Urban land use classification and modelling using cover-type frequencies

Urban laud use classi~ca~iun and m~delling using cover-type frequencies J. Ronald Eyton Department of Geography, 2H4

University of Alberta, Edmanton, Alberta, Canada T6G

Abstract A ~~~~~~~1~~~ for extracting iand use categories from a classification of heterogeneous urban cover types was developed using conventionaf chrster analysis techniques and dis~r~minaut analysis classification functions. Covertype frequencies for a convolved 15 x 15 window were extracted from densitometric data obtained by scanning a NASA high-altitude colour infrared transpareacy acquired over Champaign-Urbana, Illinois. The initial cover-type frequency classification produced a large number of boundary effects as the convolved window overlapped different areas of land cover patterns. These boundary effects were reduced by relabelling boundary classes that were statistically closest to selected core classes. Homogeneous land use classes such as old, middle-age and new residential areas were identified in the relabelled classification, but considerabIe confusion still existed between non-infrared reflecting agriculture fieIds and the urban central business district_ Cover-type frequencies obtained for the enumeration tracts of the 1986 census for Edmonton, AIberta were used to examine the relationships between Landsat Thematic Mapper data and housing characteristics (age* value, occurrence). High correlations were found for both the average age and average value of dwellings versus relative (percentage) counts of the cover-type frequencies. A strong relationship was also found between the number of single-detached dwellings and the absolute (raw count) cover-type frequencies. A single cover type in all three models accounted for approximately half of the total variation. Meaningful urban classifications have been difficult to achieve using multispectral remotely sensed data because most areas of urban land use are comprised of a number of different land covers. Land cover can be mapped on a per-pixel basis whereas mapping land use requires an examination of the cover-type mixture within a defined neighbourhood or window. Spatially based contextual ciassifiers are common (e.g. Jensen 1979; Gurney 1981; Dutra and Mars~~enhas 1984; Franklin and Peddle 1990; Gong and Howarth 1990; Marceau et aE. 1990). Gong and Howarth (1992) provide a good summary of these and more advanced spatially based contextual classifiers, discussing their shortcomings with regard to the classification of urban land cover and land use. Frequency-based contextual classifiers are less common. Gong and Howarth (1992) have introduced a scheme for the classification of urban land use utilizing image grey-level compression techniques and the neighbourhood analysis of the frequency of occurrence of land cover-types. A similar approach was presented by Wharton (1982a, 1982b), which was also based on a neighbourhood analysis of the frequency of occurrence of spectrally determined land cover classes.

112

U&t~nfand USC~~~~~~~i~~~~off and r~~dc~li~~g wing c~ver-t~~e~~~quencies

Wharton (1982a) deve.foped a two-stage classifier (CONAK) to extract ln~d use categories from high-resolution remotely sensed data. The first stage produced a conventional per-pixet spectra1 classification of Iand COWTtypes. Stage 2 consisted of two steps: 1. A vector of cover-type frequencies was determined for various fixed sized windows (3 x 3, 5 x 5, 7 X 7, etc.) extracted from the land cover classification. 2. The vectors of cover-type frequencies were then clustered using a histogram mode estimating technique. The initial test of this approach to contextual classification was performed on synthetic data (four test cases) and showed that ctassification accuracy was dependent on the size of the window used to generate the vectors of cover-type frequencies. A test of CONAN (Wharton 1982b) using high-resolution (7-5 m) data obtained from the three-band Linear Array Pushbroom Radiometer (LAPRf showed that classification accuracy improved by as much as 20 per cent in discriminating between five heterogeneous urban far& case ctasses compared to a per-pixel spectral classification. Wharton did not undertake a contextual classification of an entire image data set, focusing instead on the improvement in individual pixel classification through the addition of neighbourhood cover-type frequency information to the spectral information for selected supervised training samples, A complete contextual classification would involve the measurement of cover-type frequencies for an entire image and would produce transition classes or boundary effects as the convolution window overlapped adjacent but different patterns of land cover. Wharton was cognizant of the boundary effect, which remains the principal drawback to this unique approach to urban kind use classification. Gong and Howarth (1992) employed a different strategy for impIementing a frequency-based contextual classifier, reducing the raw grey-level vectors through compression and then using a supervised ‘block-training’ strategy to extract specific ;tretls of land use. A minimum distance classifier utilizing the city-block metric (Gonzalez and Wintz 1987) was used to classify the occurrence frequencies for the entire image. Three of their findings relevant to the current paper are: 1, Frequency-based classification can improve land use classification accuracies. Compared to a maximum-likelihood classification of the original data, the frequency-based classifier showed a significant improvement as measured by the change (O-462 to O-616) in Kappa coefficients (Cohen 1960). 2. There is no effective indicator for determining the optimal window size and the optimal number of grey-level vectors. 3. A significant ‘boundary confusion’ probtem exists that is a direct result of the windowing process. No single technique exists for eliminative or reducing this problem. An uncomplicated approach to frequency-based on conventional image classification methods, technique is easy to understand and implement. 1. It offers a different approach to frequency classification from those The proposed method is based on analysis classification functions. 2. It analyses the boundary effect for predetermined fixed-size window.

