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Remote Sensing of Environm

Normalized spectral mixture analysis for monitoring urban

composition using ETM+ imagery

Changshan Wu*

University of Wisconsin-Milwaukee, United States

Received 30 March 2004; received in revised form 1 August 2004; accepted 5 August 2004

Abstract

With rapid urban growth in recent years, understanding urban biophysical composition and dynamics becomes an important research

topic. Remote sensing technologies introduce a potentially scientific basis for examining urban composition and monitoring its changes over

time. The vegetation–impervious surface–soil (V–I–S) model, in particular, provides a foundation for describing urban/suburban

environments and a basis for further urban analyses including urban growth modeling, environmental impact analysis, and socioeconomic

factor estimation. This paper develops a normalized spectral mixture analysis (NSMA) method to examine urban composition in Columbus

Ohio using Landsat ETM+ data. In particular, a brightness normalization method is applied to reduce brightness variation. Through this

normalization, brightness variability within each V–I–S component is reduced or eliminated, thus allowing a single endmember representing

each component. Further, with the normalized image, three endmembers, vegetation, impervious surface, and soil, are chosen to model

heterogeneous urban composition using a constrained spectral mixture analysis (SMA) model. The accuracy of impervious surface estimation

is assessed and compared with two other existing models. Results indicate that the proposed model is a better alternative to existing models,

with a root mean square error (RMSE) of 10.1% for impervious surface estimation in the study area.

D 2004 Elsevier Inc. All rights reserved.

Keywords: Vegetation–impervious surface–soil model; Urban; ETM+ data

1. Introduction

Urban areas continue to expand rapidly due to

population growth and rural-to-urban migration (United

Nations, 1997). In the United States, for example, 10

million hectares of nonfederal rural lands have been

converted to urban land use from 1982 to 1997 due to

urban population increase and sprawl (U.S. Department of

Agriculture, 2000). This accelerated urban growth leads to

environmental deterioration and quality of life degradation.

Unchecked urban development, sprawl, and brownfields

have resulted in nonpoint environmental pollution. More-

over, the increasing automobile traffic due to population

growth and urban sprawl has deteriorated urban air quality.

0034-4257/$ - see front matter D 2004 Elsevier Inc. All rights reserved.

doi:10.1016/j.rse.2004.08.003

* Tel.: +1 414 2294860.

E-mail address: cswu@uwm.edu.

Further, urban sprawl contributes to congestion, which

increases more time spent in traffic and reduced regional

mobility (Newman & Kenworthy, 1999). The costs

associated with congestion are estimated to be over $40

billion a year in the United States (Transportation Research

Board, 1994). Therefore, understanding and monitoring

urban composition is becoming an important research topic

among a variety of disciplines.

Remote sensing technologies provide potential oppor-

tunities for quantifying and monitoring urban environ-

ments. For instance, medium resolution remote sensing

data (e.g. Landsat Thematic Mapper) have been widely

utilized in mapping urban land use and land cover through

classification algorithms (Harris & Ventura, 1995; Treitz et

al., 1992). These traditional classification approaches

assume only one land use and land cover class exists in

an image pixel. However, in reality, the spectrum of a

pixel may represent a combination of several land use

ent 93 (2004) 480–492

C. Wu / Remote Sensing of Environment 93 (2004) 480–492 481

types, especially for low to medium resolution images.

Therefore, the vegetation–impervious surface–soil (V–I–S)

model proposed by Ridd (1995) is becoming an accepted

alternative to parameterize biophysical composition of

urban environments. In this model, urban environments

are described as a combination of green vegetation,

impervious surface, and soil, if water surfaces are ignored.

With this conceptual model, subsequent research has been

conducted to quantify the distribution of green vegetation,

impervious surface, and soil in urban environments. In

particular, many studies have been conducted in examining

impervious surface distribution. Ji and Jensen (1999), for

example, applied subpixel analysis coupled with a layered

classification to explore urban imperviousness using Land-

sat TM imagery. Flanagan and Civco (2001) developed

subpixel-classifier and artificial neural network algorithms

to derive impervious surface fraction within a watershed.

