10CUEE CONFERENCE PROCEEDINGS
10th International Conference on Urban Earthquake Engineering
March 1-2, 2013, Tokyo Institute of Technology, Tokyo, Japan

ESTIMATION OF URBAN GROWTH USING TIME-SERIESLANDSAT SATELLITE IMAGES IN LIMA, PERU

Hiroyuki Miura1), Saburoh Midorikawa2), and Masashi Matsuoka3)
1) Associate Professor, Department of Architecture, Hiroshima University, Japan
2) Professor, Department of Built Environment, Tokyo Institute of Technology, Japan
3) Associate Professor, Department of Built Environment, Tokyo Institute of Technology, Japanhmiura@hiroshima-u.ac.jp, smidorik@enveng.titech.ac.jp, matsuoka.m.ab@m.titech.ac.jp

Abstract: In order to develop building inventory data for building damage assessment in Lima, Peru, distribution ofurban growth is estimated by time-series analysis of satellite Landsat images. Spectral indices calculated from theimages are used to evaluate changed areas from vegetated and bare ground areas to built-up areas. Threshold analysis isperformed to difference of the indices between the multi-temporal images to identify the spatial distribution of the
expansion of the built-up areas. The result shows that the older built-up areas are widely distributed in the central part ofLima and the newer built-up areas are expanded to the northern, southern and eastern suburban areas.

1. INTRODUCTION
Due to the rapid urban growth in developing countries,
built-up areas have been dramatically expanded to suburban
areas with poor ground conditions such as steep slope areas.
In order to discuss seismic vulnerability of such urban areas,
it is important to identify spatial distribution and its temporalchange of the built-up areas. The identification of the ageof the built-up areas could be also useful to estimate
construction age of the buildings and to evaluate seismic
performance of the buildings.
In developing countries, however, detailed building
inventory data that includes construction age information has
been rarely developed. Remote sensing technology would
be powerful tool to easily identify spatial distribution of thebuilt-up areas. Peru is one of the developing countries
located in a zone of high seismicity. Since Lima, thecapital of Peru, is prone to be struck by a large earthquake innear future, disaster preparedness such as building damage
assessment should be enhanced in the urban areas. In thisstudy, to develop building inventory data for the damage
assessment in Lima, spatial growth of the urbanized areas isevaluated by time-series analysis of satellite Landsat images.
2. DATA USED
Figure 1 shows the land use map in Lima with 1/25,000
scale developed in 2004. Orange and green blocks indicate
built-up and vegetated areas, respectively. The land use
map is digitized and geo-referenced in the geographicalinformation system. Each pixel of the map image isclassified into three categories; built-up area, vegetated area

and other area (bare grounds and roads). Figure 2 shows
the distribution of the land use with the resolution of 30 m.
Pink, green and gray pixels indicate built-up, vegetated andother areas, respectively. The built-up areas in Fig. 2
represent the current distribution of the urbanized areas.
In this study, the time-series satellite Landsat-TM(Thematic Mapper) images are used for the estimation ofurban growth because large number of images has been
stored since 1970s. After searching the database of theLandsat images (USGS 2012), we found an oldest cloud free
image in Lima observed in 1987. In order to capture theexpansion of the built-up areas after decades, we also
searched another images observed about ten and twenty
years after the oldest image and found cloud free images
observed in 1998 and 2006. These three Landsat images
are used in this study. Figure 3 and Table 1 show thecharacteristics of the images. As shown in Fig. 3, thewestern coastal area in Lima is covered with cloud in the2006 image. The Landsat image observed in 2002 is
supplementary used in the cloud cover area.
The
Landsat-TM data consists of seven band images that covervisible, near infrared, mid infrared and thermal spectral
range. The spatial resolution of the images is 30 m.
From the comparison between the time-series Landsat
images in Fig. 3, many vegetated areas and bare groundareas in the older images are changed to built-up areas in the
newer images. In this study, the age of the built-up areas
are estimated by identifying the changed areas from thevegetated and bare ground areas to the built-up areas in theLandsat images.