contextual classification, based is presented in this paper; the This paper has three objectives:

implementing a neighbauthood cover-type used by Wharton, or Gong and Howarth. cluster analysis techniques and discriminant a cover-type frequency classification using a Boundary effects are reduced through the

J. Ronald Eyton

3

application of a combined graphical/statistical procedure that relabels classes. It examines the potential for utilizing cover-type frequencies neighbourhoods that have been defined by boundaries associated spatial observation units of a non-spectral variable (such as enumeration This approach eliminates boundary effects and allows the investigator relationships between patterns of cover types and various dependent such as those recorded in a census.

113

boundary of image with the tracts). to explore variables

Data and initial processing

Two digital image data sets were used in this study, both obtained for urban areas familiar to the author. The first data set was generated from a colour infrared photograph in an attempt to duplicate the spatial resolution of Wharton’s (1982a,b) LAPR test data. A copy of a NASA high-altitude 1: 130000 photographic transparency (Plate 1) obtained over Champaign-Urbana, Illinois (population 100000) in October 1978 was scanned by a Dicomed Film Recorder to produce a set of red (infrared band), green (red band), blue (green band) grey-level values at an equivalent ground resolution of 7.5 m. No corrections for dye deficiencies were made. Unsupervised training was performed by clustering (k-mean) a systematic sample of pixels obtained from the three data sets. Cubic clustering criterion statistics (Sarle 1983) indicated that eight was an optimal number of groups. A discriminant analysis classifier in the form of simple classification functions (Fisher 1936) was used on the scanned data to produce a categorized data set consisting of the eight cover types shown in Plate 2; the labels for the groups, based on an interpretation of the original image (Plate l), are given in Table 1. This data set was used to achieve the goals stated in objectives 1 and 2. A more conventional data set, obtained for the City of Edmonton, Alberta (population 400000) on 9 September 1984 from the Landsat Thematic Mapper (TM), was used to meet the third objective of the study. Six spectral bands (TM 1, 2,3,4,.5 and 7) of image data were classified into 14 unsupervised categories (Table 2) and used in conjunction with the 1986 Census to examine the relationship between the frequency of cover types and characteristics of dwellings (age, value, occurrence). TM data were used partly because of the availability of a high-quality scene in close temporal proximity to a census, and partly to determine the value of using information at a relatively coarse spatial resolution (compared to Wharton’s LAPR data). Table 1. Labels for the land cover classification Class

Colour

White Lime Red Black Blue Green Orange Light blue

(Champaign-Urbana,

Illinois)

Label Rooftops of large complexes Streets, rooftops in new residential areas Very high IR reflectors, golf courses, experimental farm Ploughed fields, shadows associated with mature vegetation Mature vegetation in old residential areas Fields, railway Fields, central business district rooftops and parking lots Fields, some industrial rooftops

114

Urban land use cl~s~ficatio~~and modelling using cover-type frequencies

Table 2. Labels for the land cover cla~i~cation (Edmonton, Alberta) Class

Label -

1

2 3 4 5 6 7 8 9 10 11 12 13 14

Determining

Railway yards, airport runways Very high IR reflectors, golf courses Forest at edge of river valley Ploughed fields Parks. fields Parking lots, major thoroughfares Rooftops, streets in residential areas Water Mature vegetation in ravines Fields Fields Rooftops, streets in industrial areas Grass lawns, burms Mature vegetation in old residential areas

