Fully Fuzzy Supervised Classification Approach

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int. j. remote sensing, 2001 vol. 22, no. 4, 615628

Fully-fuzzy supervised classication of sub-urban land cover from

remotely sensed imagery: statistical and articial neural network

approaches

J. ZHANG

Department of Geography, University of California, Santa Barbara,CA 93106-4060, USA

G. M. FOODY

Department of Geography, University of Southampton, Higheld,Southampton, England, UK; email: [email protected]

(Received 6 May 1998; in nal form 11 May 1999 )

Abstract. Fully-fuzzy classication approaches have attracted increasing interestrecently. These approaches allow for multiple and partial class memberships atthe level of individual pixels and accommodate fuzziness in all three stages of asupervised classication of remotely sensed imagery. A fully-fuzzy classicationstrategy may be deemed more objective and correct than partially-fuzzy

approaches where fuzziness is only accommodated in one or two of the threeclassication stages. This paper describes two approaches to the fully-fuzzy classi-cation of remotely sensed imagery: a statistical approach based on a modiedfuzzy c-means clustering algorithm performed in a supervised mode and anarticial neural network based approach. This is followed by the documentationof a case study using Landsat Thematic Mapper (TM) data of an Edinburghsuburb. Both approaches were applied to derive fully-fuzzy classications of landcover, with fuzzy ground data, critical for training and testing the classications,derived from indicator kriging. Results conrmed the superiority of fully-fuzzyover their respective partially-fuzzy classication counterparts, which is benecial

given their more relaxed requirements for training pixels ( i.e. training pixels neednot be pure). Similar accuracies were obtained with the articial neural networkand statistical approaches to classication. It is suggested that due emphasis mustbe placed on derivation and analysis of fuzzy ground data as well as fuzzyclassied data in order to further improve fully-fuzzy classications.

1. Introduction

Supervised image classication is a commonly performed analysis of remotely

sensed data. This is essentially a three-stage process. Firstly, a number of well-

distributed training pixels, representative of their respective classes, are located inthe image under consideration. These training pixels are used to calculate descriptive

statistics (e.g. mean and variability) for each class. Secondly, on the basis of the class

descriptions derived, each pixel is allocated to the class with which it has the greatest

similarity, as assessed relative to the classiers decision rules. In a maximum likeli-

hood classication, for example, this is to label each pixel as belonging to the class

with which it has the highest posterior probability of membership (Lillesand and

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online 2001 Taylor & Francis Ltd

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J. Zhang and G. M. Foody616

Kiefer 1994, Campbell 1996). Thirdly, the accuracy of a classied image is assessed

with respect to an independent set of pixels for which reference or ground data on

class membership is available. This testing of the classication is usually based on

an error matrix, which shows the correspondence between the predicted and the

actual classes of membership for an independent testing set, and from which it is

possible to derive a range of quantitative measures of classication accuracy. The

end result of the classication is eectively a thematic map depicting the spatial

distribution of the selected classes accompanied by an accuracy statement. The

accuracy of the classication is controlled by many factors related to the methods

used as well as the nature of the classes and remotely sensed data (Campbell 1996).

In a conventional supervised classication, the output for each pixel comprises

only the code of the class with which it has the highest strength of membership. This

kind of classication technique is termed as being hard or crisp, as it is based on

the conventional crisp set theory; the terms crisp and hard are used interchangeablyin this paper. In this type of classication, each pixel has a single membership in a

mutually exclusive classication scheme, that is, full membership to the named class,

and zero membership to other classes. The intermediate data about membership

strength or similarity calculated in the determination of the class label, usually

obtained through computationally intensive procedures, are generally not provided

to the end users, although they may be very informative (Foody et al. 1992). The

training and accuracy assessment stages of the classication also use conventional

crisp set theory. The training pixels are selected such that they belong (or are assumed

to belong) to their named classes with full membership and have zero membershipto other classes. Similarly, testing pixels, again, posses single membership, allowing

for cross-tabulation of the classied and reference (ground) class labels.

