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Landscape and Urban Planning 101 (2011) 338–348

Contents lists available at ScienceDirect

Landscape and Urban Planning

journa l homepage: www.e lsev ier .com/ locate / landurbplan

orpho-spatial extraction of urban nuclei in diffusely urbanizedetropolitan areas

téphane Couturiera,∗, Mauricio Ricárdezb, Javier Osornoa, Ricardo López-Martíneza

Laboratorio de Análisis Geo-Espacial (LAGE), Instituto de Geografía, Universidad Nacional Autónoma de México (UNAM), Circuito Exterior,iudad Universitaria, Del. Coyoacán, Apdo Postal 20850, CP 04510 Mexico City, MexicoDepartamento de Geografía Social, Instituto de Geografía, Universidad Nacional Autónoma de México (UNAM), Mexico

r t i c l e i n f o

rticle history:eceived 30 June 2010eceived in revised form 24 February 2011ccepted 25 February 2011vailable online 14 April 2011

eywords:prawlandsatasseled Cap

a b s t r a c t

Remote sensing has permitted estimates of the built-up surface as a regional measure of urban sprawl.However, the accuracy of the estimates and the urban forms associated with this measure are still scarcelydocumented, especially on the periphery of metropolitan areas where urban land use is scattered inthe landscape. An operational framework is presented for the structural description of metropolitanurbanization at regional scale, with a view to enhancing the urban cartography in Mexico. This frameworkis composed of (1) the extraction of the regional urban sprawl pattern, (2) the accuracy estimate perpopulation density zone, and (3) the automated extraction of urban nuclei within this pattern.

The method was applied to the Toluca-Atlacomulco valley, a significant component of the diffuse urban-ization surrounding Mexico City. In the first step, a Landsat TM image is classified using a decision tree

athematical morphologyccuracy

mpervious

based on prior knowledge and a combination of unsupervised and supervised algorithms. In the secondstep, the results of the classification strategy are compared with alternative classification strategies. Inthe third step, compact objects are extracted from the built-up diffuse pattern using operators of mathe-matical morphology. The distribution of sizes and shapes of the extracted urban nuclei is compared withthose appearing in existing fine scale national land use maps, generated via aerial photograph delineation.Among the assets of the method are the relatively objective criteria in the extraction of the urban sprawl

s gen

pattern, the low cost of it

. Introduction

Urban growth has reached a magnitude unprecedented in his-ory, a phenomenon driven mainly by the integration of countriesnd cities into the global economy. In 2005, more than 400 citiesxceeded one million inhabitants and, according to the projectionsf the United Nations Organization, population growth in the next0 years will occur almost exclusively in urban places, and willoncern towns of all sizes (Cohen, 2004). This tendency has alreadyeen observed for at least two decades, and includes the conversion

f rural to urban spaces on the periphery of cities (Murakami, Zain,akeuchi, Tsunekawa, & Yokota, 2005).

The many implications of urban sprawl can include transforma-ion of the urban structure, the relevance of new social paradigms

∗ Corresponding author at: Laboratorio de Análisis Geo-Espacial (LAGE), Institutoe Geografía, UNAM, Circuito Exterior, Ciudad Universitaria, Del. Coyoacán, Apdoostal 20850, CP 04510 Mexico City, Mexico. Tel.: +52 55 5623 0222x45488;ax: +52 55 5616 2145.

E-mail addresses: stephcamelo@mailcity.com, andres@igg.unam.mxS. Couturier), magland3@gmail.com (M. Ricárdez), fjosorno@yahoo.com.mxJ. Osorno), rlm8010@gmail.com (R. López-Martínez).

169-2046/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.landurbplan.2011.02.039

eration, and the description of urban nuclei at a user-defined scale.© 2011 Elsevier B.V. All rights reserved.

(such as the spread of informal labour and the perception of inse-cure landscapes), and new challenges in the relationship betweenhumans and the environment. The classical center–peripheryapproach in urbanism has been questioned and is confronted withalternative concepts of rural–urban territories (Cohen, 2004).