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10km■：Built-up■：Vegetation■：Others (Road,
Bare ground and etc. )10km

Fig. 1 Landuse map in Lima (2004)

Fig. 2 Digitized landuse image

10km

10km
1998/5/6

1987/3/5

10km

10km
2002/01/17

2006/5/12

Fig. 3 Landsat images observed in 1987, 1998, 2002 and 2006 (False color composite)- 180 -

Table 1 Characteristics of Landsat images used in this study
Satellite

SensorDate

Num. of Bands

Resolution

Landsat-5

Thematic Mapper (TM)1987/3/5

7 bands

30 m

Landsat-5

Thematic Mapper (TM)1998/5/6

7 bands

30 m

Landsat-5

Thematic Mapper (TM)2002/1/17

7 bands

30 m

Landsat-5

Thematic Mapper (TM)2006/5/12

7 bands

30 m

indicating that NDVI is useful to evaluate vegetated areas in
the image.
3.2 Evaluation of Bare Ground Areas

NDSI (normalized difference soil index) has been used
as one of the spectral indices to evaluate bare ground areasfrom satellite images (Takeuchi and Yasuoka 2005). NDSI
is also calculated from the combination of the multi-band
images by the following equation.

3. SPECTRAL INDEX CALCULATION
3.1 Evaluation of Vegetated Areas
Spectral indices calculated from combination ofmulti-band images have been widely used to evaluate
vegetated and bare ground areas in remote sensing
technology.
NDVI (normalized difference vegetationindex), one of the powerful indices to evaluate vegetatedareas in satellite images, is calculated from the following
equation.
NDVI =

B 4 − B3
B 4 + B3(−1 ≤ NDVI ≤ 1)

(1)

NDSI =

B5 − B 4

NBI =Bn − AveBn
SDBn

(4)

× 50 + 100 ( n = 3, 4, 5, 6)

1998/5/6

Vegetated area

NDVI■：0.14■：0.10-0.14■：0.07-0.10■：0.05-0.07■：0.00-0.05■：-0.04-0.00■：-0.07--0.04■：-0.10- -0.07
■：
-0.10

2002/01/17

(3)

B4

NBI (new built-up index) proposed by Chen et al.
(2010) is based on the characteristics that DNs of band 3 inbare ground areas are generally larger than those in built-up
areas.
Higher NBI values would indicate greater
possibility of bare ground areas in the image. NUI(normalized urban index) proposed by Saito et al. (2002) iscalculated based on the characteristics that DNs in built-up
and bare ground area are higher in band 3 and 6 (thermal)

10km

10km

B3 × B5

NUI = B 3 + B 6 − B 4 − B 5

Bn =1987/3/5(2)Here, B5 indicates the DN of the band 5 (mid infrared)
image. Higher NDSI values would indicate greater
possibility of bare ground in the image. Chen et al. (2010),
however, pointed out that it is sometimes difficult todiscriminate bare ground areas from built-up areas from only
NDSI image because their spectral characteristics are similar
each other in the near and mid infrared band images. In
this study, other spectral indices are also calculated toevaluate bare ground areas.

Here, B3 and B4 indicate the digital number (DN) of
the band 3 (red) and band 4 (near infrared) images,
respectively. Higher NDVI values represent greater densityof greenness. Figure 4 shows the distribution of NDVI
calculated from the images. Figure 5 illustrates theclose-up of the 2004 land use map and the 2006 NDVI
image. As shown by arrows in the figure, the green areasin the land use map show high NDVI in the image,

10km(−1 ≤ NDSI ≤ 1)

B5 + B 4

Vegetated area

500m
Cloud area

NDVI■：0.14■：0.10-0.14■：0.07-0.10■：0.05-0.07■：0.00-0.05■：-0.04-0.00■：-0.07--0.04■：-0.10- -0.07
■：
-0.10

Fig. 5 Comparison of 2004 landuse map and2006 NDVI image

2006/5/12

Fig. 4 NDVI images in 1987, 1998, 2002 and 2006

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Landuse

Bare ground

NDSI
Bare ground

NDSI■：0.35■：0.30-0.35■：0.275-0.30■：0.25-0.275■：0.20-0.25■：0.15-0.20■：0.10-0.15■：0.05-0.10
■：
-0.05

NBI

10km

NUI
Bare ground

10km

Bare ground1987/3/5

NBI■：130■：110-130■：100-110■：90-100■：80-90■：70-80■：60-70■：50-60■： -50NUI■：180■：170-180■：160-170■：150-160■：140-150■：130-140■：120-130■：110-120
■：
-110