window size

principal problem involved in defining cover-type frequencies is determining the correct convolution window size. Analysis of Wharton’s classification statistics (1982b) showed that windows greater than 15 x 1.5 in size produced no significant increase in classification accuracy for the 7.5 m LAPR data. There appeared to be a window size threshold beyond which no additional useful information could be extracted. Eight samples were obtained from the Champaign-Urbana land cover digital classification for 12 windows ranging in size from 3 X 3 to 25 X 25 in increments of two (3 x 3, 5 x 5, 7 x 7, and so on) while retaining the same centre pixel location. The samples were chosen to extract the cover-type frequencies for one of eight specific urban land use categories (see Table 3). Eight sets of 12 histograms were generated and the relative frequencies of the cover types were compared for the differently sized windows. Almost all of the land use sets of histograms showed a stabilized frequency count of cover types for windows that were at least 15 x 15 in size-the same size threshold observed in Wharton’s (1982b) data. Figure 1 shows the histogram sequence for an old residential training sample as an example. The cover-type frequency distributions for windows 15 x 15 and larger are similar and the 15 x 15 window was adopted as the minimum size for generating a data set of cover-type frequencies from the Champaign-Urbana land cover data set.

The

Table 3. Land use samples (Champaign-Urbana, Illinois) a. h. c. d.

Old residential Middle-aged residential New residential Residential development

e. f. g. h.

Central business district Institutional Commercial Highway interchange

J. Ronald Eyton 100

100

100 r

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3x3

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Figure 1. Histogram

sequence for old residential window, Champaign-Urbana, Illinois. Frequency is given as a percentage and the numbers 1-8 refer to the cover type (see Table 1)

Cover-type frequency classification

A cover-type frequency classification was generated from the eight cover types that were initially determined from the Champaign-Urbana spectral data. A 15 x 15 convolution was used to count the frequency of cover types and create eight new data sets. The first contains the frequencies of cover type 1 for the 15 x 15 window; the second data set the frequencies of cover type 2 for the 15 X 15 window, and so on. An unsupervised training procedure was used to extract cover-type frequencies by clustering a systematic sample (n = 2700) taken from the eight cover-type frequency data sets; the FASTCLUS (k-means) procedure in the Statistical

116

Urban land use cl~ss~icat~or~and ~ode~l~~~ trsing cover-type frequencies

Analysis System (SAS 1985) was employed for the clustering. Classification function coefficients (Fisher 1936) were obtained by subjecting the clustered data to the SAS DISCRIM procedure. Since the IS x 15 window will always produce a constant sum, the pooled variance-covariance matrix will be less than tull rank and cannot be inverted; only seven out of the eight classification function coefficients were defined and used to produce the classified image shown in Plate 3. Core regions of the urban land use types were identified in Plate 3 by inspection. These were found to usually exhibit a substantial area1 shape while boundary regions presented themselves as ‘lines’ or ‘strings’ surrounding the core. The pairwise squared generalized distance matrix produced by the SAS DISCRIM procedure was used to construct Table 4 showing the proximity of the boundary regions to the core regions. The rows of the table contain the generalized squared distances for a particular boundary region to all of the core regions. Each boundary region was assigned to the nearest core region by simply assigning the boundary class pixels to the appropriate core. Plate 4 shows the results of relabelling the boundary pixels (the labels are given in Table 5). Inspection of the relabelled classification showed a significant reduction in boundary effects. The residential classes benefited the most from the relabelling process and appeared the least confused of the eight categories in the new classification. Delineation of the three residential categories (old, middle-aged and new) resulted from the land cover patterns comprising mature vegetation and almost no rooftops or streets for older areas and the converse situation for newer areas; middle-aged areas represented the transition between these two extremes. However. a considerable amount of confusion remained between fields containing stubble or unharvested but n~~n-il~frared-reflecting crops and the asphalt, concrete and rooftops that made up the central husincss district and institutional land use catcgorics. A small amount of confusion also existed between regions of low

Table 4. Generalized

squared distances of boundarv clusters to core clusters for the 15 X 15 window classification (Champaign-Urbana, Illinois) Core clusters 7

x

72 15 26 107 92 67 57 102 32 20” 14“

106 i-1” 32 -tfi 100 X6 SC) 75 17 79 36

Boundary clusters I 2 3 4

s 6 0

10 12 14

17 y Distance

between

each boundary

II

15

16

18

67” 284 268 316 4,-P

YS 18 25” 84 c)x 71 46” 86 21 66 28

129

115 50 57 lRU

‘59 241 101 276

105 S-3 70 51

272 62” 56 279 223 249 206

l9ct 2X8 312 263 24s 154

64 61 III 130 100 52 104 46 107 64

16” 95 52

cluster and the closest core cluster for KW

Noic~: The pairwise squared generalized distance between groups used by SAS (1985) is given by:

WI,

1, = (X, - X.,i cm;,-’

19

13

(Xf - X,J + LA! COV,

J. Rim&

Eyton

if7

Table 5. Labels far combined care and bmmdary classesof the f5 X 15 window c~a~i~ca~on (Champaign-Urbana, litfinois) _~~_ Care class

5 11 13 15 16 18 19

Boundary class 14, 17 2 10 1, 5 3, 9 4, 12 6

Colour

Label

Dark blue Dark green Lime green Y&X=V Medium blue cyan Pink Red

Old residential Institutional and fields Stubble fields Ploughed fiefds ~~iddIe-aged residentiaf New residential Central business district and fields Growing vegetation

reflectance, principally between mature residential areas and ploughed fields; large trees and the accompanying shadows in these older neighbourhoods appears to have been the cause of the misclassification. Much of this intra-urban versus extra-urban confusion might have been eliminated by obtaining an image at a more appropriate date or by acquiring several images for a multitemporal cover-type frequency classification.

Relationships between socioeconomic variables and Landsat ~u~tispectral Scanner System response have been investigated by Forster (1980, 1983) whose initial research (1980) focused on the use of multiple regression models to examine the relationships between the Landsat digital data and the percentage of urban cover types (buildings, concrete, roads, trees, grass, water and soil) at the pixel level for metropolitan Sydney. Later work (Forster 1983) used a similar approach to examine the relationships between Landsat data and a number of urban measurements, including surface cover proportions, housing density, relative average house values and a residential quality index. A number of significant relationships were found between tandsat data at the pixel level and the urban measurements (for example, r ’ = 0.76 for a residential quality index as the dependent variabte). A texture measure (standard deviation of the spectral data within a 5 x 8 pixel block) substantially increased the explained variation for models employing housing density and average house size as the dependent variables. Forsfer considered multiple regression analysis to be the more appropriate method for examining the relationships between remotely sensed data and urban socioeconomic measures, principally because of the absence of a methodology to classify urban land use: ‘Residential areas in large cities are typically heterogeneous and as such are not amenable to classification by cluster or discriminant analysis’ (Forster 1980). Cover-type frequencies describing land cover patterns are amenable to cluster analysis and discriminant analysis, and can also be used in multiple regression models to examine the relationships between urban measures and the heterogeneous patterns of urban cover types. Census tract outlines for the 1986 Edmonton enumeration were registered to the land cover data and cover-type frequencies determined for all r~s~~~F~t~~~ polygons. Census tracts with population counts Less than 100 were excluded from the data set;

118

Urban land use classification and modelling using cover-type frequencies

this removed all commercial-industrial regions from the analysis with the exception of the municipal airport. The two tracts enclosing this complex, although containing a substantial population, were also excluded from the final data set because the extent of runways, terminal buildings, hangars and warehouses produced anomalous cover-type frequencies for a residential area. Of the 145 tracts making up the City of Edmonton, 131 were retained for analysis. The cover-type frequencies for each of these tracts were recorded as both raw and percentage values in two separate data sets. Two subsets (raw and percentage cover-type frequencies) were generated from the 131 tracts by dropping all census tracts with less than 1000 single-detached dwellings (n = 47). These 47 tracts comprising the major residential areas within the City of Edmonton were used in the analysis as more homogeneous residential areas, with the expectation of obtaining better relationships between the housing characteristics (age, value, occurrence) and the cover-type frequencies. All four data sets were used in the SAS multiple regression procedure REG; the results are given in Table 6. The average age of dwelling and the average value of dwelling show strong relationships (89 per cent and 79 per cent of the total variation explained by the regression model) for the percentage count of the subset data. Raw count coefficients (subset data) show only a small reduction in the percentage of explained variation. The large number of single-detached dwellings in the 47 tracts reflects a more homogeneous dwelling type with the absence of high and low-rise apartment complexes; this probably accounts for the relatively high coefficients of determination. The number of single-detached dwellings, however, shows a strong relationship with raw frequency counts for the larger (n = 131) data set. This is expected; a stronger relationship should exist between an absolute count (rather than a relative count) of cover-type frequencies and the census count of the number of single-detached dwellings. The SAS RSQUARE and STEPWISE procedures were used to facilitate an understanding of the multiple regression model producing the largest ? value for each census-dependent variable. The RSQUARE procedure was used to select optima1 subsets of independent variables and a plot of Mallows’ Cp statistic