Clearly, a conventional classication of remotely sensed imagery assumes that

the study area is composed of a number of unique, internally homogeneous classes

that are mutually exclusive and that a classication based on remotely sensed data

and ancillary data can be used to identify these classes with the aid of ground data

( Townshend 1981, Lillesand and Kiefer 1994). However, such assumptions are often

invalid in areas where the classes exist as continua rather than as a mosaic of discrete

classes. For instance, dierent land cover types are rarely internally homogeneous

and mutually exclusive. Consequently, the classes intergrade and are not separated

by sharp boundaries (Wood and Foody 1993, Kent et al. 1997 ). This is to say that

there is signicant fuzziness in many geographical phenomena. Moreover, there is a

problem concerning the complex relationship between spectral responses recorded

by a remote sensor and the corresponding ground situations; similar entities at

dierent locations may exhibit varied spectral responses, while similar spectral

responses may relate to dissimilar entities (Forster 1983 ). Finally, fuzziness often

occurs due to the presence of mixed pixels (mixels), particularly for coarse spatialresolution remotely sensed imagery, which are not completely occupied by a single,

homogeneous category (Duggin and Robinove 1990, Campbell 1996). Thus, even if

the classes are discrete and mutually exclusive on the ground, they may be mixed in

the representation provided by the remotely sensed imagery.

To adapt to the fuzziness intrinsic to many natural phenomena, fuzzy classication

approaches have been proposed (Wang 1990 ). These approaches are fuzzy in the sense

that they allow for the multiple and partial class membership properties of mixed

pixels; note that the approaches are often based more on soft computing than fuzzy

logic (e.g. Gopal and Woodcock 1994, Foody 1996) . Fuzzy approaches allow more


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Fully-fuzzy classication of sub-urban land cover 617

information on the relative strengths of class membership at the pixel level to be made

available to end users. Information on per-pixel class membership has, for example,

been used for post-processing of image classications to improve change detection in

the urbanrural fringe (e.g. Pathirana and Fisher 1991 ). Moreover, the extent of classes

at the sub-pixel level may be obtained, as the proportional coverage of the classes in

the area represented by the pixel may be strongly related to their corresponding classmembership values (Foody and Cox 1994, Foody 1996, Bastin 1997).

There are various ways to derive a fuzzy or soft classication. A fuzzy classication

may, for example, be derived from the maximum likelihood classier by retaining

the probabilities of membership of individual pixels belonging to all the candidate

classes (Campbell 1984, Wang 1990, Foody et al. 1992). Fuzzy classications may

be derived from a range of other popular and available approaches. For instance,when an articial neural network is used for classication, the strength of class

membership can be measured by the activation level of the network output nodes

(Foody 1996, Foschi and Smith 1997).

The fuzzy approaches generally used, however, do not take into account fuzziness

that may be characteristic of the ground data as well as of the image-based data(Foody 1995, 1996). That is, these fuzzy approaches deal with fuzziness in the class

allocation stage of the classication of remotely sensed data, but do not accommodate

fuzziness in the ground data used in training and testing the classication. Such a

classication may be termed partially-fuzzy (Zhang and Foody 1998), as fuzzinessis not fully accommodated throughout the classication. The ground data for a pixel

used in the training and testing stages of a supervised classication are supposed todescribe the class membership properties of the area on the ground represented by

the pixel. If the pixel is fuzzy, in the sense that it comprises more than one class, its

ground data equivalent should also be conceived as being fuzzy. Fuzziness in thetraining and/or testing set may be accommodated in a supervised classication

( Foody and Arora 1996, Foody 1997 ). For this, however, detailed ground data are

required. It is therefore necessary to explore suitable ways for deriving fuzzy ground

data for training and testing a supervised classication. Then, a fully-fuzzy classica-

tion (Foody 1995, 1997 ), which accommodates fuzziness in all three stages of the

classication, may be performed.The derivation of fuzzy ground data is not, however, straightforward. The crisp

ground data conventionally used, such as those extracted from rigorously orientated

photographic stereo models, are commonly represented in form of discrete polygonsof classes, with the boundary fuzziness and interior heterogeneity ltered out.

Methods for deriving fuzzy ground data may ideally start from and retain the

heterogeneities within each mapping unit. It is then possible to use the proportions

of dierent classes within a polygon or other mapping units such as the equivalent

area of a pixel on the ground, as probabilities or other similar measures of class

membership (Foody 1995 ). When this is not the case or where the acquisition ofsuciently detailed ground data is dicult, a technique such as indicator kriging

may be applied to derive fuzzy ground data (Zhang and Kirby 1997).