For instance, in the recent urban history of Mexico peripheralurban growth is a significant process, especially in the ‘CentralRegion’ of the country composed of a consortium of 6 cities, includ-ing the Mexico City megalopolis (Aguilar & Ward, 2003). Diffuse– or non concentrated, as classically presented – urbanizationconstitutes a challenge for spatial planning and environmentalsustainability. Among features aiding the interpretation of diffuseurbanization is the establishment of urban satellite centers, or sub-centers, in the metropolitan area of cities. In Mexico, the urbanstructure and its potential polycentricity have been approachedin terms of socio-economic parameters (typically housing andemployment densities) derived from census in urban statistical

spatial units (Suárez & Delgado, 2009). However, the physical urbanstructure would be a useful complement to these official databecause it relates to population density and socio-economic con-ditions to some extent (Huang, Lu, & Sellers, 2007; Taubenboeck,Roth, & Dech, 2008). This complement would be especially useful in

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he outer periphery of the metropolitan area and for places wherehe socio-economic parameters remain poorly documented partlyecause of the importance of the informal economy. Additionally,ome morphological aspects of the urban physical structure suchs the size and spatial distribution of potential sub-centers arenvolved in the debate on polycentricity of cities (Adolphson, 2009).

. Background

In Mexico, information on the physical urban structure isecorded in the INEGI (National Institute of Statistical andeographical Information) medium scale (1:50,000) land useartography: urban nuclei were visually delineated, within therban sprawl pattern, on aerial photographs which were acquiredetween 1996 and 2000 throughout the country. A more preciseecord of urban use (scale 1:10,000) in the vicinity of cities was pro-uced for the 1968–88 period by the DETENAL agency (‘Direccióne Estudios del Territorio Nacional’, the former INEGI institution).nfortunately, none of this cartography reflects urban use in theuter periphery of metropolitan zones. On the other hand, none ofhe more recent national datasets, based on urban geo-statisticalreas, contain information on the extent of the physical urban struc-ure. The objective of the present research is twofold:

to present a new method for an updated cartography of thephysical urban structure, including compact urban nuclei inmetropolitan zones andto discuss the criteria, accuracy and perspectives of this methodwith respect to the previous cartographic methods.

The use of satellite imagery has permitted estimations of theuilt-up surface – sometimes also related to the impervious sur-ace in the remote sensing community – at the regional scale,or an assessment of land use change and urban growth. Landsatmagery has been tested with some success for the extraction ofhe built-up surface (e.g. Kaya & Curran, 2006; Prol-Ledesma, Uribe-lcántara, & Diaz-Molina, 2002; Yuan, Sawaya, Loeffelholz, & Bauer,005). However, the heterogeneous nature of periurban areas hasampered the establishment of a standard automatic processingechnique for the classification of satellite imagery; the diversityf sites and environmental settings requires a range of classifi-ation strategies. However, several studies have favored a hybridpproach combining unsupervised algorithms (e.g. segmentationechniques), supervised algorithms, and the use of ancillary datae.g. Clapham, 2003; Khorram, Gregory, Stallings, & Cakir, 2003).ome studies also recommend the use of the Tasseled Cap (see CristKauth, 1986; Huang, Wykie, Yang, Homer, & Zylstra, 2002) trans-

ormed Landsat image instead of the original image (Seto et al.,002) for the supervised step, because of the better discriminationf urban land use by some of the principal components, and forheir enhanced biophysical interpretation.

Contextual or object-based approaches have also been appliede.g. Guindon, Zhang, & Dillabaugh, 2004; Jacquin, Misakova, & Gay,008), but post-classification manual correction was deemed nec-ssary in periurban areas to ensure the required accuracy after themplementation of these more sophisticated methods. A main con-ern of this research was to retain low-cost, easily repeatable andnterpretable strategies in order to extend the approach to the 56

etropolitan Zones of the National Urban System (‘Sistema Urbanoacional’) defined by CONAPO, the National Demographic Council

n Mexico (CONAPO, 2007).By contrast with the development of numerous classification