Table 6. Coeffkients

of determination (r’) for cover-type frequencies variables (Edmonton, Alberta)

versus

Raw count n = 47

Census variable Average age of dwelling Average value of dwelling Number of single-detached

“ Maximum

Percentage count

n = 131

n = 47

n = 131

0.85

0.71

0.89”

0.75

0.77 0.64

0.54 0.78”

0.79” 0.27

0.40 0.39

values

Norm: Average where:

dwellings

1986 census

age of dwelling

d, = number

dz = number d, = number d4 = number

dS = number

of of of of of

= (40,0d,

dwellings dwellings dwellings dwellings dwellings

built built built built built

+ S3.0d2 + 65,5d,

before 1946 1946-1960 1961-1970 1971-1980 1981-1986

+ 75.5d, + 83~5d,)l(d,

+ d2 + d, + d, + d,)

J. Ronald Eyton Table 7. Stepwise regression models (Edmonton,

119

Alberta)

Variable

Partial

Model

entereda

r2

r2

F

>Fb

A. Single-detached dwellings model (n = 131) 1 R7 0.509 2 R14 0.058 3 -R2 0.118 4 R6 0.012 5 -R12 0.015 6 R13 0.030 7 R3 0.021 8 -RlO 0.005

0.509 0.567 0.685 0.697 0.712 0.742 0.763 0.768

133.9 17.1 47.7 5.2 6.3 14.3 11.1 2.4

0*0001 0~0001 0~0001 0.0246 0.0135 0.0002 0.0011 0.1254

B. Average age of dwelling model (n = 47) 1 P13 0.437 2 P6 0.123 3 P3 0.231 4 PI1 0.050 5 -P12 0.031

0.437 0.560 0.791 0.841 0.872

13.9 12.3 47.5 13.2 10.0

0~0001 0.0011 0~0001 0.0008 0.0030

C. Average value of dwelling model (n = 47) 1 P3 0.471 2 -P14 0.098 3 P9 0.076 4 -P2 0.038 5 -Pll 0.016 6 PlO 0.052

0.471 0.569 0.645 0.683 0.699 0.751

40.1 10.0 9.1 5.1 2.1 8.4

0~0001 0.0029 0.0042 0.0290 0.1562 0.0060

Step

Probability

a See Table 2 for cover types (R = raw count, P = percentagecount). Negative sign indicates

inverse

relationship ’ A small significance level would exclude variables that do not contribute model. A significance level of 0.05 would exclude variable R10 from model and variable Pll from the average value of dwelling model

to the predictive power of the the single-detached dwellings

(Mallows 1973; Hocking 1976) against the number of parameters (p) in the model was used to determine a ‘best’ model from the graph where Cp first approaches p. The STEPWISE procedure was used to examine the contribution of each independent variable in the best model; Table 7 shows the results of the analyses. A single independent variable in each of the three models accounted for roughly half of the total variation for the model. With the number of single-detached dwellings as the dependent variable, the most highly (and positively) correlated independent variable was the residential rooftop/street cover type. Average age of dwelling as the dependent variable showed a strong positive relationship with a cover type defined as residential landscaping (grasses and shrubs). The third model, with average value of dwelling as the dependent variable, did not produce an intuitively easy-to-understand relationship. The independent variable accounting for 47.1 per cent of the total variation was a forest cover type. However, when the census tracts were overlaid on the land cover classification, the tracts containing the larger dwelling values were found to be adjacent to the North Saskatchewan River valley, which contains substantial areas of forest cover (up to 26 per cent).

