Improving urban classification through fuzzy supervised …lewang/pdf/Lewang_sample14.pdf · 2010. 5. 5. · methods, nevertheless, were inadequate in classifying urban landscape

Improving urban classification through fuzzy supervised classificationand spectral mixture analysis

J. TANG*{, L. WANG{ and S. W. MYINT§

{Department of Geography and Environmental Systems, University of Maryland,

Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

{NCGIA, Department of Geography, University of Buffalo, State University of New

York, Buffalo, NY 14261

§Department of Geography, Arizona State University, Tempe, AZ 85287-0104, USA

(Received 22 July 2006; in final form 15 November 2006 )

In this study, a fuzzy-spectral mixture analysis (fuzzy-SMA) model was

developed to achieve land use/land cover fractions in urban areas with a

moderate resolution remote sensing image. Differed from traditional fuzzy

classification methods, in our fuzzy-SMA model, two compulsory statistical

measurements (i.e. fuzzy mean and fuzzy covariance) were derived from training

samples through spectral mixture analysis (SMA), and then subsequently applied

in the fuzzy supervised classification. Classification performances were evaluated

between the ‘estimated’ landscape class fractions from our method and the

‘actual’ fractions generated from IKONOS data through manual interpretation

with heads-up digitizing option. Among all the sub-pixel classification methods,

fuzzy-SMA performed the best with the smallest total_MAE (MAE, mean

absolute error) (0.18) and the largest Kappa (77.33%). The classification results

indicate that a combination of SMA and fuzzy logic theory is capable of

identifying urban landscapes at sub-pixel level.

1. Introduction

Understanding the extent, distribution and evolution of urban landscape is critical

in analysing and explaining its structure. Such information plays a vital role in

predicting future urban landscape pattern and guiding the direction of urban

planning for satisfying both environmental and socioeconomic sustainability.

Moderate resolution satellite images such as Thematic Mapper (TM) provide a

distinctive opportunity to capture urban landscape over a large area in a timely and

cost-effective manner (Yang and Lo 2002, Song 2005). Traditional per-pixel

methods, nevertheless, were inadequate in classifying urban landscape from

moderate satellite imagery due to the presence of mixed land cover categories in

each pixel, as a result of the rapid alternation of artificial and natural objects within

a small distance in a typical urban setting (Mesev et al. 2001, Small 2003, Lu and

Weng 2004). Specifically, treating each individual pixel to a pure class, as has been

assumed in such per-pixel classifiers, prevents the representation of varying land

cover and land use information below the inherited pixel resolution (Gong and

Howarth 1989, Foody and Arora 1996, Small 2004).

*Corresponding author. Email: [email protected]

International Journal of Remote Sensing

Vol. 28, No. 18, 20 September 2007, 4047–4063

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2007 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160701227687

Downloaded By: [University at Buffalo (SUNY)] At: 20:50 26 August 2008

Instead of assigning only one class per pixel, sub-pixel classification approachesquantify multiple class memberships for each pixel (Foody and Cox 1994, Foody 1996,Foody 1997, Myint 2006). Spectral mixture analysis (SMA) represents a widely usedmethod for tackling the decomposition of mixed pixels. The linear SMA has so far beenthe most popular approach among the SMA family methods given its simplemathematical form. It has been adopted to generate fractions of urban physicalconstituents according to the spectral variability inherited in either multi- orhyperspectral imagery (Settle and Drake 1993, Tompkins et al. 1997, Small 2001, Wuand Murray 2003, Lu and Weng 2004). To standardize the application of linear SMA,Ridd (1995) first proposed the vegetation-impervious surface-soil (VIS) model torepresent the biophysical composition of an urban environment as vegetation, imper-vious surface and soil. This model was later widely adopted as a scheme for choosingappropriate endmembers in the linear SMA model (Madhavan et al. 2001, Phinn et al.

2002). Some recent studies have further refined the VIS model, e.g. impervious surfacewas classified into low-albedo and high-albedo endmember (Small 2001, Wu and Murray2003) or shade endmember was added as a separate endmember (Lu and Weng 2004).