trategies, very little information is related to the accuracy of theesults in periurban areas; a global accuracy measurement is typ-cally given (e.g. in Mexico: Prol-Ledesma et al., 2002) for the

n Planning 101 (2011) 338–348 339

urban use class over the entire study area. This information islikely to conceal large variations of accuracy in densely urbanizedversus sparsely urbanized zones. Indeed, the latter zone should bemore prone to classification errors than the former because of theincreased mixture of land uses within pixels containing built-upsurfaces. An exception to this practice is the study of Jacquin et al.(2008) in a watershed near Toulouse, France, where the accuracy isdocumented per population density slice in a region of 507 km2. Thedetailed measurement of classification accuracy in our study willcreate a firm foundation for the subsequent urban object extractionin Mexico.

Urban object extraction from remote sensing imagery is a vastfield of research. Mathematical morphology has been used mainlyat local scale on very high resolution imagery, for road networkextraction (e.g. Mohammadzadeh, Tavakoli, & Valadan Zoej, 2006)or for the identification of building structure (e.g. Banzhaf & Höfer,2008). However, we propose that mathematical morphology couldbe used at regional scale as well, for the extraction of urban nuclei.

A framework is presented for the identification of urban nucleiin the metropolitan zones of the main cities of Mexico. Theframework, composed of three techniques, is applied to the Toluca-Atlacomulco valley (TAV), a pilot area which contains a significantcomponent of the diffuse urbanization west of Mexico City (seeFig. 1). First, a technique is developed for the extraction of the urbansprawl pattern based on a Landsat ETM+ image. A classificationstrategy is built in the form of a decision tree which combines foursteps, including the prior selection of regions according to smallscale land cover cartography, an unsupervised ISODATA cluster-ing algorithm, and finally a supervised Maximum Likelihood (ML)algorithm applied to the Tasseled Cap transformed Landsat image.The second technique is the accuracy assessment of the classifica-tion; the accuracy is measured at two levels of population densityand compared with the accuracy of alternative, simpler classifica-tion strategies. The third technique is derived from mathematicalmorphology; compact objects are extracted from the built-up sur-face pattern, using a compactation operator derived from basicmorphology operators. Finally, the distribution and shape of theextracted urban nuclei are compared with the urban land usereflected in the INEGI 1:50,000 database. The perspectives and lim-itations of the method are discussed.

3. Study area and previous information on urban use

The study area corresponds to the Toluca-Atlacomulco Val-ley (TAV), which extends over 4238 km2, and includes the city ofToluca, administrative capital of the State of Mexico. Toluca is oneof the 6 cities, together with Mexico City, which constitute the ‘Cen-tral region’ of the country. Its contiguity to the Valley of Mexico andits environmental characteristics have favored its sustained popu-lation and urban growth. In the twenty years from 1980 to 2000, thepopulation doubled in size from about 645,000 to 1,233,000 inhabi-tants. Among the 364 cities and towns of the National Urban System(CONAPO, 2007), Toluca (61 km west of Mexico City) is classifiedas rank 3. Its Metropolitan Area is contiguous to the MetropolitanArea of the Valley of Mexico (MAVM), and hence pertains to the‘Megalopolitan’ category. The area hosts one of the most importantindustrial zones in the country, as a result of a national plan ini-tiated in the 1960s. Not until the 1990s, however, did the TolucaValley actually consolidate itself as an industrial valley through thedecentralization policy.

The wetland environment of the Toluca Valley (1582 km2),within the upper watershed of the Lerma river, has served since1942 as a major reservoir supplying water to Mexico City and theMAVM as a whole. However, the above-mentioned industrializa-tion has caused pollution of the wetland environment and of the

340 S. Couturier et al. / Landscape and Urban Planning 101 (2011) 338–348

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ig. 1. Color composite of a 2003 Lansat TM image of parts of the Toluca metropoliartography, the most updated available. (For interpretation of the references to co

erma river, throughout the TAV. The water extraction from the val-ey and the downturn in agriculture activity associated with sparserbanization have also affected the environment in the valley.

