Computer Processing of Remotely-Sensed Images

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					                 Computer Processing of
                 Remotely-Sensed Images

                           An Introduction
                           Second Edition

                             Paul M. Mather
          School of Geography, The University of Nottingham, U K

2 lower
   Non-parametric feature selection methods d o not                    operator as belonging to class i that have been correctly               A
rely on assumptionsconcerning the frequency distribu-                  labelled by the classifier. The other elements of row i                 I .(
tion of the features. O n e such method, which has not                 give the number and distribution of pixels that have                    P"
been widely used, is proposed by Lee and Landgrebe                     been incorrectly labelled. T h e classification accuracy for            (I!
(1993). Benediktsson and Sveinsson (1997) demonstrate                  class i is therefore the number of pixels in cell i divided             sh
its application.                                                       by the total number of pixels identified by the operator                wl
                                                                       from ground data as being class i pixels. The overall                   gu
                                                                       classification accuracy is the average of the individual                da
8.10 CLASSIFICATION ACCURACY                                           class accuracies, which are usually expressed in percen-                tri
                                                                       tage terms.
The methods discussed in section 8.9 have as their aim                    Some analystsuse a statistical measure. the kappa
the establishment of the degree of separability of the k                                                the               provided
                   to which the image pixels are          be
                                                                       by thecontingency matrix(Bishop er                     (I,,.
                                                                                                                    1975). Kappais
allocated (though the Bhattacharyya distance is more                   computed from:
like a measure of the probability of misclassification).
Once a classification exercise has been carried out there                               r                r
is a need to determine the degree of error in the end-
product. These errors could be thought of as being due
                                                                                   N   x
                                                                                       i= l
                                                                                              .xii -     x
                                                                                                       i= l
to incorrect labelling of the pixels. Conversely, the de-
gree of accuracy could be sought. First of all, if a method
allowing a 'reject' class has been used then the number
                                                                                       N'     -   xr

                                                                                                  i= I

of pixels assigned to this class (which is conventionally
labelled 601) be an indication of the overallrepresen-
              will                                                     The xi; are the diagonal entries of the confusion matrix.
tativeness of the training classes. If large numbers of                T h e notation x i + and . x + ~indicates, respectively, the
pixels are labelled aO' then the representativeness of                 sum of row i and the sum of column i of the confusion
t3e training data sets is called into question - d o they              matrix. N is the number of elements in the confusion
adequately sample      the feature space? ~h~ most                     matrix. Row totals ( x i + for the confusion matrix shown
manly used method of representing the degree of accu-                  in Table 8.4 are listed in the column headed (1) and
 racy of a classification is to build a            confusio,l          column totals are given in the last row. The sum of the
matrix (or error matrix), ~h~ elements of the rows of                  diagonal elements bii) 350 (Ej=I .xi; for I. = 6). and the
 this matrix give the number of pixels that the operator                        the products       the      and cOiumn marginal
 has identified as beiflg members ofclass i that have been                                     ~ is
                                                                       totals(Ej=, ~ ~ + . x + 28)820. Thus the value ofkappais:
allocated to classes I to k by the classification procedure
(see Table 8.4). Element i of row i (the ith diagonal                              410x350-28820                         114680
                                                                               =                                   -               - 0.82
element) contains the number of pixels identified by the                               168 100 - 28 820                  139 280
Table 8.4 Conlusion or error matrix lor six classcs. The row labels (Rel.)are those given by an operalor usins pound reference
data. The column labels (Class.)are those generated by the classification procedure. See text for explanation. The lour r~ght-hand
columns are as lollows: (i) number of pixels in class from ground reference data; (ii) estimated classificarion accuracy (per cent);(iii)
class i pixels in relerence data but not given label by classifier; and (iv) pixels given label i by classifier but not class i in rererence
data. The sum of the diagonal elements of the confusion matrix is 350, and the overall accuracy is therefore
(350/410) x 100 = 85.4%.