Wu and Murray (2003) implemented a constrained linear

SMA to estimate impervious surface distribution in

Columbus Ohio, and found that impervious surface

fraction can be estimated by a linear model of low and

high albedo endmembers. Besides the quantification of

urban imperviousness, vegetation distribution in urban

areas has been explored. Small (2001,2002) examined

urban vegetation distribution and temporal changes in New

York City using a three-endmember (low albedo, high

albedo, and vegetation) spectral mixture analysis (SMA)

model. Weng et al. (2004) quantified urban vegetation

abundance and its relationship with urban heat island

effects. Further, the potential of the V–I–S based model in

improving urban land use land cover classification has

been explored. In particular, Rashed et al. (2001) described

the urban composition of Cairo, Egypt as vegetation,

impervious surface, soil, and shade, and consequentially

applied the derived urban composition into detailed land

use classification. Phinn et al. (2002) generated a V–I–S

fraction image using a constrained SMA method with

endmembers chosen from aerial photographs in Southeast

Queensland, Australia, and suggested that the V–I–S based

model performed better than traditional per-pixel classi-

fication. Lu and Weng (2004) utilized green vegetation,

impervious surface/soil, and shade to describe urban/rural

environments, and indicated that the V–I–S based

approach can significantly improve urban land use classifi-

cation accuracy.

Although the V–I–S model has proven valuable in

describing urban composition, there are still technical

difficulties in applying it in heterogeneous urban/suburban

areas. One difficulty is associated with the spectral

variation of each V–I–S component due to brightness

differences. Impervious surface shows the most significant

brightness variation, with spectra ranging from low albedo

(e.g. asphalt) to high albedo (e.g. glass and plastic) (Ben-

Dor et al., 2001; Herod et al., 2004). Similarly, the spectra

of green vegetation, especially in near-infrared bands, may

vary substantially depending on leaf characteristics (e.g.

chlorophyll content) and canopy elements (e.g. density,

shape, angle, etc.) (Asner, 1998). Moreover, different types

of soil illustrate much spectral variation due to changes in

soil composition, grain size, and water content (Ben-Dor et

al., 1999; Irons et al., 1989). Therefore, in a complex

urban system, it is difficult to identify ideal endmembers

representing each of these components. The other difficulty

relates to shade. Shade is always considered an important

component in urban environments (Lu & Weng, in 2004;

Rashed et al., 2001). However, shade is not a biophysical

component of an urban area, but a factor representing

urban topography. Therefore, the explanation of the

endmember shade in SMA models becomes a complex

issue. Lu and Weng (2004) and Rashed et al. (2001)

considered shade as a separate factor describing an urban

landscape. Wu and Murray (2003) note confusion between

shade and other low albedo materials and suggest the

removal of shade using a topological correction method

developed by Adams et al. (1993). Camacho-de Coca et al.

(2004) eliminate shade caused by vegetation canopy using

a renormalization method. Although these studies have

some success in explaining shade, the causes of endmem-

ber shade in SMA models are still not clear and few

studies address the confusion issues between shade and

low albedo materials.

In this paper, a normalized spectral mixture analysis

(NSMA) model is proposed to address the problems

associated with brightness variation and shade. This model

was applied in Columbus Ohio using Landsat ETM+

imagery. The rest of this paper is organized as follows.

The study area is described in Section 2. The brightness

variation and shade issues are discussed in Section 3.

Further, a normalized spectral mixture analysis model for

describing urban composition is implemented in Sections 4

and 5, among which Section 4 details the spectral normal-

ization method and Section 5 reports the spectral mixture

analysis model with normalized spectra. Accuracy assess-

ment and model comparisons are detailed in Section 6, and

finally, conclusions and future research are discussed in

Section 7.

2. Study area

The metropolitan region of Columbus OH in the

United States was chosen as our study area (see Fig. 1).

This region has an area of 1407 km2, including a central

business district (CBD), urban/suburban residential areas,

and some rural areas (e.g. vegetated areas and soil) along

urban boundaries. This area has encountered rapid urban

development and population growth in the last 20 years.

Urban sprawl and population growth also lead to traffic

congestion along major transportation networks. More-

over, it is expected that the growth will continue for the

next 25 years (Horner & Grubesic, 2001). Therefore,

monitoring urban composition and predicting its future

Fig. 1. Columbus Metropolitan Area in Franklin County, Ohio. The lower left corner shows census tracts, and the lower right corner shows an ETM+ image

acquired on September 10, 1999 for the study area.