The cartographic information currently available for the urbanhysical structure in the TAV is composed of

. high scale (1:10,000) DETENAL topographic maps (referred tolater as the DETENAL cartography), which contain built-up struc-tures in the vicinity of Toluca (DETENAL, 1982),

. medium scale (1:50,000) INEGI topographic maps (referred tolater as the INEGI cartography), which include contours of set-tlements, and

. small scale (1: 250,000) national land cover maps, one of whichis the 2000 National Forest Inventory map (or NFI map), wherethe ‘human settlement’ class represents urban use.

In the DETENAL and INEGI cartography, urban objects wereisually delineated on orthorectified aerial photographs acquiredn year 1982 and 1999 respectively over our study area. Unfortu-ately, the visual delineation was far from exhaustive at regionalcale, since urban objects near to the main agglomerations werehe focus of the cartographic effort. Additionally, the more recentrban national datasets do not include features associated withhe physical urban structure. For example, in year 2003, the geo-

tatistical frame ‘Marco Geo-estadístico Municipal’ (INEGI, 2005)nly refers to administrative statistical units. In this sense, thistudy is expected to characterize the likely biases in the distribu-ion of sizes and shapes of urban objects as described in the INEGIrchive.

ne including the city of Toluca. The red contours refer to the 1999 INEGI urban usethis figure legend, the reader is referred to the web version of the article.)

4. Method

The method comprises three techniques: the decision tree clas-sification strategy, the accuracy assessment of the classification,and finally the extraction of compact objects, from which the anal-ysis of urban nuclei is derived.

4.1. Preprocessing steps and rationale for the classificationapproach

An ETM+ Landsat image was acquired for the year 2003 (Fig. 1),which covered the entire TAV. The image was geo-referenced, withless than 1 pixel RMS interpolation error, to the 1:50,000 INEGItopographic maps using a set of 55 control points and a polynomialinterpolator. Both the original Landsat bands (all except thermaland panchromatic bands) and the three first components of theTasseled Cap transformed (TCT) image were used in the classifica-tion approach. Prior to the Tasseled Cap transformation, the originalimage was radiometrically converted to sensor reflectance valuesusing the standard irradiance calibration parameters.

The first step of the classification approach consisted in reducingthe signal dynamics contained in the image for subsequent classifi-cation algorithms. The study area was split into a densely populatedzone (DPZ) and a sparsely populated zone (SPZ), according to exist-ing small scale cartography (the 1:250,000 NFI map of year 2000),

where DPZ corresponded to the ‘human settlement’ class of themap and SPZ corresponded to the remaining area.

For the large region under study, an unsupervised algorithm (forexample the Iterated Self Organizing or ISODATA algorithm) waslikely to produce a more objective and repeatable general picture,

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n terms of specific land cover and land uses, than an algorithmupervised by an analyst (Clapham, 2003; Khorram et al., 2003);herefore, as a second step, an ISODATA algorithm was launched,eparately over the DPZ area and the SPZ area. 60–80 clusters wereelected for SPZ and 40–60 clusters for DPZ because the latter wasxpected to be more homogeneous in terms of the spectral responsef built-up areas.

The third step consisted in the visual labeling of clusters inerms of their membership to the built-up and non built-up classesClapham, 2003). The GoogleEarth database was used as the basiceference for the visual labeling of clusters. The ambiguous clus-ers, containing many pixels in both built-up and non built-upategories, were set aside for a fourth processing step.

In many cases, ‘ambiguous’ clusters contained pixels of man-ade features and pixels of fallow agricultural fields, since these

and uses are sometimes spectrally similar (Guindon et al., 2004).The fourth step consisted in a Maximum Likelihood (ML) super-

ised classification of the Tasseled Cap Transformed (TCT) Landsatmage. The analyst selected, in training sites extracted from theoogleEarth database, pixels from either land uses within thembiguous clusters. The enhanced thematic content of the Tas-eled Cap dimensions for the land uses of interest, especially inerms of greenness and wetness, was expected to be useful for theiscrimination of the two classes in the case of ambiguous clusters.