Provision of both fuzzy classied data and fuzzy ground data would enable an

assessment of classication accuracy based on fuzzy measures such as entropy andcross-entropy as well as crisp measures such as the percentage correct allocation

and kappa coecient of agreement if desired (Foody 1996, Zhang and Foody 1998 ).

This may be a more correct and objective approach than the use of the standard

hard approaches for classication accuracy assessment alone, in which fuzziness

(e.g. arising from mixed pixels) is often deliberately avoided (Foody 1995, 1997 ).


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When fuzzy approaches are extended to the training as well as the class allocation

and accuracy assessment stages, a fully-fuzzy supervised classication is developed.

The so-called fully-fuzzy classication has been implemented previously with articial

neural networks and maximum likelihood classication (Foody and Arora 1996,

Foody 1997, 1999 ). This paper explores alternative approaches to fully-fuzzy classi-

cation of remotely sensed data in a challenging environment and uses a relatively

large sample size. This is seen more realistic than previous tests in which, as it was

dicult to acquire fuzzy ground data, simulated datasets were used with only a

limited number of classes and pixels.

The next section will describe a statistical and an articial neural network based

approaches to fully-fuzzy supervised classication. This is followed by an empirical

test of the methods for the classication of sub-urban land cover.

2. Methods for fully-fuzzy supervised classicationNumerous approaches may be used to derive a fully-fuzzy classication. Here,

the two approaches for fuzzy training and classication adopted in this paper are

briey discussed; the assessment of classication accuracy in the testing stage is not

reviewed, as this is independent of the method of classication production.

2.1. A supervised fuzzy c-means classication using fuzzy training data

The rst method for fully-fuzzy supervised classication is based on the

well-known fuzzy c-means clustering algorithm (Bezdek et al. 1984 ). Let X5

{x1 , x2 ,..., xn} be a sample of n observations (pixels) in an s-dimensional Euclideanspace (i.e. with s spectral bands). A fuzzy clustering is represented by a fuzzy set

{Uc n|m

ik [0.0,1.0 ]} with reference to n pixels and c clusters or classes. The

interpretation is that U is a real cn matrix consists of elements denoted by mik

,

and mik

is the fuzzy membership value of an observation xk

to the ith cluster. The

fuzzy membership values range from 0.0 and 1.0 and are positively related to the

strength of membership of a pixel to a specied class.

There are a variety of algorithms that aim to derive an optimal fuzzy c-means

clustering. One widely used method operates by minimizing a generalized least-

squared error function Jm

,

Jm5

n

k=1

c

i=1

(mik

)m(dik

)2 (1)

where m is the weighting exponent which controls the degree of fuzziness (increasing

m tends to increase fuzziness; usually, the value of m is set between 1.5 and 3.0), d2ik

is a measure of the distance between each observation (xk

) and a fuzzy cluster centre

(vi) (Bezdek et al. 1984 ). Often, the Mahalanobis distance is used in remote sensing,

which is calculated fromd2ik5 (x

k v

i)T C1 (x

k v

i) (2)

where C is the covariance matrix of the sample X, and the T indicates transposition

of a matrix.

The minimization of the error function Jm

begins from random setting ofmik

. An

optimal fuzzy partition is then sought iteratively to derive an unsupervised classica-

tion. The algorithm may, however, be modied for the derivation of a supervised

classication. For this, the class centroids (vi) are determined from the training data.

This reduces the fuzzy c-means clustering algorithm to a one-step calculation,


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resulting in the fuzzy membership value for each pixel in each of the dened classes.

The fuzziness of the classication can be modulated by varying the magnitude of

the parameter m. For a given value of m, the strength of class membership may be

adjusted by using per-class covariance matrices rather than the global matrix in

equation (2). Using per-class covariances as well as per-class means allows supervised

fuzzy c-means clustering to be easily adapted to a supervised implementation using

fuzzy training data. Suppose that the training pixels set are Y5 {y1

, y2

,..., yn

}, and

the fuzzy training data are represented as a fuzzy set {Gc n|g

ij [0.0, 1.0]} with

reference to n training pixels and c clusters. The element gij

represents the fuzzy

membership value of a training pixel yj

(1


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Figure 1. A typical feed-forward neural network for image classication. The structure showncorresponds to the network used in the case study.

where wqp is the weight for the connection linking node p and node q, b is the totalnumber of nodes having links with node q in the same layer as node p, o

pis the

input to node q from node p, oq

is the output from node q, known as activation

level, f stands for an activation function such as the sigmoid (Schalko 1992).