C. Wu / Remote Sensing of Environment 93 (2004) 480–492482

changes are essential for this area. A Landsat Enhanced

Thematic Mapper (ETM+) scene (path 19, row 32)

acquired on September 10, 1999 was used in this study.

These data were processed using ground control points

and have a geometric error within 15 m. The digital

numbers (DNs) of the ETM+ image were converted to

normalized exo-atmospheric reflectance measures with the

radiance to reflectance conversion formula provided by

the Landsat 7 handbook (Irish, 1998). Black and white

digital orthophotographs acquired in 2000 were obtained

from Franklin County Auditor office. These 0.15-m

resolution aerial photographs are in MrSID format and

with state plane coordinate system. The geometric error of

these photos is within 12 m. For this research, the data

were resampled to 1-m resolution in order to reduce

image processing time and storage space requirements. In

addition, they were converted to ERDAS Imagine format

with UTM projection to be consistent with the ETM+

image. With 1-m spatial resolution, these aerial photos are

suitable for checking accuracies of urban composition

estimates derived from the normalized spectral mixture

analysis model.

3. Brightness variation and shade

In most SMA models, the composition of each pixel in

an urban environment is derived through modeling the

pixel’s spectra with spectra of a set of pure land cover types

(e.g. V–I–S components), named endmembers (Roberts et

al., 1998). However, significant brightness variation exists

for the spectra of these pure land cover types. Fig. 2

illustrates the extent of spectral variation for each V–I–S

component selected from the ETM+ reflectance image for

the study area. These spectra are exo-atmospheric reflec-

tance without atmospheric correction, thus may include the

effects of atmospheric scattering and attenuation. Atmos-

pheric correction techniques, such as the dark object

subtraction (Chavez, 1988), empirical line calibration

(Moran et al., 2001), or the 6S atmospheric correction

Fig. 2. Spectral variations of V–I–S components and their normalized spectra (a—original spectra of vegetation; b—normalized spectra of vegetation; c—

original spectra of impervious surface; d—normalized spectra of impervious surface; e—original spectra of soil; f—normalized spectra of soil.) It indicates that

significant spectral variation due to brightness differences exists in the original spectra of urban components, but much variation was reduced in the normalized

spectra.

C. Wu / Remote Sensing of Environment 93 (2004) 480–492 483

model, may provide better reflectance spectra. An improved

reflectance retrieval method, however, is unlikely to have a

significant effect on the modeling results. Therefore, in this

paper, exo-atmospheric reflectance is utilized. More dis-

cussions about calibrated spectra for urban areas can be

found in Herold et al. (2004). The categorization of dark,

medium, and bright is according to the visualization of the

ETM+ reflectance image with a combination of bands 4, 3,

and 2. The spectral fluctuations of a variety of vegetation are

shown in Fig. 2a. It indicates that although all vegetation

shares a similar spectral shape, the reflectance of band 4

(near infrared) illustrates much fluctuation, varying from

28% (dark vegetation) to near 50% (bright vegetation). This

may be due to the variations of leaf chlorophyll, water

content, or canopy structure. Compared to green vegetation,

impervious surfaces represent a worse condition in terms of

brightness variation, with significant differences in reflec-

tance for each ETM+ band (see Fig. 2c). In particular, dark

impervious surface (e.g. asphalt) has the lowest reflectance

(about 10%), while bright impervious surface (e.g. glass or

steel) illustrates the highest reflectance (about 40%) for each

ETM+ band. The brightness variation of impervious surface

may be because of the variability of manmade materials

used for housing development and road construction.

Similarly, a variety of soil also shows obvious brightness

differences (Fig. 2e), with the lowest reflectance for dark

soil, and the highest reflectance for bright soil in every

ETM+ band. These brightness differences of soil may be

C. Wu / Remote Sensing of Environment 93 (2004) 480–492484

explained in the aspect of soil composition and structures

(Irons et al., 1989). Overall, significant spectral variation

due to brightness differences exists in each V–I–S compo-

nent, among which impervious surface shows the highest

variability.

