracy from the classifications were similar, the accuracy with which individual classes were classified varied. Combining the class memberships from the different classifications through fuzzy logic operations may therefore be expected to increase the classification accuracy. The accuracy of the classifications derived from the application of the fuzzy logic operations to the results of the CLASS2 and CLASSM classifications were very slightly, but insignificantly, higher than from either classification alone (table 4). The results obtained from post-processing (summation of the memberships within a local neighbourhood) of the fuzzy classifications was, however, more encouraging with an approximately 10 per cent increase in the average classification accuracy obtained with the use of the CLASSM algorithm (table 3). Application of homogeneity measures derived from the fuzzy classification can also increase the classification accuracy. The application of homogeneity (allside local homogeneity and equation A2, see Appendix) increased the average classification accuracy from 86·5 to 91·2 per cent for training data and from 74·8 to 79·9 per cent for testing data (table 3). It was also apparent that by assigning the global homogeneity measures of all classes to the maximal value (i.e., I) the average classification accuracy was increased to 94·2 per cent for training data and to 83·2 per cent for testing data, which were similar to the results obtained from the simple summation of the memberships in the neighbourhood.

4.2. Texture-based classification Using a different set of training and testing pixels (table 5), a consequence of the algorithms used, the potential of the texture-based classifiers was assessed. Table 6 gives the average classification accuracy derived from ten classifiers applied to Landsat-TM data based on a 3 by 3 pixel window size. In general the results showed that the classes could be mapped to a relatively high accuracy. For the training data the average classification accuracy ranged from 84·0 per cent from M DIST to 99·7 per cent from OMARKI. With the testing data the accuracies were, as expected, slightly less and varied from 69·2 per cent from MOIST to 93-5 per cent from OMEANIN03. It was also apparent that the texture-based approaches consistently gave higher classification accuracies than the conventional classifiers, MDIST and PIX. Comparison of the results from the fuzzy and texture-based approaches to classification showed that in terms of classification accuracy, both performed similarly. From the fuzzy approaches investigated the highest classification accuracy for a classification of the training data obtained (based on summation of memberships from CLASSM) was of slightly lower but comparable magnitude to the highest

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756 Table 5.

Number of pixels sampled for training and testing the texture-based approaches to classification for each of the eleven classes. Abbreviation

Class

A B C 0 E F

Forest Type I, age 4-6 years Forest Type I, age 7-10 years Forest Type I, age> 14 years Forest Type II, age < 3 years Forest Type II, age 4-10 years Fallow (herbaceous vegetation) Riverine vegetation Mature closed forest Pasture Burnt pasture Plantation

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G H 1 J K

Train

Test

128 84 76 15 228 24 25 855 171 49 159

72 157 75 16 192 193 25· 553 75 166 159·

"The same data were used for training and testing due to an inability to acquire a independent sets.

Table 6.

The average classification accuracy (%) for the ten classifiers (includes 8 texturebased approaches). Classification accuracy (%) Classifier

Train

Test

MoiST PIX OMARKI OINOI OMEANINOI OMEANI OMARK3 OlND3 OMEANIN03 OMEAN3

84·0 88-4 99·7 99·2 98·7 92·6 96'5 96-4 95·9 94·0

69·2 81 ·7 89·8 91·9 92·3 73-8 87·7 93,) 93·5 74·6

accuracy derived from the texture-based classification approaches (OMEANIND3). For the testing data set it was apparent, however, that the highest accuracy derived from the fuzzy approaches to classification was some 8·9 pCI' cent less than that from the OMEANIND3 classification.

5.

Conclusions Two classification approaches based on the use of image texture and fuzzy c1assitication outputs were investigated for mapping eleven classes of regenerating forest from Landsat-TM data. Texture-based classifiers (based on a Markov random field model) consistently provided higher classification accuracies. Alternatively,

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post-classification (summation in the neighbourhood or application of homogeneity approach) of fuzzy classification outputs may also be used to increase classification accuracy by of the order of 10 per cent in comparison with maximum likelihood classification. Texture-based classification and post-classification of fuzzy classification output gave comparable classification accuracies, although the texture-based approaches were generally slightly more accurate. Both approaches were able to significantly increase the accuracy with which the classes could be classified, relative to conventional maximum likelihood and minimum distance classifiers, and this in turn could provide valuable information for the mapping of regenerating tropical forests. Acknowledgments We are grateful to the Commission of the European Communities for providing a 'Cooperation in Science and Technology with Central and Eastern European Countries Fellowship' to GP which was held at the University of Wales Swansea and to Miroslav Honzak for valuable assistance with aspects of the image processing. The authors acknowledge the financial support provided by the Natural Environment Research Council through its Terrestrial Initiative in Global Environmental Research (TIGER) programme award GST/02/0604. Appendix A I. All-side local homogeneity All side local homogeneity is calculated for all 8 neighbours of the central pixel of the neighbourhood. Four methods for calculating of a local homogeneity were investigated (equations AI-A4). In (AI) the spectral memberships of 8 pixels are summed in the neighbourhood and the sum is linearly mapped into interval [0,1]:

m1=(~mj)/8,

(AI)

where mJ-membership of local homogeneity for the central pixel of the neighbourhood (the index) of the summation stands for all pixels in neighbourhood except the central pixel), mj-spectral membership of the pixel j. In (A2) the spectral memberships are summed in the neighbourhood and the sum is non-linearly mapped into interval [0, I]: (A2) where if 0< if

=mJ < = 5 then mJ=0·5 x (mJ/5) (m1/5),

5 j' J J1/2 ' if 0·6< =1I1~