Col. sums                   71         72          76          67         81                43               410                      60
                                                                                                                           8.10 CIassiJicationaccuracy         207

,en correctly               A value of zero indicates no agreement, while a value of
                                                                                                                  A    A     A    A    F    A    A
nts of row i                1.0 shows perfect agreement between the classifier out-
Is that have                put and the reference data. Montserud and Leamans                                     A    A     A    F    F    U    U
;iccuracy for               (1992) suggest that a value of kappa of 0.75 or greater
:ell i divided              shows a 'very good to excellent' classifier performance,                              A    A     A    F    A    A    A
;he operator                while a value of less than 0.4 is 'poor'. However, these                              A    A     A    A    A    A    A
  The overall               guidelines are only valid when the assumptio'n that the
                                                                                                                             F    A    U    U     A
 e individual           I data are randomly sampled from a multinomial dis-
 :d in percen-          i   tribution, with a large sample size, is met.              ,
                                                                                                                            A    A     U
                                  Values of kappa are often cited when classifications
.. the kappa             : are compared. If these classifications refer to different
on provided              ;  procedures (such as maximum l~kelihood                and artificial
: 5 ) . Kappa is         j neural networks) applied to the same data set, then
                            comparisons or kappa values are acceptable, though the
                          : percentage accuracy (overall and for each class) pro-
                         ! vides as much, if not more, information. If the two
                         j classifications have different numbers of categories then                              A    A     A    A    A    A     A
                         4 it is not clear whether a straightforward logical com-                                 A    A     A    A    A    A     A
                       4     parison is valid. It is hard to see what additional infor-
                             mation is provided by kappa over and above that given                                A    A     A    A    A    A     A
                             by a straightrorward calculation of percentage accu-
                             racy. See Congalton (1991). Kalkhan e t a / . (1997). Steh-                          A    A     A    A    A    A    A
 ~sion  matrix.
 ectively. the               man (1997) and Zhuang er a/. (1995).                                                 A    A     A    A    A    A     A
 l e confusion                    The confusion matrix procedure stands or falls by the
                             availability of a test sample of pixels for each of the k                            A    A     A    A    A    A    A
 ie confusion
 latrix shown                classes. The use of training-class pixels for this purpose
 ;ided (i) and               is dubious and is not recommended - one cannot logi-
  e sum of the               cally train and test a procedure using the same data set.
                                                                                                   Figure 8.20 Cover type categories derived from (a) ground
 = 6). and the               A separate set of test pixels should be used for the
                                                                                                   reference data and (b) auromatic image classifier.The choice of
 nn marginal                 calculation of classification accuracy. Users of the                  sample locations (solid or dashed lines in (a))will influence the
  2 or kappa is:              method should be cautious in interpreting the results if             outcome of accuracy assessment measures.
                              the ground data from which the test pixels were identifi-
                              ed were not collected on the same date as the remotely-
                              sensed image, for crops can be harvested or forests                  values could be summarised by a conventional prob-
                              cleared. Other problems may arise as a result of differen-           ability distribution, for example the hypergeometric dis-
  >undreference               ces in scale between test and training data and the image            tribution, which describes a situation in which there are
  , u r right-hand            pixels being classified. So far as is possible, the test pixel       two outcomes to an experiment, labelled P (successful)
    (per cent);(iii)           labels should adequately represent reality.                         and Q (failure), and where samples are drawn from a
  s i in reference                 The literal interpretation of accuracy measures de-             population of finite size. If the population being sam-
      is therefore             rived from a confusion matrix can lead to error. Would              pled is large the binomial distribution (which is easier to
                               the same level of accuracy have been achieved if a                  calculate) can be used in place of the hypergeometric
                               different test sample of pixels had been used? Figure 8.20          distribution. These statistical distributions allow the
                               shows an extract from a hypothetical classified image               evaluation of confidence limits, which can be inter-
                                and the corresponding ground reference data. If the                preted as follows: If a very large number of samples of
                                section outlined in the solid line in Figure 8.20(a) had           size N are taken and if the true proportion P of success-
                                been selected as test data the user would infer that the           ful outcomes is P, then 95% of all the sample values will
                                classification accuracy was loo%, whereas if the area              lie between P, and P, (the lower and upper 95% confi-
                                outlined by the dashed line had been selected then the             dence limits around P,). The values of the upper and
                                accuracy would appear to be 75%. For a given spectral              lower confidence limits depend on (i) the level of prob-
                                class there are a very large number of possible configur-          ability employed and (ii) the sample size N. The confi-
                                ations of test data and each might give a different accu-          dence limits get wider as the probability level increases
                                 racy statistic. It is likely that the distribution of accuracy    towards 100% so that we can always say that the 100%
208     Classification