Based on preliminary tests, we found that splitting the regionn two population density zones (step 1) efficiently constrainedhe dynamics of the signal; applying the unsupervised ISODATAlgorithm separately on these two zones permitted a significanteduction of the number of ambiguous clusters.

.2. Decision tree classification algorithm

As a synthesis of the above considerations, a decision tree wasuilt (Fig. 2) to cover the following processing steps:

. Stratification of the area into a densely populated zone (DPZ) anda sparsely populated zone (SPZ).

. Application of the ISODATA classifier.

. Visual labeling of pure and ambiguous clusters.

. Application of a Maximum Likelihood (ML) supervised algorithmto the TCT image for ambiguous clusters.

.3. Accuracy assessment of the classification

The accuracy of the classification was measured at two lev-ls of population density (SPZ and DPZ), and compared with theccuracy of alternative, simpler classification strategies (ML super-ised algorithm based on pixels visually selected as training sites,nd ISODATA unsupervised algorithm followed by visual label-ng of clusters). The GoogleEarth database (mainly Quickbird datarom 2005 to 2006 at the time of access of the online database)as the main reference for verification sites; additionally, ground

isits were conducted and associated with parallel research forhe characterization of urban sprawl. Interview information wasollected during ground visits to correct for the case of post-003 urbanization which would induce inconsistent labeling of theoogleEarth-based reference data. In order to significantly reduce

he cost of ground visits, a two-step sampling design was builto select the verification sites (Couturier et al., 2010), consideringoth built-up and non built-up categories, and 8 geographic sectors.he entire region (comprising the 8 geographic sectors) was sliced

nto regular squares, which constituted the primary sampling unitsPSUs) for a first selection. Two hundred verification points werehen selected within the previously sampled PSUs, for built-up andon built-up categories in each of the two population density strataa total of 800 points). These secondary sampling units were located

n Planning 101 (2011) 338–348 341

on the GoogleEarth archive and visually transferred onto the 2003Landsat imagery using conspicuous features of the landscape, with-out knowledge of the classification results. The two-step samplingdesign is fully explained in Couturier et al. (2010). Fig. 3 illustratesthe verification points derived from the sampling of the built-upcategory, in the vicinity of the Toluca agglomeration. Accuracyindices were derived from the inclusion probabilities applied atboth steps (primary and secondary unit selection) of the samplingprocedure, as described in Cochran (1977).

4.4. Mathematical morphology

Compact objects were then extracted from the built-up surfacepattern, using a combination of mathematical morphology oper-ators. The 1:50,000 scale INEGI database generally focussed, forurban use, on objects larger than 150 m × 150 m (a minimum of3 mm on the map), although some objects smaller than this sizewere also delineated in the vicinity of megacities. The MinimumMapping Unit (MMU) was set to 150 m × 150 m for comparisonpurposes, and served as a guide for mathematical morphologyoperations. After a visual appraisal of the distribution of errorsamong small objects, this scale of analysis of compact objects wasconsidered reasonable. A compactation operator C was designed asa sequence of convolutions of the basic mathematical morphologyoperators erosion E and dilation D (Fig. 4A–C and E–G).

First, the operators Opening On and Closing Cn are derived asfollows (illustrated in Fig. 4D and H):

On = En ⊗ Dn (1)

Cn = Dn ⊗ En (2)

where ⊗ is the convolution sign and the exponent n indicates thenumber of iterations of the basic operators. The compactation oper-ator is finally derived as follows (illustrated in Fig. 4I):

C = On ⊗ Cn (3)

In this application, n was set to three (n = 3) and the kernel asso-ciated with the basic operators was a 3 × 3-pixel cross-shapedkernel. In terms of compactness, the procedure with n = 3 ensuredthat urban objects smaller than 150 m × 150 m were removedfrom the urban pattern, while non built-up surfaces smaller than150 m × 150 m within urban objects were transformed into urbanuse.