NUI
■：180■：170-180■：160-170■：150-160■：140-150■：130-140■：120-130■：110-120■：-110

Fig. 6 Comparison of 2004 landuse map, NDSI, NBI
and NUI images in 2006
10km

than in band 4 and 5. NUI values in built-up and bareground areas would be higher than in vegetated areas.
Figure 6 shows the distribution of the indicescalculated from the 2006 Landsat image with thecomparison of the 2004 land use map. Arrows in the
figures indicate bare ground and mountain areas. The
distribution of NDSI shows that NDSI in the bare groundareas is generally lower than that in the built- up areas.
However, the boundary between the bare ground and thebuilt-up areas could not be clearly identified in the NDSI
image because many low NDSI pixels are distributed in thebuilt-up areas. Also in the NBI image, it is difficult to
identify the boundary between the bare ground and built-up
areas because low NBI pixels are distributed not only in thebare ground areas but also in the built-up areas. On thecontrary, in the NUI image, it is much easier to identify theboundary because NUI in the bare ground areas is muchhigher than that in the built-up areas. This may be becausethat the surface temperature in the bare ground is higher thanthat in the built-up areas and NUI is only the index based on
the thermal band (band 6). In this study, the NUI image isused to evaluate bare ground areas. Figure 7 shows the
distribution of NUI calculated from the Landsat images.
4. BUILT-UP AGE CLASSIFICATION
4.1 Methodology

The NDVI values are high in vegetated areas while
they become lower in built-up areas changed from thevegetated areas. The NUI values are also high in bareground areas while they become lower in newly developed
built-up areas. Therefore, the differences of NDVI andNUI between the multi-temporal images are used to estimate
the growth of the built-up areas.

1998/5/6

2002/01/17

2006/5/12

Fig. 7 NUI images in 1987, 1998, 2002 and 2006
In order to apply the method, validation data such as
high-resolution images observed in the past and the present
is necessary. Aerial photographs observed in 1984 areavailable in Lima. As shown solid line area in Fig. 8, theaerial photos are acquired in newly developed area located at
the northern part of Lima. We assume that the 1984 aerial
photos timely correspond to the 1987 Landsat image. The
aerial photos are black-and-white images and the spatial
resolution is approximately 20 cm.
Recently,
high-resolution satellite images are easily available. The
satellite WorldView-2 (WV2) images observed in 2010 areused for the validation. The coverage of the 2010 WV2images is shown in Fig. 8. We assume that the 2010 WV2images timely correspond to the 2006 Landsat image. The
spatial resolution is 50 cm.
Firstly, the built-up pixels are extracted from the 2004
land use map shown in Fig. 2 and only the built-up pixels areanalyzed in the following procedure. The difference of
NDVI and NUI between the 2006 and 1987 Landsat images
is calculated for each pixel. Larger negative difference of
the indices indicates greater possibility of the area where
vegetation or bare ground is changed to built-up area.
Figure 9 shows the comparison of (a) the 1984 aerial
photos, (b) the 2010 WV2 images and the distribution of thedifference of (c) NDVI and (d) NUI. Purple and red color
pixels in Fig. 9 (c) and (d) represent larger negative values ofthe difference of the indices. As shown in solid line
polygons, training pixels are visually selected as changed
areas. Green and orange line polygons represent thechanged areas from the vegetated and bare ground areas tothe built-up areas, respectively. Purple line polygons- 182 -