A commonly used learning algorithm for classication with an articial neural

network is back-propagation (Schalko1992 ). With this, training pixels are presented

to the network via the input layer and fed forward through the network using

equations (5) and (6). In the output layer, network outputs are compared with the

target outputs, which are known for training pixels. The error, if any, is propagated

backward, with weights for relevant connections corrected via a relation such as

Dwqp (t+1)

5 gdq

op1 a Dw

qp (t)(7)

where t indicates the iteration, g represents the learning rate, dq

is a computed error

and a is the momentum term. The procedure of forwarding signals and back-feeding

errors is usually performed iteratively until the overall error is minimized or declines

to an acceptable level.

The outputs from an articial neural network exist as activation levels. These

activation levels range from 0 to 1, and may be treated as fuzzy membership values.This characteristic makes articial neural networks easily extendable to fuzzy classi-

cation. Moreover, training for an articial neural network can be performed either

in a crisp or a fuzzy mode. In crisp training, each training pixel is associated fully

with a single class and thus discrete classes are presented to the network. An approach

to fuzzy training is to feed the network with the proportional coverage of each class

in the training pixels (Foody 1997 ). Using this approach to training, together with

the derivation of a fuzzy class allocation and use of an approach to accuracy

assessment that accommodates fuzziness, a fully-fuzzy classication may be under-

taken with a neural network (Foody 1997, 1999 ).


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3. An empirical study

The fuzzy c-means and neural network based approaches were evaluated for

fully- and partially-fuzzy classications of remotely sensed data.

3.1. Study area and data acquisition

An area of~2 km2 located around Blackford Hill within the city of Edinburgh

(gure 2) was selected. A sub-urban area was chosen because it would be rich in

geographical diversity and so appropriate and challenging for fuzzy classication.

Mapping urban and sub-urban land covers is also recognized as an important but

dicult task (Barnsley and Barr 1996). There were a variety of urban thematic and

topographic features at the site, notably a wooded valley, residential, commercial

Figure 2. An extract of an aerial photograph (1:24 000 scale) of the test site.

Figure 3. Sub-scene of the Landsat TM image used in the case study (TM bands 3, 4 and 5) .


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and academic buildings, road networks, footpaths, recreational areas, a small lake,

worked allotments, hills and at ground. The residential areas were compact and

their component roads, pavements, roofs, walls and hedges were arranged in a

complex spatial pattern. The dispersed individual trees or groups of trees blended

into neighbouring land cover types. Shrubs dominate the west end of the Blackford

Hill and grassland cover tended to occur in those areas not covered by concrete,

bare ground, tall trees or shrubs.

Landsat TM data of the site were used (gure 3). All analyses were based on the

data acquired in three of the TMs seven wavebands. These were TM bands 3, 4 and

5 which often represent the main dimensions of the full TM dataset (Townshend

1984, Horler and Ahern 1986). Ground data on land cover were derived from the

1:24 000 scale colour aerial photographs. Both the Landsat TM data and 1:24 000

scale aerial photographs were acquired in the summer of 1988, and can be safely

assumed free of signicant temporal dierences in land cover. For the purpose ofthis study, the USGS land use and land cover classication system for use with

remote sensing data was used, with the following ve classes appropriate to the

scene dened: grass (grassland, including parkland), built (built-up land, including

barren land), wood (wooded land, with no distinction between deciduous and

coniferous woodland), shrub (shrubland, including open wooded land ) and water

(water bodies, including lakes and water works).