5. Results

5.1. Classification of the urban sprawl pattern

The urban sprawl pattern in the TAV derived from the deci-sion tree classification of the Landsat image (Fig. 5), was spatiallymore comprehensive than the INEGI cartography, in the first placebecause of urban growth between 1999 and 2003, but also possiblybecause of the non-exhaustive character of the photograph delin-eation that served as a basis for identifying main urban areas. Somefeatures of the oldest parts of Toluca City as described in the detailedDETENAL 1982 cartography (Fig. 6a), especially urban parks, can berecognized on the built-up pattern (Fig. 6b).

Fig. 5 also shows the distribution of verification points assess-ing the accuracy of the classification—two-class (built-up and nonbuilt-up surface) assessment stratified by geographic sector and bypopulation density zone. The overall accuracy of all three meth-

ods (Table 1) is high, reflecting mostly the good performanceof the Landsat classification in terms of spectrally discriminatingnon built-up surfaces in sparsely populated zones (SPZ, the mostextended surface of the classified image). However, a major chal-lenge of the classification (and main goal of this research) was

342 S. Couturier et al. / Landscape and Urban Planning 101 (2011) 338–348

Fig. 2. Flow chart of the decision tree classification algorithm. SPZ and DPZ are respectively sparsely populated zone and densely populated zone.

Table 1Percentage accuracy of the classification results for the built-up and non built-up categories in the Toluca Atlacomulco Valley (TAV), for each population density zone.SPZ = sparsely populated zone; DPZ = densely populated zone. Accuracy figures in parenthesis refer to the assessment of a map with post-classification visual cleaning. Theconfidence interval at 95% probability was estimated for each index and did not exceed 0.5%.

Classification strategy MaximumLikelihood

ISODATA Decision tree

Characteristics: Supervisedclassification

Unsupervisedclassification withvisual labeling ofclusters:

Classificationcombiningunsupervised andsupervisedalgorithms

Overall accuracy, total TAV area 89.4% 92.2% 93.0%Built-up area in the densely populated zone (DPZ) 84.0% 93.2% 92.4%Non built-up area in the sparsely populated zone (SPZ) 91.2% 94.8% 96.3%Built-up area in the SPZ 24.8% (46.8%) 33.2% (57.7%) 56.3% (70.1%)Non-built-up area in the DPZ 65.0% 59.0% 63.4%

S. Couturier et al. / Landscape and Urban Planning 101 (2011) 338–348 343

Fig. 3. Verification points in the vicinity of the Toluca agglomeration (San Mateo urban settlement). The transparent layer over the GoogleEarth online imagery representsthe built-up surface derived from the decision tree classification.

Fig. 4. Processing chain of the compactation morphological operator. Compactation is derived from a convolution of Opening and Closing. In this illustration, Opening andClosing are based on Erosion and Dilation using a 3 × 3-pixel cross shaped kernel; (A and E) urban settlement in the TAV region (black); (B) deleted pixels by erosion in grey;(C) eroded pattern (black); (D) opened pattern (black) obtained after dilation of C; (F) added pixels by dilation in grey; (G) dilated pattern (black); (H) closed pattern (black)obtained after erosion of G; (I) compacted urban settlement, obtained by a Closing of the D pattern.

344 S. Couturier et al. / Landscape and Urban Planning 101 (2011) 338–348

Fig. 5. Regional urban sprawl pattern in the Toluca Atlacomulco Valley (2003), and distribution of the verification sites using a two-step sampling strategy, stratified bygeographical sector and by population density zone.

Fig. 6. Built-up surface of Toluca city (central area) in the 1982 DETENAL cartography (a) and derived from the decision tree classification of the 2003 Landsat image (b). In1982, the main central circuit (in red) is the Paseo Tollocán avenue. In 2003, the built-up surface (black) has covered the entire area except the North-western mountainouszone. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

S. Couturier et al. / Landscape and Urban Planning 101 (2011) 338–348 345

Fig. 7. Distribution of urban compact objects derived by the morpho-spatial method in the periphery of the Toluca Metropolitan Area (2003). Sizes are differentiated bycolor tones. INEGI urban use cartography (1999) appears as blue contours. (For interpretation of the references to color in this figure legend, the reader is referred to the webversion of the article.)