represent the built-up areas in all the images, indicating
the old built-up areas. The distribution of NDVI
difference shows that many purple and red color pixels
are concentrated in the green polygons. The distribution
of NUI difference also shows that many purple and red
pixels are concentrated in the orange polygons.
Histograms of the NDVI and NUI difference areillustrated in Fig. 10 (a) and (b) by extracting the training
pixels of the polygons in Fig. 9. Red and blue lines in
the histograms indicate the pixels of the changed areasfrom the vegetated and bare ground areas to the built-up
areas, respectively. Black lines indicate the pixels of theold built-up areas in all the images.
From Fig. 10(a), the difference of NDVI in the oldbuilt-up areas shows almost larger than -0.1 while thedifference of NDVI in the changed areas from thevegetated areas are widely distributed from -0.6 to 0.0.
In this study, the threshold value for the difference of
NDVI is selected at -0.1 to discriminate the changed
areas from the unchanged areas.
From Fig. 10(b), the difference of NUI in the oldbuilt-up areas shows larger than 10 while the differenceof NUI in the changed areas from the bare ground areas
are distributed from -60 to 40. In this study, thethreshold value for the difference of NUI is selected at 10
to discriminate the changed areas from the unchanged
areas.
Table 2 shows the result of the classification
accuracy based on the threshold analysis proposed above.
The table shows the number of pixels in each land use,the percentages of correct classification andmis-classification. From the result of the thresholding
using the difference of NDVI, about 75% of the changed
pixels in the vegetated areas are correctly classified.
Almost 100% of the bare ground and the old built-up
areas are classified. From the result of the thresholding
using the difference of NUI, about 80% of the changed
pixels in the bare ground areas are correctly classified.
Almost 100% of the vegetated and old built-up areas areclassified.

1984 Aerial Photo2010 WV2 images

Cloud area

10km

Fig. 8 Coverage of 1984 aerial photos and2010 WV2 images
1984 Aerial Photo2010 WV2

1984□：Vegetation□：Bare ground□：Built-up

2km
Difference of NDVI
(2006-1987)

Difference of NUI(2006-1987)

Dif_NDVI■： ～-0.2■：-0.2～-0.15■：-0.15～-0.1■：-0.1～-0.06■：-0.06～-0.03■：-0.03～0.00■：0.00～0.03■：0.03～0.06■：0.06～

4.2 Result of Built-up Age Classification

Based on the threshold values examined in theprevious section, the built-up age classification is
performed using the time-series Landsat images. Figure
11 shows the flowchart of the classification. First, thebuilt-up pixels are extracted from the 2004 land use map.
The difference of NDVI and NUI between the 2006 and1998 Landsat images is calculated for the built-up pixels.
The threshold analysis is performed based on the thresholdvalues. The pixels whose difference values are lower than
the thresholds are classified to the newer built-up areas
developed after 1998. The pixels whose difference values
are higher than the thresholds are classified to the older
built-up areas and analyzed in the following steps. The
difference of NDVI and NUI between the 1998 and 1987
Landsat images is calculated for the older built-up pixels.

2010
Built-up
2km
Built-up
Built-up

Dif_NUI■：～-20■：-20～-10■：-10～0■：0～10■：10～20■：20～30■：30～40■：40～50■：50～

Fig. 9 Comparison of (a) 1984 aerial photo, (b) 2010 WV2image, (c) difference of NDVI and (d) difference of NUIThe pixels whose difference values are lower than thethresholds are classified to the newer built-up areas
developed between 1987 and 1998. The pixels whose
difference values are higher than the thresholds are classified
to the older built-up areas developed before 1987. In thecloud-cover areas of the 2006 image, same procedure isapplied to the 2002 image instead of the 2006 image.
Finally, the built-up age classification is estimated by
combining the results.
Figure 12 shows the result of the built-up age
classification. The pink, red and yellow pixels indicate the- 183 -

Threshold1

Landuse from 1984 to 2010
Vegetation to Built-up
Bare ground to Built-up
Built-up to Built-up

0.5

0
-0.6

-0.4

-0.2

Threshold(b)

Normalized Frequency

Normalized Frequency

(a)

0

0.2

Landuse from 1984 to 2010
Vegetation to Built-up
Bare ground to Built-up
Built-up to Built-up

1

0.5

0
-80

-40

Difference of NDVI(NDVI2006-NDVI1987)

0

40

80

120

Difference of NUI(NUI2006-NUI1987)

Fig. 10 Histograms of difference of NDVI and difference of NUI

Table 2 Classification accuracy of threshold by difference of NDVI and NUI
Landuse change
from 1984 to 2010