3.2. Derivation of fuzzy ground dataTo generate fuzzy ground data, photogrammetric digitizing of land cover from

the aerial photographs was carried out based on a reconstituted stereo model on an

analytical plotter. This process resulted in a polygonal land cover ground dataset

covering approximately half the area of the test site. These data could be used for

deriving the proportions of the land cover comprising the area represented by each

pixel, a form of fuzzy ground data. Alternatively, the probabilities of class membership

may be derived via kriging (Zhang and Foody 1998). Specically, indicator kriging

was used to spatially interpolate class membership (Deutsch and Journel 1992). For

this, a set of classied samples was identied from screen-displayed photogrammetric

data. These sample points were carefully selected to ensure each could be considered

as a pure point, and thus have full membership (100%) to the named class with zero

memberships to the other classes. The data were then transformed to a grid coordin-

ate system with a grid cell size of 2.52.5 m2 and the semi-variograms were calculated.

The kriging procedure was eventually run with the output grid cell sizes equal to

Landsat TM data pixel size (30 m). The fuzzy ground data derived from indicator

kriging were stored as a ve-band image, one for each class.

3.3. Fuzzy classications

To compare fully-fuzzy and partially-fuzzy classications, two random samples

of training pixels, a crisp set consisting of only pure pixels and a fuzzy set containing

pixels of varied class composition (with mixed and pure pixels) were obtained from

the fuzzy ground data. For comparative purposes, the sample size for each class was

the same in the crisp training set as in the fuzzy training set if hardened to show the

dominant class label (table 1). For practical reasons, a pixel was assumed to be pure

if it was highly dominated by a single class. Specically, pixels were considered


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Table 1. Training pixels.

Fuzzy training

Crisp training Fuzzy membership values (%)No. of pixels

Land cover type No. of pixels when hardened Minimum Maximum Mean

Grass 13 13 49 98 71Built 12 12 41 99 76Wood 14 14 49 100 77Shrub 10 10 46 100 73Water 3 3 73 99 89Total 52 52

pure if their maximum membership values were above certain thresholds, namely

95% cover for grass, built, wood and shrub land cover types, and 75% (due to the

high spectral distinctiveness of the class and limited number of pixels) for water.

The statistical and the neural network based classiers were applied with both

crisp and fuzzy training data. Firstly, the modied fuzzy c-means clustering algorithm

was used, with parameter m set at a value of 2.5. The algorithm was applied in a

supervised mode to calculate the fuzzy membership values for each pixel in each of

the ve classes using crisp and fuzzy class training statistics, respectively. Secondly,

a three-layer articial neural network comprising three input, eight hidden and veoutput nodes (gure 1) was used to derive a fuzzy classication of land cover. The

number of input and output nodes was determined by the number of wavebands

and classes, respectively. The number of hidden units and other network properties

were selected subjectively on the basis of empirical results from trial runs. The

network was applied with a learning rate of 0.4 and momentum of 0.1, to derive a

fuzzy classication of the Landsat TM image using crisp and fuzzy training datasets.

The termination of training in an articial neural network classication is a

dicult but important issue (Ripley 1996). When using relatively pure training pixels,

as in a conventional implementation, a useful rule of thumb is to stop the training

when all training pixels have been correctly allocated to their known classes so as

to avoid over-training. When using fuzzy training pixels, on the other hand, it was

necessary to adopt a combination of a conventional criterion such as the percentage

of training pixels correctly allocated, and fuzzy criteria, based on measures such as

the entropy of the outputs derived from the network. Here, a trial-and-error strategy

was adopted. With increasing iteration, the correctness of class allocation showed

an increase from the start, but seemed to reach an upper limit after certain number

of iterations, and then tended to decrease gradually if iteration continued. Entropy,which indicates degree of fuzziness, on the other hand, decreased (i.e. tending to be

less fuzzy) with increased number of iterations. It was found that stopping network

training after 4279 and 4221 iterations when using crisp training data and fuzzy

training data, respectively, seemed to give an acceptable compromise in terms of

correctness of allocation and degree of fuzziness as implied by entropy.

3.4. Classication evaluation

All the pixels not used in training a classication and for which class member-

ship was known from the ground data were used to evaluate the accuracy of the


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classication. These testing pixels varied greatly in class composition, from crisp

( pure) to highly mixed or fuzzy (table 2). To enable a conventional evaluation of

classication accuracy, both the fuzzy image classication and fuzzy ground data

were hardened and the overall percentage correct allocation derived using an inde-

pendent test set (Congalton 1991, Janssen and van der Wel 1994). In other words,

hard classications of the remotely sensed and ground dataset were derived by using

the maximization operation (Zhang and Foody 1998 ). This resulted in the production

of conventional datasets used, or assumed, in remote sensing studies. The accuracies

of the hardened fuzzy classications, based on the modied fuzzy c-means clustering

and the articial neural network trained with crisp and fuzzy data, showed that

the fully-fuzzy approach was more accurate than the partially-fuzzy approach.