Fig. 8. INEGI 1999 ortho-photograph (left) and Quickbird 2005 imagery (right) close ups in the eastern periphery of Toluca City. The Quickbird imagery is extracted fromthe GoogleEarth online database with an overlay of additional material. The semi-transparent layer with dark contours represents the built-up surface derived by themorpho-spatial method. The brighter (red color) contour indicates INEGI urban use cartography, based on the visual interpretation of the 1999 ortho-photograph.

346 S. Couturier et al. / Landscape and Urban Planning 101 (2011) 338–348

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ig. 9. Area, perimeter and shape index distributions of urban objects in the ToluNEGI urban use cartography. The uneven intervals on the X axis correspond to therom circularity.

he identification of the built-up surface in the SPZ. An accuracygure is indicated in parenthesis for each classifier, which referso accuracy results after visual cleaning was applied; this visualleaning consisted in masking from the classification process vastural areas where no urbanization was visible on the verification

aterial. The results suggest that the method based on a deci-

ion tree, detailed in the method section, improved classificationccuracy (56.3% or 70.1%) with respect to concurrent methods inhe SPZ (24.8–33.2% or 46.8–57.7%). For comparison, 25% accuracy

acomulco Valley (TAV), derived from: (A) the morpho-spatial method and (B) theral breaks of the overall data distribution. The shape index measures the variance

was reported by Jacquin et al. (2008) for the built-up surface in‘spread urbanization’ zones in their object-oriented classification(65% after manual cleaning). Their built-up area was obtained with93% accuracy in the ‘dense urbanization’ zone, and in the presentstudy the built-up area was obtained with 92.4% accuracy in the

DPZ zone. The results of these two studies suggest that the use ofboth automatic algorithms and visual controls within the classifi-cation strategy achieves an acceptable classification accuracy forbuilt-up surfaces in sparsely populated zones.

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.2. Urban compact object extraction

The distribution of compact objects derived from the compacta-ion operator for the Toluca Metropolitan Area (Fig. 7) is similaro the distribution shown in the INEGI cartography, for the largerbjects (>73.5 ha). Two cases of discrepancy were attributed tolassification errors of the morpho-spatial method. Indeed, someparsely vegetated areas as well as sandy and rocky terrain includ-ng quarry sites tended to be confounded with built-up surfacesnd remained difficult to classify with our method. More discrepan-ies occur for objects in the 20.3–73.5 ha category; a visual analysisf the 1999 ortho-photographs reveals heterogeneous delineationriteria for the INEGI photo-interpretation, apparently leaving outome urban settlements even though their physical structure isore compact than that of some other settlements that it did

nclude. One of these cases is illustrated in the eastern periphery ofoluca (Fig. 8). In fact, criteria other than the density of built-up sur-ace influenced the INEGI photo-interpretation and its selection ofrban forms within the urban use cartography, such as the admin-

strative importance of the settlement, connectivity to neighboringenters, etc. Nevertheless, the morpho-spatial method presentedere could provide a more objective way to delineate potentialrban nuclei within the inter-twined, diffuse urban thread of theetropolitan Area.For comparison purposes, a statistical exploration of the data

as performed through the calculation of simple parameters suchs area, perimeter and shape (Fig. 9). The shape index representedhe dissimilarity of the object with respect to a circle and was com-uted as follows: IS = p/2

√a, where p is the perimeter and a is the

rea of the object.A considerably higher number of objects was detected by

he morpho-spatial method than with the INEGI cartography.his result reflected an overall overestimation of objects by theorpho-spatial method in rocky, sparsely vegetated areas, an

nderestimation of objects in the INEGI cartography (bias towardsbjects in the vicinity of the main agglomerations), and the group-ng of small objects into bigger ones in the INEGI cartography (seeig. 7).