One critical problem encountered in the application of linear SMA is that thenumber of endmembers has to be kept at a fairly limited size since it is constrainedby the number of available bands offered by the remotely sensed imagery (Radeloffet al. 1999). Moreover, the impervious surface in the VIS model is not appropriate tobe treated as one endmember given that the presence of various components is notunusual (Wu and Murray 2003, Lu and Meng 2004). A number of approaches havebeen developed to address this question by either modification of endmembers oralternation from a simple linear SMA to a nonlinear function. Examples of thesemethods include iterative spectral unmixing (Meer 1999, Theseira et al. 2002);endmember bundles approach (Bosdogianni et al. 1997, Bateson et al. 2000); neuralnetwork (Foody 1997, Carpenter et al. 1999, Linderman et al. 2004); mixturediscriminant analysis (Ju et al. 2003); and Bayesian spectral unmixing (Song 2005).

Fuzzy classification is another robust method which provides class membershipsat the pixel level. After Zadeh (1965) introduced the fuzzy set concept in 1965 todescribe imprecision, fuzzy set concept was then widely applied to sub-pixel imageanalysis. Fuzzy C-means (FCM) algorithm (Bezdek et al. 1984, Foody 1992), fuzzy-maximum likelihood classification (Wang 1990), and neuro-fuzzy (Carpenter et al.

1999), are three prevalent approaches in this category. Based on an iterativeoptimization of clustering, FCM limits its application when the a priori knowledgeof number of cluster and local optima is not enough (Bandyopadhyay 2005) beforeclassification. Fuzzy-maximum likelihood classification and neuro-fuzzy are twosupervised soft classifications by softening the output of traditional maximumlikelihood classification and neural network classification. Typically, these twomethods need to identify the training samples to characterize the classes in theimage. However, inability to account for mixed pixels when collecting informationfrom the training samples, as a general practice when the aforementioned methodswere applied, has circumvent the implementation of a ‘fully’ fuzzy classification(Zhang and Foody 2001). Therefore, it is critical to choose proper endmembers andsolve the mixed pixel problem for the fuzzy training data in order to perform anaccurate supervised soft classification in urban area.

In this study, we propose a new fuzzy-SMA method to improve the estimation of

urban land use/land cover fractions from Landsat ETM + imagery. The method is

based on both fuzzy supervised classification and linear SMA. Particularly,

endmember signatures of training samples in the fuzzy classifier are not treated as

4048 J. Tang et al.


constants, but as ratios derived from the linear SMA. In order to examine the

effectiveness of this method, we finally compare the classification results from fuzzy-

SMA with those from partial-fuzzy and linear SMA.

2. Study site and data preparation

The study site was selected in the eastern metropolitan area in Houston, Texas

(figure 1), covering an area of 1200 km2. Surrounded by the Buffalo Bayou, this

region is one of the fastest growing centres of petroleum manufacturing,

warehousing and transportation in Houston. The typical land use/land cover classes

include: residential area, commercial/industrial area, transportation, woodland,grassland and barren/soil. Considering the practical value for later applications, we

adopt a class system with both the land use and land cover classes. Based on the field

experience and spectral attribute in the image, the residential area, transportation

and commercial/industrial area can be referred to as the impervious surface with

low, medium and high albedo, respectively.

A subset image from Landsat 7 ETM + (path 25, row 39) acquired on 2 January

2003 is employed in this study. For the sake of reducing atmospheric distortion, the

digital numbers (DN) at each band were first converted to the normalized at-sensorreflectance using the method that was introduced in Markham and Barker (1987).

The minimum noise fraction (MNF) transformation was then applied to remove the

correlation existing between the six bands (the thermal band was excluded since it

has a different spatial resolution). Bundled IKONOS images, comprising a 1-metre

panchromatic and a 4-metre multispectral image, that was acquired on 2 January

2002, was adopted as reference for choosing the training samples for different

endmembers as well as the test samples of known fractions from Landsat ETM + .

3. Methodology

A systematic framework of our model is presented in figure 2. Three sets of

proportion maps were derived using linear SMA, partial-fuzzy and fuzzy-SMA

Figure 1. Study site in Houston, Texas from a Landsat ETM + imagery in January 2003.