The brightness variation of pure land cover types makes

endmember selection a complex research topic. Typically, a

principal component (PC) or maximum noise fraction

(MNF) transformation is utilized to facilitate the selection

of image endmembers (Green et al., 1988; Rashed et al.,

2001; Small, 2001). After the transformation, spectral

scatterplots (feature spaces) are generated, and the vertices

of these plots are typically chosen as endmembers after

verification with reference data. Fig. 3 shows the feature

space representation of the first three PC components for the

study area. The correlation matrix, eigenvalue, and eigen-

vector associated with this PC transformation are shown in

Table 1. It indicates that the first three PCs can explain about

99.4% of the total variances while the first PC has an

explanatory power of 85.4%. Moreover, the eigenvectors

and eigenvalue of the first PC show that brightness variation

is the dominant source of spectral variability. The clusters of

each pure land cover type were identified according to

visual interpretations of the original ETM+ image. For the

study area, bright vegetation, bright impervious surface, and

Fig. 3. Scatter plots (feature spaces) of the first three PC components for the origin

around the vertexes, but also scatters along the edges of the plots.

bright soil are likely to be selected as endmembers because

they are clustered in the vertices of the plots. Moreover,

shade (low albedo) may also be an endmember in order to

successfully model mixed pixels. This set of endmembers,

however, creates problems for modeling other pure land

cover types. In particular, dark and medium impervious

surfaces are modeled as a mixture of shade and bright

impervious surface. Similarly, dark vegetation is represented

as partial shade and bright vegetation, and dark soil is

considered as a combination of shade and bright soil.

Therefore, the endmember shade may represent a portion of

actual shade or shadow, but it is also likely to be a part of

vegetation, impervious surface, or soil, thereby making the

fraction calculation of urban composition problematic.

4. Spectral normalization

To address the difficulties in quantifying urban compo-

sition, a brightness normalization method is proposed in

this paper. As shown in Fig. 2a, c, and e, although the

spectra for each pure V–I–S component show significant

brightness differences, they share a common characteristic,

the spectral shape. Therefore, it is possible to highlight the

shape information while minimizing the effects of absolute

al reflectance image. It indicates that a pure urban land cover not only exists

Table 1

Correlation matrix, eigenvalues, and eigenvectors associated with PC

transformation of the original ETM+ reflectance image

(a) Correlation matrix

Correlation matrix PC1 PC2 PC3

PC1 1 �8.34e�12 5.40e�12

PC2 1 1.72e�09

PC3 1

(b) Eigenvalue

Eigenvalue Normalized

1 0.854

2 0.105

3 0.035

4 0.004

5 0.002

6 0.000

(c) Eigenvector

Vector 1 Vector 2 Vector 3 Vector 4 Vector 5 Vector 6

0.38 0.13 0.51 0.67 �0.18 �0.31

0.34 0.18 0.37 �0.09 0.10 0.84

0.36 0.41 0.24 �0.56 0.38 �0.44

0.48 �0.82 0.11 �0.26 �0.12 �0.08

0.51 0.03 �0.64 0.34 0.46 0.05

0.36 0.34 �0.35 �0.20 �0.77 0.01

Fig. 4. Normalized reflectance image for the study area. It illustrates that

much spectral variability for each urban component in the original

reflectance image is removed (e.g. bright and dark vegetation is not

distinguishable in the normalized image, while the differences are clear in

the original reflectance image (Fig. 1)).

Table 2

Correlation matrix, eigenvalues, and eigenvectors associated with PC

transformation of the normalized ETM+ reflectance image

(a) Correlation matrix

Correlation matrix PC1 PC2 PC3

PC1 1 3.03e�07 1.60e�06

PC2 1 �2.31e�05

PC3 1

(b) Eigenvalue

Eigenvalue Normalized

1 0.826

2 0.140

3 0.031

4 0.003

5 0.001

6 0.000

(c) Eigenvector

Vector 1 Vector 2 Vector 3 Vector 4 Vector 5 Vector 6

0.28 0.16 0.53 0.62 �0.40 �0.29

0.24 0.20 0.44 �0.03 0.19 0.82

0.20 0.36 0.38 �0.39 0.54 �0.49

0.71 �0.66 0.02 �0.23 �0.05 �0.06

0.50 0.36 �0.60 0.41 0.31 0.02

0.25 0.49 �0.16 �0.50 �0.65 0.02

C. Wu / Remote Sensing of Environment 93 (2004) 480–492 485

reflectance values through a normalization method (see

Eq. (1)).