The INEGI cartography includes some very small objects (<2 ha),elow the minimum mapping unit assigned to the morpho-spatialethod for this study. However, visual inspection of the 1999

rtho-photographs reveals that a majority of the objects of thisategory were not mapped in the INEGI cartography either, andhis indicates a bias against the representation of very small urbanbjects. Likewise, objects between 2 and 43 ha, according to a visualnspection of the ortho-photographs, were underrepresented inhe INEGI cartography; this may have been one reason why theyere fewer than those recorded by the morpho-spatial method.y contrast, INEGI cartography reports more objects than theorpho-spatially derived cartography in the high-area categories

43–519 ha, excluding the agglomeration of Toluca City). The visualelineation of large objects on the ortho-photographs may haveended to include relatively large non built-up areas within thebjects, while the morpho-spatial method might have left thesereas out of the object (see Fig. 8).

Altogether, the morpho-spatial method detects objects with anrea distribution approaching a decreasing exponential curve, aendency that might be closer to reality than the flatter area distri-ution produced by the INEGI method. One of the reasons for thisnder-representation of objects may be cost optimization in visualhoto-interpretation.

Likewise, the perimeter distribution, in the case of the morpho-patial method, is a sharp decreasing function for the smallerbjects (as far as the 37.3 km perimeter), whereas the distributions a flatter function in the INEGI cartography. In contrast to area, theerimeter of larger objects tends to be larger in the morpho-spatial

n Planning 101 (2011) 338–348 347

cartography than in the INEGI cartography, probably because of thecontribution of the perimeter of non built-up areas within urbanobjects in the morpho-spatial cartography, compared with morecompact objects in the INEGI cartography.

The shapes of INEGI urban objects tended to be more com-plex than those derived by the morpho-spatial method. Thelatter tended to be closer to circular, probably because of thesimplification of shapes incurred by mathematical morphologytransformations. INEGI urban objects may therefore contain moreinformation, more details, than the objects derived from themorpho-spatial method. This uniform simplification of shapes(elimination of details), according to a given mapping scale,however, may reflect more consistency in urban object shapesthroughout the region than the one given by INEGI cartography.Indeed, visual delineation at a consistent scale throughout a vastarea is difficult.

6. Conclusion

This research proposes an operational algorithm for (1) theclassification of an urban sprawl pattern at regional scale and(2) the extraction of compact objects from this pattern in orderto study potential urban nuclei in extended metropolitan zones.The attractive characteristics of the method include (1) its opera-tional use (limited input and low cost, incurred within a reasonableprocessing time), (2) the accuracy of information on the urbansprawl pattern at two levels of population density, according toa probability sampling scheme, and (3) its ability to generate analternative urban use cartography at the national level. The methodwas applied to the Toluca-Atlacomulco Valley (TAV) with promis-ing levels of accuracy, with respect to past studies, such as 92.4%accuracy for the built-up category in the densely populated zone,and 56.3% (and 70.1% after visual cleaning) accuracy in the sparselypopulated zone—the most challenging for mapping urban use. Theadvantages of the morpho-spatial method over the existing pro-duction techniques of urban use cartography in Mexico included amore exhaustive coverage of urban objects at regional scale, a morerealistic distribution of the objects in terms of sizes and perimeters,and the availability of more objective and flexible criteria – such asuser-defined minimum size – for the physical characterization ofurban nuclei.

Classification errors did affect the accuracy of the product, espe-cially in sparsely vegetated, rocky terrains of the altiplano andquarry sites, for which more research should be undertaken. Pos-sible improvements include the prior topographic correction ofthe image (although early explorations showed over-correctioneffects), and a fusion strategy with Radar data.

The method is about to be extended to the National UrbanSystem in Mexico. Change detection algorithms are under devel-opment with SPOT data, the best available national coverageat regional scale, in order to update the cartography. Some ofthe perspectives of this work are new horizons for defining andcharacterizing urban structure. Future research could explorerelationships of the urban sprawl/urban nuclei patterns withsocio-economic statistical information, the traditional input forcharacterizing urban structure.

Acknowledgments

This research has been conducted under PAPIIT project num-bers IN113609 and IN307410, funded by DGAPA-UNAM. Thanks

are due to the INEGI institution for providing the DETENAL and1:50,000 scale cartography. We also would like to thank the Cen-troGeo Institute where some of the late stage of this research hasbeen conducted, and the LAGE colleagues in charge of the precisegeo-referencing of the Landsat imagery to the INEGI maps.

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