Improving urban classification 4049


classifications, respectively. The major difference between the partial-fuzzy and

fuzzy-SMA lies in the training spectrum among these classes. In the fuzzy-SMA, we

applied the linear SMA to obtain the fuzzy mean and fuzzy covariance matrix for

the training samples instead of treating them as constants. Based on these statistical

measures, we derived the fractions of urban images using the fuzzy set theory. The

following sections will describe the fuzzy logic and SMA in details.

3.1 Fully-fuzzy supervised classifier and its training data

Conventional discriminant analysis is a widely used classifier in the classification of

remotely sensed data. This method allocates each pixel to the class which has the

highest a posteriori probability of membership (Foody 1996, Richards and Jia

1999). Without considering the prior probability, the a posteriori probability, also

named as discriminant function, is expressed as:

gi xð Þ~{ln Mij j{ x{mið ÞtMi{1 x{mið Þ ð1ÞWhere x is the b-dimension pixel vector for b bands; mi and Mi are the mean vector

and variance–covariance matrix of training samples of class i, respectively (Richards

and Jia 1999).

To implement a fully-fuzzy supervised classification, we derived the fuzzy mean

and fuzzy variance matrix (Wang 1990) from the training samples in addition to

‘soften’ the output of conventional ‘hard’ classifiers by the fuzzy classifier. The fuzzy

mean mi* and fuzzy variance matrix Mi can be calculated using equations (2) and (3):

m�i ~

PS

i~1

f xið Þxi

PS

i~1

f xið Þð2Þ

Figure 2. Flowchart for the fuzzy-spectral mixture analysis (fuzzy-SMA) model. Note:IKONOS image is used to select pure endmembers/training samples and assess theclassification accuracy of the resultant proportion maps from fuzzy-SMA model.

4050 J. Tang et al.


and

Mi~

PS

i~1

f xið Þ xi{m�i� �

xi{m�i� �T

PS

i~1

f xið Þð3Þ

where xi is the pixel spectral vector of the training samples of class i; S is the total

number of training samples; and f(xi) is the membership function of class i.

Training samples for six classes, including residential area, commercial/industrial

area, transportation, woodland, grassland and barren/soil, were selected from the

Landsat ETM + image by referring to the IKONOS image. Water was masked out

before the analysis since it only occupies a small area in the study site. Samples for

each class come from thirty training plots and each training plot covering 90690 m2

on the ground. Due to the mixture of membership in each training plot, it is

important to identify the proportions of endmembers in these training plots before

an accurate fuzzy mean vector and fuzzy variance matrix can be derived. For

example, Wang (1990) estimated the endmembers’ fractions from training plots with

manual interpretations from the aerial photography. However, the inaccurate

estimation of fuzzy mean vector and fuzzy variance matrix through manual

digitization often leads to poor classification results. In this research, we applied the

SMA to identify the fraction membership of the training samples.

3.2 Spectral mixture analysis

Spectral mixture analysis (SMA) aims to map the fractions of landscape classes

within the mixed pixels using an inverse least square devolution method and the

spectra of pure endmembers (Shimabukuro and Smith 1991). In this study, we

employed a modified constrained least square method for the linear spectral

unmixing analysis using the following expression:

Rn~XE

e~1

rn, efezen withXE

e~1

fe~1 and 0ƒfeƒ1 ð4Þ

where Rn is the normalized spectral reflectance for each band n; fe is the fraction of

endmember e; E is the total number of endmembers; rn,e denotes the normalized

spectral reflectance of endmember e within a pure pixel on band n; and en is the

residual.

The choice of spectral reflectance for the endmembers is critical for the spectral

mixture analysis. An optical approach for selecting endmembers is to use

laboratory-based spectra from the field. However, substantial problems exist in

accounting for the atmospheric conditions when upscaling the field spectral value to

the level that can be employed with the satellite sensor data (Settle and Drake 1993,

Wu and Murray 2003). Alternatively, the endmembers’ spectra can be obtained by

locating pure pixels on the same image (Lu and Weng 2004). In our study, the

endmember for each class is carefully selected from the representative homogenous

pixels, i.e. having a full membership to the specified class and zero membership to

the other classes. To ensure the purity of the chosen pixels from the ETM + image,

higher spatial resolution IKONOS image was employed as a reference image. The

clear delineation of feature spaces among the six classes in the first three principle



components (figure 3) suggests that the reflectance spectra of ETM + image could be

represented by a six-endmember linear mixing model.