R̄b ¼Rb

l� 100 ð1Þ

where

l ¼ 1

N

XNb¼1

Rb

where R̄b is the normalized reflectance for band b in a

pixel; Rb is the original reflectance for band b; l is the

average reflectance for that pixel; and N is the total

number of bands (6 for ETM+ image). The normalized

spectra for the sampled pure land cover types are shown

in Fig. 2b, d, and f, respectively. The internal variation

within each land cover type is much smaller than that

associated with the original reflectance image. This

indicates that much brightness variation has been removed

or reduced through this normalization. Moreover, the

normalized reflectance image (Fig. 4) indicates that

spectral variation for pure land use types has been

reduced. For example, the differences between dark

vegetation and bright vegetation are clear in the original

reflectance ETM+ image (see Fig. 1), but only minor

differences between them exist in the normalized reflec-

tance image. The similar situation applies to impervious

surface and soil also. Although this spectral normalization

process can reduce spectral variation within each land

cover type, it does cause significant loss of information.

As an example, different vegetation types (e.g. pines and

maples) may not be differentiated with the normalized

spectra, though they may be identifiable with the original

spectra. However, in urban applications, especially under

the framework of the V–I–S model, only three major land

cover types, vegetation, impervious surface, and soil need

to be differentiated. Redundant information in remote

sensing images adversely affects SMA modeling results

since only one or two endmembers may be selected for

C. Wu / Remote Sensing of Environment 93 (2004) 480–492486

each land cover type. The normalization process reduces

this redundant information while maintaining useful

information for separating vegetation, impervious surface,

and soil land cover types.

A PC transformation was performed with the normalized

reflectance ETM+ image. The three PC components explain

about 99.7% of total variances (see Table 2b) and the

correlation between PCs is near zero (see Table 2a). In

comparison to the PC transformation before normalization,

it indicates that the explanation power of the first PC

(82.6%) is lower, while the contribution of the second PC is

higher. In addition, the values of eigenvector elements are

similar to those before normalization (see Tables 1c and 2c).

The feature space representation for the normalized

reflectance image is created after a PC transformation.

Fig. 5 illustrates the scatterplots of the first three PC

components. It indicates that instead of being dispersed, as

Fig. 5. Feature space representation of the first three PC components for the n

impervious surface, and soil, can successfully model heterogeneous urban land c

shown in Fig. 3, the pixels of each pure land cover pixels

are clustered around the vertices of each plot. Moreover, it

shows that an endmember shade is unnecessary and the V–

I–S components can successfully model the heterogeneous

urban composition.

5. Spectral mixture analysis

5.1. SMA theory

With a selected set of endmembers, SMA methods are

typically utilized to calculate the fraction of each endmem-

ber in a mixed pixel using an inverse least square devolution

method and endmember spectra (Shimabukuro & Smith,

1991). One basic assumption of SMA models is that the

spectrum for each pixel is a linear or nonlinear combination

ormalized reflectance image. It shows that three endmember, vegetation,

overs.

C. Wu / Remote Sensing of Environment 93 (2004) 480–492 487

of endmember spectra dependent on the significance of

multiple scattering of light on land cover types. A detailed

discussion about linear and nonlinear SMA models can be

found in Gilabert et al. (2000) and Roberts et al. (1993). In

urban applications, linear SMA models are typically utilized

and proven to be effective (Phinn et al., 2002; Rashed et al.,

2001; Wu & Murray, 2003).

5.2. SMA with normalized spectra

With the normalized spectra, a fully constrained linear

SMA method was applied to quantify urban composition:

R̄b ¼XNi¼1

f̄i R̄i;b þ eb ð2Þ

where

XNi¼1

f̄i ¼ 1 and f̄iz0

where R̄b is the normalized reflectance for each band b

in an ETM+ pixel; R̄i,b is the normalized reflectance of

Fig. 6. Fraction images generated from the normalized spectral mixture

endmember i in band b for that pixel; f̄i is the fraction

of endmember i; and eb is the residual. The fraction of

each endmember in a pixel can be calculated using a

least squares method in which the residual eb is

minimized.

