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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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J. Zhang and G. M. Foody618
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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Fully-fuzzy classication of sub-urban land cover 619
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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J. Zhang and G. M. Foody620
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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Fully-fuzzy classication of sub-urban land cover 621
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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J. Zhang and G. M. Foody622
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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Fully-fuzzy classication of sub-urban land cover 623
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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J. Zhang and G. M. Foody624
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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Fully-fuzzy classication of sub-urban land cover 625
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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J. Zhang and G. M. Foody626
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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Fully-fuzzy classication of sub-urban land cover 627
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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