Num. of
PixelsVegetation to Built-up
Bare ground to Built-up
Built-up to Built-up

Threshold by Difference of NDVI

Threshold by Difference of NUICorrectlyclassified (%)

Misclassified (%)

Total (%)

Correctlyclassified (%)

Misclassified (%)

Total (%)

486,540

75.2

24.8

100.0

30,105

100.0

0.0

100.0

99.3

0.7

100.0

80.5

19.5

149,859

99.5

0.5

100.0

100.0

99.3

0.7

100.0

2004 Land use map

Built-up area

Difference of NDVI
(2006-1998)

Vegetated area

Others (bare ground,road and etc.)

Difference of NUI(2006-1998)

Less than TH

Larger than TH

Less than TH

Larger than TH

Built-up area
after 1998

Difference of NDVI
(1998-1987)

Built-up area
after 1998

Difference of NUI(1998-1987)

Less than TH

Larger than TH

Less than TH

Larger than TH

Built-up areafrom 1987 to 1998

Built-up area
before 1987

Built-up areafrom 1987 to 1998

Built-up area
before 1987

Built-up age classification

Fig. 11 Flowchart of built-up age classification using landuse map, NDVI and NUI images(TH: Threshold value)
built-up areas developed before 1987, between 1987 and1998 and after 1998, respectively. Green and gray pixels
represent vegetated areas and others, respectively. The
result shows that most of the built-up areas in Lima had beendeveloped before 1987. The newer built-up areas are
expanded to the suburban areas in the northern, southern andeastern part of Lima.
Table 3 shows the number of pixels in each built-up

area calculated from Fig. 12. The total area in eachbuilt-up area is also calculated from the mesh size of theLandsat images (30m x 30m). The total built-up area in
Lima is about 1600 km2. About 70% of the total wasdeveloped before 1987. About 20% and 10% of the total
were developed between 1987 and 1998, and after 1998,
respectively.

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■：Built-up area
before 1987■：Built-up area
between 1987-1998■：Built-up area
after 1998■：Vegetation■：Others

10km

Fig. 12 Result of built-up age classification- 185 -

Table 3 Number of pixels and area of each built-up area
2

Num. of Pixels

Area (km )Percent (%)

Built-up before 1987

1,192,567

1,073

68.1

Built-up between 1987-1998

314,830

283

18.0

Built-up after 1998

243,192

219

13.9

Total

1,750,589

1,576

100.0

Age

5. CONCLUDING REMARKS

In order to develop the building inventory data in Lima,
Peru, the distribution of the age of the built- up areas is
estimated using the existing land use map and the time-series
Landsat images. The changed areas from the vegetated andbare ground areas to the built-up areas are evaluated basedon the spectral indices calculated from the images. The
difference values of NDVI and NUI between themulti-temporal images are used to extract the changed areas.
The threshold analysis is performed to estimate the spatial
distribution of the built-up ages. The result shows that theolder built-up areas before 1987 are widely distributed in
Lima and the newer built–up areas are expanded to thesuburban areas.
Acknowledgements:
This study was done as a part of SATREPS project“Enhancement of Earthquake and Tsunami Disaster Mitigation
Technology in Peru” (Principal Investigator: Prof. Fumio Yamazaki,
Chiba University) financially supported by JICA and JST.
References:Chen, J., Manchun, L., Liu, Y., Shen C. (2010) “Extract Residential
Areas Automatically by New Built-Up Index”, Proceedings of
18th International Conference on Geoinformatics, 1-5.
Saito, I, Piao, M. and Ishihara, O. (2002) “Extraction of Land
Covering Changes by Landsat TM Data”, Journal ofArchitecture, Planning and Environmental Engineering, 561,
79-85 (in Japanese).
Takeuchi, W. and Yasuoka, Y. (2005) “Development of Normalized
Vegetation, Soil and Water Indices Derived from Satellite
Remote Sensing Data”, Journal of the Japan Society
Photogrammetry and Remote Sensing, 43(6), 7-19 (in Japanese).
USGS (2012), “Landsat Search and Download”, http://landsat.usgs.
gov/Landsat_Search_and_Download.php.

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