Additionally, the articial neural network classications had higher accuracies than

the comparable fuzzy c-means classications (table 3), although the dierences were

insignicant (95% level of condence, di

erence between proportions test).The conventional methods of classication accuracy assessment are unlikely

to yield an appropriate and representative statement of the accuracy of a fuzzy

Table 2. Testing pixels.

Sample of testing pixels

Pure Mixed

No. of No. of pixels Mean of fuzzyLand cover type Sum pixels when hardened membership values (%)

(a) W ith hard trainingGrass 252 13 239 67Built 226 26 200 71Wood 183 5 178 71Shrub 55 2 53 72Water 10 2 8 56Total 726 48 678

(b) W ith f uzzy trainingGrass 252 23 229 67Built 226 37 189 71Wood 183 18 165 70Shrub 55 9 46 73Water 10 3 7 53Total 726 90 636

Table 3. Evaluation of fuzzy classications (number of test pixels: 726).

Partially-fuzzy Fully-fuzzy

FCM ANN FCM ANN

Percentage correct allocation 31.6% 35.4% 38.2% 40.4%Entropy 1.28 0.69 1.37 1.08Cross-entropy 2.03 2.07 1.67 1.70Distance 0.28 0.35 0.26 0.28

FCM, modied fuzzy c-means clustering; ANN, articial neural network.


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classication (Foody 1996). Although there are few techniques for evaluating fuzzy

classications (Goodchild 1994 ), there are a range of measures which can be used

to indicate classication accuracy. For a fuzzy classication, it is possible to calculate

entropy measures on a pixel basis to describe the partitioning of membership between

the classes (Maselli et al. 1994, Foody 1995 ). The articial neural network based

approach produced classications with lower entropy values than the statistical

approach (table 3). The entropy values are, however, dicult to interpret, with any

entropy value having the potential to indicate an accurate classication (Foody

1995 ); entropy reects only the degree of fuzziness, but not necessarily accuracy.

Cross-entropy is more suitable for assessing the accuracy of a fuzzy classication

( Foody 1995 ) as it indicates the closeness of a fuzzy classication to a fuzzy ground

dataset (Foody 1996). The closer the classication is to the ground data the lower

the cross-entropy and the higher the classication accuracy; further details on the

background and calculation of cross-entropy may be found in Klir and Folger (1988)and its use in remote sensing in Foody (1996 ). The mean of the cross-entropy

measures was 2.03 and 2.07 for partially-fuzzy classications using the statistical and

articial neural network approaches, respectively. For fully-fuzzy classications, the

mean of the cross-entropy was 1.67 and 1.70 from the statistical and the articial

neural network approaches, respectively (table 3). This suggested that the fully-fuzzy

approach was more accurate than the partially-fuzzy approach. Furthermore, the

cross-entropy values suggest that the statistical classier was marginally more accur-

ate than the articial neural network classier, in both fully- and partially-fuzzy

classications. An alternative measure for the closeness between a fuzzy classicationand its fuzzy ground data are distance measures (Foody 1996 ). Table 3 includes

results of accuracy evaluations based on the distance between the predicted and

actual class composition of the testing pixels for both fully- and partially-fuzzy

classications derived from both the statistical and the articial neural network

approaches. Interpretations for measures of distance are similar to those of cross-

entropy.

A variety of approaches for classication evaluation were undertaken. These

sometimes revealed dierent and/or inconsistent relationships to those reported

above. For instance, it is interesting to note that measures of entropy in table 3 could

give a misleading impression about classication accuracy, if one were to regard a

lower measure of entropy as a sign of higher accuracy. As noted above, any entropy

value could be associated with an accurate classication and this greatly limits the

value of entropy as an index of classication accuracy. Additionally, with the

hardened classications, the percentage correct allocation was higher for the articial

neural network than for the statistical classications. Accuracy may also be assessed

for individual classes. This is often measured by correlation coecients (Foody 1996,

Maselli et al. 1996). Here, correlation coe

cients were calculated for partially- andfully-fuzzy classications with respect to the fuzzy ground data. The results do not

indicate a clear trend (table 4). The dierences in accuracy indicated by the various

measures used also highlights some of the problems associated with the evaluation

of image classications and the need for continued development in this area.