Three endmembers, vegetation, impervious surface,

and soil, are selected to model heterogeneous urban

environments. These endmembers were chosen based on

the feature space representation (Fig. 5) of the first three

PC components for the normalized reflectance image,

together with visual interpretation of the original ETM+

image. With applying this normalized SMA model, the

fraction images for each endmember were generated (see

Fig. 6). These fraction images illustrate that the

distribution of vegetation, impervious surface, and soil

correlates with their actual distribution in the image. In

particular, the fraction of vegetation is near zero in the

CBD area, 20–40% in residential areas, and near 80–

100% in known vegetated areas. Besides vegetation,

impervious surface also shows a clear distribution pattern

coherent with known land use information. In particular,

the impervious surface fraction is about 80–100% in the

CBD area, 30–60% in residential areas, and near zero in

rural areas. Moreover, the distribution of soil shows that

analysis model (a—vegetation; b—impervious surface; c—soil).

C. Wu / Remote Sensing of Environment 93 (2004) 480–492488

this model also effectively addresses the confusions

between impervious surface and soil. In particular, the

fraction of soil is near zero in the CBD and residential

areas, and increases to 80–100% in rural areas along the

city boundary.

5.3. SMA with original spectra

In comparison to the normalized SMA model, a four-

endmember SMA model based on the ETM+ reflectance

image was also implemented. The model formulation is

similar to the normalized SMA model, except for the

replacement of the normalized reflectance (R̄) with the

original reflectance (R). Four endmembers, bright vegeta-

tion, bright impervious surface, bright soil, and shade,

were selected as endmembers according to the feature

spaces of the first three PC components of the ETM+

reflectance image (see Fig. 3) and visual interpretations.

Endmember fraction images (Fig. 7) were created through

solving this four-end member linear mixing model with the

original reflectance image.

Fig. 7. Fraction images generated from the four-end member spectral mixture mode

c—shade, d—soil).

In addition to this model, the model proposed by Wu

and Murray (2003) was also applied in this paper for

comparison. Their model can be divided into two steps.

The first step involves generating fraction images for four

endmembers: low albedo, high albedo, soil, and vegeta-

tion. Initially, the spectra of these four endmembers were

obtained through analyzing the feature space representa-

tion of the first three maximum noise fraction (MNF)

components. With the endmember spectra, a fully con-

strained linear mixture analysis was performed to generate

fraction images for each endmember. The second step of

their model was to build a relationship between imper-

vious surfaces and high and low albedo materials. In

particular, they found that impervious surfaces in urban

areas could be modeled by low albedo and high albedo

endmembers, and the fraction of impervious surfaces for a

pixel could be calculated by adding low and high albedo

fractions for that pixel. Wu and Murray reported the

overall root mean square error (RMSE) of the impervious

surface fraction estimation was 10.6% in urban areas.

Following the methodology proposed by Wu and Murray,

l with the original reflectance image (a—vegetation; b—impervious surface;

Fig. 8. Impervious surface fraction image derived from Wu and Murray’s

spectral mixture analysis model.

C. Wu / Remote Sensing of Environment 93 (2004) 480–492 489

the fractions of impervious surfaces for the study area

were calculated and the result is shown in Fig. 8.

6. Accuracy assessment and model comparisons

Black-and-white aerial photographs acquired in 2000

were utilized as ground reference for assessing model

accuracy. For the whole study area, 200 random samples

were generated with the ERDAS Imagine accuracy assess-

ment module. A 3�3 sampling unit was utilized to reduce

the impacts of geometric errors associated with ETM+ and

DOQQ images. The geometric errors of the DOQQs and

ETM+ images are within 12 and 15 m, respectively. While

the geometric accuracies of these images are adequate for

Fig. 9. A sample validation site using DOQQs with a 3�3 sampling unit. (a) ETM

DOQQ image (square with solid white line indicates the corresponding area of the 3

surfaces, including houses, drive ways, roads, etc).

most applications, a small registration error may create

significant bias in calculating impervious surface areas

through screen digitizing. Therefore, instead of using a

single pixel, a 3�3 sampling unit was utilized (see Fig. 9).