confidence limits range from minus infinity to plus infin-      of erroneous labels besides allowing the calculation o     f          of cc
ity. Confidence limits also get wider as the sample size N      classification accuracy. Errors of omission are commit-               inter
becomes smaller, which is self-evident.                         ted when patterns that are really class i become labelled             pixel
   Jensen (1986, p. 228) provides a formula for the calcu-      as members of some other class, whereas errors of com-                espel
lation of the lower confidence limit associated with a          mission occur when pixels that are really members o         f         map
classification accuracy value obtained from a training          some other class become labelled as members of class i.                bet^
sample of N pixels. The formula used to determine the           Table 8.4 shows how these error rates are calculated.                 grad
required r% lower confidence limits given the values of          From these error rates the user may be able to identify              data
P, Q and N is:                                                   the main sources of classification accuracy and alter his            nece
                                                                 or her strategy appropriately. Congalton et al. (1983),              scrir
                                                                Congalton (1991) and Story and Congalton (1986) give                  clas5
                                                                 more advanced reviews of this topic. .
                                                                    How to calculate the accuracy oTa fuzzy classification
                                                                 might appear to be a difficult topic; refer to Gopal and
where z is the (100 - r)/100th point of the standard             Woodcock (1994) and Foody and Arora (1996). Bur-                     Con
normal distribution. Thus, if r equals 95% then the              rough and Frank (1996) ~ o n s i d e rthe more general               shot
z value required will be that having a probability of            problem of fuzzy geographical boundaries. The Clues-                 edit1
(100 - 95)/100 or 0.05 under the standard normal                 tion of estimating area from classified remotely-sensed              autl
curve. The tabled z value for this point is z = 1.645. I f r     images is discussed by Canters (1997) with reference to              clas
were 99% then z would be 2.05. T o illustrate the pro-           fuzzy methods. Dymond (1992) provides a formula to                   bee1
cedure assume that, of480 test pixels, 381 werecorrectly         calculate the root-mean-square error of this area                    om1
classified, giving an apparent classification accuracy (P)       mate for 'hard' classifications (see also Lawrence and               fuz/
of 79.375%. Q is therefore (100 - 79.375) = 20.625%.             Ripple, 1996). Cza~lewski     (1992) discusses the effect of         feat
If the lower 95% confidence limit was required then z            misclassification on areal estimates derived from re-                OCCl
would equal 1.645 and                                            motely-sensed data, and Fitzgerald and Lees (1994)                   ly sc

                                                                 examine classification accuracy of multisource remote                follc
                                                                 sensing data.                                                        hav
                                   79.375 x 20.625                   The use of single summary statistics to describe the             of c
      s = 79.375 - [1.645/-                          +                                                                                ord
                                                                 degree of association between the spatial distribution o    f
                                                                 class labels generated by a classification algorithm and             In t
        =   79.375 - C1.645 x 1.847 + 0.1041                      the corresponding distribution of the true (but un-                 be
        =   76.223%                                               known) ground cover types is rather simplistic. First,              tail
                                                                  these statistics tell us nothing about the spatial pattern           Pro
This result indicates that, in the long run, 95% of train-       of agreement or disagreement. An accuracy level of               ,   eas
ing samples with observed accuracies of 79.375% will              50% for a particular class would be achieved if all the         .    twa
have true accuracies of 76.223% or greater. As men-               test pixels in the upper half of the image were correctly            net
tioned earlier, the size of the training sample influences        classified and all those in the lower half of the image              Pro
the confidence level. If the training sample in the above         were incorrectly classified, assuming an equal number                acq
example had been composed of 80 rather than 480                   of test pixels in both halves of the image. The same                 agc
pixels then the lower 95% confidence level would be               degree of accuracy would be computed if the pixels in                me

      s = 79.375   -   [I645  -/   79.375 x 20.625
                                                     +   g]
                                                               . agreement (and disagreement) were randomly distrib-
                                                                  uted over the image area. Secondly, statements of 'over-
                                                                -all accuracy' levels can hide a multitude of sins. For
                                                                                                                                  j      1
                                                                  example, a small number of generalised classes will             )    an!
                                                                  usually be identified more accurately than would a lar-         !    Ea
        = 71.308%                                                 ger number of more specific classes, especially i f one o   f
                                                                  the general classes is 'water'. Thirdly, a number of re-
This procedure can also be applied to individual classes          searchers appear to use the same pixels to train and to
in the same way as described above with the exception             test a supervised classification. This practice is illogical    I    agl
that P is the number of pixels correctly assigned to class        and cannot provide much information other than a                1    im;
j from a test sample of N j pixels.                               measure of the 'purity' of the training classes. More           F    len
   The confusion matrix can be used to assess the nature          thought should perhaps be given to the use of measures
                                                                                                                          8.12 Questions 209