1211

Urbm Imtd me ~Lass~fic~tio~~ and ~n~de~li~gusing cover-t?;pefrequencies

Proximity to the river valley in terms of both view and access to parks and recreation appears to account, in part, for the higher housing prices. Although these three models have fewer independent variables (k = 8, k = 5, k = 6) than the complete cover-type frequencies model (k = 13), the 2 values still remained relatively high (0.76. 0.87, 0.75). The value of these models is in the understanding provided by the relationships of cover types to the various socioeconomic variables. The high 2 value obtained for the average age of dwelling multiple regression model also corroborates the identification of old. middle-aged and new residential lnnd use categories in the Champaign-Urbana cover-type frequency classification. Conclusions Cover-type frequencies were partially successfuf constructs used in the classification of heterogeneous urban land covers for the Champaign-Urbana, Illinois scanned image data. Specific conclusions include: 1. Window size reached a limit beyond which no useful information was gained. This is likely to be related to the resolution of the image for North American urban centres. 2. Boundary effects in the classification were substantially reduced by relabelling the classes that were statistically closest to the core classes. A more robust method for identifying core classes is needed. 3. Cover-type frequencies did produce interpretable land use classes such as old, middle-aged and new residential categories. However, considerable confusion was present between areas that exhibited more homogeneous patterns of cover types, such as the misclassification between harvested fields and the urban central business district. Relationships between urban housing characteristics (age, value, occurrence) and cover-type frequencies determined from TM data bounded by the enumeration tracts of the 1986 census for Edmonton, Alberta were significant. This approach to modelling eliminated boundary effects, producing strong coefficients of determination for average age of dwelling (r2 = O-89) and average value of dwelling (r2 = O-79) using relative (percentage) counts of the cover-type frequencies for a subset (number of single-detached dwellings >lOOO) of the census tracts (n = 47). A strong relationship (r2 = O-78) also existed between the number of single-detached dwellings and the absolute (raw count} cover-type frequencies for all of the residential census tracts (n = 131). In all three models a single cover type explained approximately half of the total variation. Higher-resolution data sets, such as those obtained from the SPOT sensors, may improve these relationships. Acknowledgements I appreciate image data Engineering

the efforts of D. Hemenway, who assisted with the classification of the sets. This research was funded in part by the Natural Sciences and Research Council of Canada.

References Cohen, J. (1960) A coefficient of agreement for nominal scales. Educat~u~ and Ps~~c~~f~~ic~l

Me~s~~r~~e~t, 20(l), 37-46.

J. Ronald Eyton

121

Dutra, L. V. and Mascarenhas, D. A. (1984) Some experiments with spatial feature extraction methods in multispectral classification. Znternational Journal of Remote Sensing, 5(2), 303-313. Fisher, R. A. (1936) The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 1799188. B. C. (1980) Urban residential ground cover using Landsat digital data. Forster, Photogrammetric Engineering and Remote Sensing, 46(4), 547-558. Forster, B. C. (1983) Some urban measurements from Landsat data. Photogrammetric Engineering and Remote Sensing, 49(12), 1693-1707. Franklin, S. E. and Peddle, D. R. (1990) Classification of SPOT HRV imagery and texture features. International Journal of Remote Sensing, 11(3), 551-556. for improving Gong, P. and Howarth, P. J. (1990) Th e use of structural information land-cover classification accuracies at the rural-urban fringe. Photogrammetric Engineering and Remote Sensing, 56(l), 67-73. Gong, P. and Howarth, P. J. (1992) Frequency-based contextual classification and gray-level vector reduction for land-use identification. Photogrammetric Engineering and Remote Sensing, 58(4), 423-437. Gurney, C. M. (1981) The use of contextual information to improve land cover classification of digital remotely sensed data. International Journal of Remote Sensing, 2(4), 379-388. Gonzalez, R. C. and Wintz, P. (1987) Digital image processing, 2nd ed. Reading, MA: Addison-Wesley. Hocking, R. R. (1976) The analysis and selection of variables in linear regression. Biometrics, 32, l-49. Jensen, J. R. (1979) Spectral and textural features to classify elusive land cover at the urban fringe. Professional Geographer, 31(4), 400-409. Mallows, C. L. (1973) Some comments on Cp. Technometrics, 15(4), 661-675. Marceau, D. J., Howarth, P. J., Dubois, J-M. M. and Gratton, D. J. (1990) Evaluation of the grey-level co-occurrence matrix method for land-cover classification using SPOT imagery. IEEE Transactions on Geoscience and Remote Sensing, 28(4), 513-519. Sarle, W. S. (1983) Cubic clustering criterion. Cary, NC: SAS Institute, SAS Technical Report A-108. SAS Institute Inc. (1985) SAS User’s Guide: Statistics, Version 5 Edition. Cary, NC: SAS Institute. Wharton, S. W. (1982a) A contextual classification method for recognizing land use patterns in high resolution remotely sensed data. Pattern Recognition, 15(4), 317-324. Wharton, S. W. (1982b) A context-based land-use classification algorithm for highresolution remotely sensed data. Journal of Applied Photographic Engineering, 8(l), 46-50. (Revised manuscript received 3 December 1992)