For each sample, the corresponding dtrueT impervious

surface was digitized through interpreting DOQQ images

and the area of imperviousness was measured from the

digitized map (see Fig. 9). In particular, for a 3�3

sampling unit, area of interests (AOIs) were drawn

following the boundaries of interpreted impervious surfa-

ces (e.g. houses, driveways, roads, etc.). The area of each

AOI was obtained using AOI property functions in

ERDAS Imagine. Therefore, the dtrueT fraction of imper-

vious surface in this specific sample unit can be calculated

through dividing the total areas of AOIs by the total

sampling area (90 m � 90 m).

Two types of error measurement, root-mean-square error

(RMSE) (Eq. (3)) and systematic error (SE) (Eq. (4)), were

utilized in this research to evaluate the accuracy of urban

composition estimation.

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1

ðV̂V i � ViÞ2

N

vuuutð3Þ

SE ¼

PNi¼1

ðV̂V i � ViÞ

Nð4Þ

where V̂i is the modeled urban composition fraction for

sample i; Vi is the dtrueT urban composition fraction

digitized from DOQQs for sample i; and N is the total

number of samples. RMSE measures the overall estimation

+ image (square with solid white line indicates a 3�3 sampling unit). (b)

�3 sampling unit; polygons with dashed line indicates digitized impervious

C. Wu / Remote Sensing of Environment 93 (2004) 480–492490

accuracy for all samples, while SE evaluates the effects of

systematic errors (e.g. overestimation). For detailed analy-

sis, the study area was subdivided into two categories: less

developed areas with 0–30% of impervious surface (125

samples) and developed areas with more than 30% of

impervious surface (75 samples). The RMSE and SE for the

whole study area, and two subareas were calculated and

illustrated in Table 3.

Results (see Table 3) indicate that the normalized SMA

model has a promising accuracy in estimating impervious

surface fraction for the whole study area, with an overall

RMSE of 10.1% for all samples. Detailed analysis shows

that this model performs better in estimating impervious

surface in less developed areas (RMSE=6.1%) than in

developed areas (RMSE=14.5%). Further, the analysis of

systematic error indicates that no significant bias estima-

tion exists for the whole study area (SE=�3.4%), with

slightly overestimation in less developed areas (SE=1.0%)

and underestimation in developed areas (SE=�10.7%).

Residual analysis (Fig. 10a and b) also indicates that this

model slightly overestimates impervious surface fraction

when its dtrueT value is near zero, and underestimates it

when the dtrueT value is larger than 60%. This effect may

be due to the specification of the constrained SMA model,

in which the endmember fractions are positive and sum to

1. Relaxing one or both constrains may help to solve this

problem.

In comparison to the normalized SMA model, the

popularly applied four-endmember SMA model has a

much higher overall RMSE (18.3%). In detail, this model

performs well in less developed areas (RMSE=9.1%), but

produces large errors when applied in developed areas

(RMSE=27.5%). Further analysis shows that impervious

surface fraction is consistently underestimated (overall

SE=�10.8%). This underestimation is likely due to the

utilization of endmember shade. In particular, dark and

Table 3

Comparisons of impervious surface estimation accuracy for the normalized

SMA, four-endmember SMA, and Wu and Murray SMA models

Error assessment Normalized

SMA (%)

Four-

endmember

SMA (%)

SMA

(Wu and

Murray, %)

RMSE Overall 10.1 18.3 22.2

Less developed

areas (%impb30%)

6.1 9.1 26.6

Developed areas

(%impz30%)

14.5 27.5 11.7

SE Overall �3.4 �10.8 15.9

Less developed

areas (%impb30%)

1.0 �3.6 24.2

Developed areas

(%impz30%)

�10.7 �22.6 �1.2

Two types of error measurement: root-mean-square error (RMSE) and

systematic error (SE) are utilized and the accuracies are assessed for the

overall study area, less developed areas, and developed areas, respectively.

medium impervious surface is considered as a mixture of

bright impervious surface and shade. As a result, part of

impervious surface is misinterpreted as shade, thus

causing the underestimation of impervious surface. The

degree of underestimation is worse in developed areas

(SE=�22.6%) than in less developed areas (SE=�3.6%).

This is due to the significant confusion between imper-

vious surface and shade in developed areas, but little

confusion in less developed areas. The RMS misfit

analysis (Fig. 10c and d) also shows the same pattern

of underestimation. In particular, the degree of under-

estimation is near zero when the dtrueT impervious surface

fraction is near zero, and keeps increasing when the actual

fraction increases.