 lation of           of confidence in pixel labelling. It is more useful and           becoming available. The early years of the new millen-
 commit-             interesting to state that the analyst assigns label x to a        nium will see a very considerable increase in the volumes
: labelled           pixel, with the probability of correct labelling being y,         of Earth observation data being collected from space
s of com-            especially if this information can be presented in quasi-         platrorms,and much greatercomputerpower(with intel-
 rnbers of           map form. A possible measure might be the relationship            ligent software) will be needed if the maximum value is to
of class i.          between the first and second highest membership                   be obtained from these data. An integrated approach to
~lculated.           grades output by a fuzzy classifier. The use of ground            geographical data analysis is now being adopted, and
. identify
 )                   data to test the output from a classifier is, of course,          this is having a significant effect on the way image
I alter his          necessary. It is not always sufficient, however, as a de-         classification is performed. The use of non-remotely-
11. ( 19831,          scription or summary of the value or validity of the             sensed data in the image classification process is provid-
 986) give            classification output.                                           ing the possibility of greater accuracy, while - in turn -
                                                                                       the greater reliability ofimage-based products is improv-
                 1   8.11 SUMMARY
                                                                                       ing the capabilities of environmental GIS, particularly
;opal and
196). Bur-
s general
                 1   Compared to other chapters of this book, this chapter
                     shows the greatest increase in size relative to the 1987
                                                                                       with respect to studies of temporal change.
                                                                                          All or these factors will present challenges to the
                                                                                       remote sensing and GIS communities, and the focus of
The ques-            edition. T o some extent this is a reflection of the              research will move away from specialised algorithm
:I?-sensed           author's own interests. However. the developments in              development to the search for methods that satisfy user
I'erence to          classification methodology over the past 10 years have            needs and are broader in scope than the statistically
)rmula to            been considerable, and the problem has been what to               based methods of the 1980s, which are still widely used
 area estl-          omit. The introduction of artificial neural net classifiers,      in commercial GIS and image processing packages. If
rence and            fuzzy methods. new techniques for computing texture               progress is to be made then high-quality interdisciplin-
e effect of          features, and new models of spatial context have all              ary work is needed, involving mathematicians, statisti-
  from re-           occurred during the past decade. This chapter has hard-           cians, computer scientists and engineers as well as Earth
:es (1994)           ly scratched the surface, and readers are encouraged to           scientists and geographers. The future has never looked
ce remote        4    follow up the references provided at various points. I            brighter Tor researchers in this fascinating and challeng-
                      have deliberately avoided providing potted summaries             ing area.
.scribe the            f
                      o each paper or book to which reference is made in
ibution of            order to encourage readers to spend some of their time
                                                                                       8.12 QUESTIONS
 rithm and            in the library. However, 'learning by doing' is always to
   (but un-           be encouraged. The C D supplied with this book con-              1. Explain the following terms: labelling, classification,
stic. First,          tains some programs for image classification. These                 clustering, unsupervised, supervised, pattern, feature,
ial pattern            programs are intended to provide the reader with an                pattern recognition, Euclidean space, per-pixel, per-
.y level of            easy way into image classification. More elaborate sof-            field, texture, context, divergence, decision rule,
d i f all the          tware is required if methods such as artificial neural             spatial autocorrelation, prior probability, neuron,
c correctly            networks. evidential reasoning and fuzzy classification            reed-forward, multi-layer perceptron, steepest de-
 the image             procedures are to be used. It is important, however, to            scent, geostatistics, variogram, image segmentation,
al number              acquire familiarity with the established methods of im-            GLCM, fractal dimension, kappa.
 The same              ageclassification before becoming involved in advanced          2. What is meant by the term 'feature space'? How can
ie pixels in            methods and applications.                                         you measure similarities between points (represen-
~ly  distrib-              Despite the efforts of geographers following in the            ting objects to be classified) in a feature space of n
~ t of 'over-
    s                   footsteps of Alexander von Humboldt over the past 150             dimensions, where n > 3?
r sins. For             years, we are still a long way from being able to state with   3. Compare the operation of the k-means and also
:lasses will            any acceptable degree of accuracy the proportion of the           ISODATA unsupervised classifiers. Use the pro-
 ould a lar-            Earth's land surface that is occupied by different cover          grams k-means and isodata (described in Appen-
~ l y one of
    if                  types. At a regional scale, there is a continuing need to         dix B) to carry out two unsupervised classifications
nber of re-             observe deforestation and other types of land cover               of one of the test images on the CD. Summarise your
rain and to             change, and to monitor the extent and productivity of             experiences in note form.
: is illogical          agricultural crops. More reliable, automatic, methods of       4. The parallelepiped, supervised k-means and maxi-
her than a               image classification are needed if answers to these prob-        mum likelihood classifiers are described as paramet-
 sses. More              lems are to be provided in an efficient manner. New              ric. Explain. These three classifiers use, respectively,
)f measures                                                                               the extreme pixel values in each band, the mean pixel