Although the results indicate that the adoption of a fully-fuzzy rather than

partially-fuzzy approach may increase classication accuracy the magnitude of the

accuracies derived were relatively low. It is likely that the issues such as mis-

registration of the ground and remotely sensed data account for a large part of the

error (e.g. Townshend et al. 1992 ) but it is apparent that considerable further


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Table 4. Correlation coecients (r) between the estimated and actual class coverage (numberof pixels: 726); insignicant coecients not shown.

(a) Partially-fuzzy ( b) Fully-fuzzy

Land cover type FCM ANN FCM ANN

Grassland Built-up land 0.42 0.28 0.37 0.48Wooded land 0.32 0.33 0.12 0.33Shrubland 0.30 0.34 0.21 Water bodies 0.29 0.31 0.24

FCM: modied fuzzy c-means clustering; ANN: articial neural network.

development is required to operationalize fuzzy classication techniques. The incorp-oration of contextual information into the classication is, for example, one way of

signicantly raising the accuracy of the classication ( Zhang and Foody, submitted ).

Nonetheless, the fully-fuzzy classications were generally more accurate than their

widely used partially fuzzy counterparts. For instance, increases in the percentage of

cases correctly classied of 6.6% and 5.0% were obtained through the use of fully-

rather than partially-fuzzy classications using the fuzzy c-means and neural network

approaches, respectively. The results also indicate that useful training data can be

derived from a sample of mixed or impure pixels. Since remotely sensed data often

contain a high proportion of mixed pixels, this may further enhance the potential offully- over partially-fuzzy classication approaches as it may be dicult to obtain

an appropriate sample of pure pixels for training.

4. Conclusion

Both statistical and articial neural network approaches to fully-fuzzy supervised

classication of remotely sensed data have been investigated. The approaches used

were based on a modied fuzzy c-means clustering and a neural network using a

back-propagation learning algorithm. Both were found to derive more accurate

classications than their partially-fuzzy counterparts and able to produce a classica-

tion with only limited training data of variable class memberships. The accuracy of

the classications derived from the neural network and statistical classier did not

dier markedly but there was some inconsistency in the relative accuracies of the

classications as indicated by the measures based on hard data (e.g. the percentage

correct allocation) and fuzzy data (e.g. cross-entropy). These results highlight the

need for further work on methods of accuracy assessment.

Fuzzy ground data are critical for the implementation of a fully-fuzzy approach

to the classication of remotely sensed data. However, the provision of such grounddata is not a trivial task. The suitability of a particular set of fuzzy ground data will

have to be evaluated in the context of a specic fuzzy classication. This paper has

applied a geostatistical approach to deriving fuzzy ground data which are better

suited to bench-marking fuzzy classications of remotely sensed data in areas with

signicant fuzziness, similar to that encountered in the test site, than conventional

hard ground data. Devising suitable ways of deriving fuzzy ground data will be

important for research on fully-fuzzy classication, as further improvement in the

classication of remotely sensed imagery may stem from the use of fully-fuzzy

approaches. The fuzzy ground data can then be relatively easily accommodated in


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the various stages of the classication process ( Foody and Arora 1996 ). For example,

a number of approaches to derive and evaluate fuzzy classications may be integrated

into standard classication approaches if desired. A fully-fuzzy strategy as promoted

in this paper may contribute to increased objectivity, adaptability and exibility

in the classication of remotely sensed imagery, although further renement and

development is required.

Acknowledgments

The University of Edinburgh is gratefully acknowledged for provision of the

aerial photographs and Landsat TM data used in the research reported in this paper

and its support of J.Z. during doctoral research. Most of the work was undertaken

when J.Z. was with Wuhan Technical University of Surveying and Mapping (China).

We are also grateful for the comments made on the original manuscript by the

referees.

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Fully Fuzzy Supervised Classification Approach

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