Similar to the four-endmember SMA model, the SMA

model developed by Wu and Murray (2003) produces a high

overall RMSE (22.2%). Further analysis shows that this

model performs well in developed areas (RMSE=11.7%),

but poor in less developed areas (RMSE=26.6%). More-

over, it overestimates impervious surface in less developed

areas (SE=24.2%), but accurately estimates impervious

surface in developed areas (SE=�1.2%). This result is

consistent with the report from Wu and Murray, in which

this model can be successfully applied in developed urban

areas. However, it may produce large errors when applied

in less developed areas. Residual analysis (see Fig. 10e

and f) indicates that there is a linear pattern of RMS misfit.

In particular, the impervious surface fraction is over-

estimated when its dtrueT value is low (less than 30%),

accurately estimated when the dtrueT value is medium

(greater than 30% but smaller than 70%), and under-

estimated when the dtrueT value is high (greater than 70%).

For less developed areas, the overestimation may be

because of the endmember low albedo (shade). In this

model, low albedo is considered as a portion of impervious

surface. While this assumption is valid in most urban

areas, a large bias exists in rural areas, where the low

albedo (shade) may be largely due to the effects of

vegetation or soil.

7. Conclusion and future research

In this paper, a normalized SMA method was developed

to quantify urban composition under the framework of V–I–

S model. In particular, a normalized transformation was

performed to reduce brightness variation effects of urban

land covers. As a consequence, a linear spectral mixture

analysis method with the normalized spectra was developed

to derive the fractions of green vegetation, impervious

surface, and soil. The estimation accuracy of impervious

surface was assessed and compared with two other existing

models.

Analysis of results suggests several conclusions. Firstly,

the normalized SMA model is a better alternative to the

four-endmember SMA model and the SMA model proposed

Fig. 10. Comparisons of impervious surface estimation accuracy among three SMA models (a—accuracy assessment for the normalized SMA model; b—

residual analysis for the normalized SMA model; c—accuracy assessment for the four-endmember SMA model; d—residual analysis for the four-endmember

SMA model; e—accuracy assessment for the Wu and Murray SMA model; f—residual analysis for the Wu and Murray model).

C. Wu / Remote Sensing of Environment 93 (2004) 480–492 491

by Wu and Murray. It has an overall RMSE of 10.1%, and

performs consistently better in less developed areas and

developed areas. Further, no significant systematic errors

exist in this model. Compared to this model, the other two

models have a much higher overall RMSE. For estimating

impervious surfaces, the four-endmember SMA model

consistently underestimates impervious surface for the

whole study area, especially in the developed areas

(SE=�22.6%). The Wu and Murray’s model is effective

when applied in developed areas, but significantly over-

estimates impervious surface in less developed areas

(SE=24.2%). Further, this paper highlights the brightness

variation problems in urban applications, and argues that

shade may not be considered as an urban composition, but a

factor that adversely influences modeling results. As a

consequence, this paper developed a brightness normal-

ization method to remove the effects of shade. Therefore, in

the normalized SMA model, shade is not considered as an

endmember, and the accuracy of urban composition

estimation is improved.

One future research direction could be the accuracy

assessment of the vegetation and soil fraction. In this

research, contemporaneous vegetation and soil ground

reference data were not available. This information cannot

be acquired through digitizing aerial photographs since it is

extremely difficult to distinguish vegetation and soil in these

black-and-white photos. Contemporaneous high-resolution

images, such as IKONOS imagery, should be helpful to

obtain ground truthing information of vegetation and soil.

Another future research may be exploring the effectiveness

of multiple-endmember spectral mixture analysis (MESMA)

method developed by Roberts et al. (1998). Instead of

C. Wu / Remote Sensing of Environment 93 (2004) 480–492492

normalizing urban spectral variability, the MESMA model

recognizes the heterogeneity of urban materials, and utilizes

multiple sets of endmembers for modeling each image pixel.

The MESMA model may also produce effective results in

quantifying urban composition.

Acknowledgements

Valuable comments and suggestions from Dr. Marvin

Bauer and three anonymous reviewers are gratefully

acknowledged.

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