3.3 Accuracy assessment

The accuracy assessment is an essential step for the landscape mapping from

remotely sensed data (Foody 2002). An independent set of test samples was chosen

for this evaluation. Considering the statistical requirement and the size of our study

area, we randomly selected 200 sample plots with each at the size of 90690 m2 from

the IKONOS image using ERDAS Imagine accuracy assessment module (figure 4).

For each sample unit, its actual land use types were acquired through digitizing the

IKONOS image (figure 4(b)). The actual fractions of each landscape class in the

sample units were obtained through dividing the class area by the total area of one

sample plot.

As stated by Foody (1996), conventional confusion matrix is inappropriate for the

fuzzy classification evaluation since multiple memberships exist with each pixel. In

this research, we adopted two accuracy assessment methods to evaluate the accuracy

of urban composition for each land class. The first method is the mean absolute

error (MAE) (Pontius et al. 2004, Willmott and Matsuura 2006), defined as follows:

MAEi1P, 2P� �

~

PN

n~1

1Pi{2Pi

��

��

Nð5Þ

Total MAE~

PJ

i~1

MAEi

2ð6Þ

Figure 3. Feature space representation of the first three principle components. Red:residential; magenta: commercial/industrial; yellow: transportation; green: woodland; cyan:grassland; black: barren/soil

4052 J. Tang et al.


Where 1Pi is the estimated land use composition fraction from the classification and2Pi is the ‘actual’ land use composition fraction digitized from IKONOS for class i in

the test sample n; N is the total number of test samples and J represents the number

of categories.

The generalized cross-tabulation matrix as introduced by Pontius and Cheuk

(2006) was also adopted to further analyse the disagreement between the estimated

results and reference maps. Specifically, a composite operator was used to calculate

(a) (b)

Figure 4. The sample fraction validation using IKONOS, (a) sample distribution in thestudy area; (b) Thematic Mapper (TM) and the corresponding IKONOS sample unit, themagenta line is used to digitize the residential area in this unit.

Figure 5. Classified images generated by benchmark Maximum Likelihood Classificationmethod.



the entries in the cross-tabulation matrix through:

Pi, j~min 1Pi,2Pi

� �if i~j

~ 1Pi{min 1Pi,2Pi

� �� |

2Pj{min 1Pj,2Pj

� �

PJ

j~1

2Pj{min 1Pj, 2Pj

� ��

2

6664

3

7775

if i=jð7Þ

where Pi,j is the estimated entry in the cross-tabulation matrix for classes i and j.

Once all entries were filled, overall accuracy and Kappa values were calculated in

the same manner as that applied in the traditional hard classification. Further

details about the accuracy assessment in soft classification can be found in Pontius

and Cheuk (2006).

4. Results and discussion

Figure 5 is the classified image generated by the supervised MLC method. It reveals

the central-zonal spatial pattern throughout the whole study area. Most of the

industrial or commercial area is located in the central business district (CBD) or

distributed along the major road or the Buffalo Bayou. High-density residential

areas are found around the CBD, especially around the Highway I45 and the

Buffalo Bayou in the southern study area. The woodland is mainly seen in the north-

eastern area of Houston. Grassland is mainly distributed in the southern part,

mostly around the Houston International Airport. Although the supervised

classification result describes the overall urban land use pattern, it could not

provide a realistic or accurate measurement on urban pattern since it neglected the

relative abundance of surface materials within a pixel.

Conversely, a richer amount of land use information has been derived by the ‘soft’

classification. Figure 6 illustrates six fraction images unmixed from the ETM +image using the linear SMA model. We used the grey level to designate the

percentage of a specific class that a pixel contains. Therefore, a brighter pixel means

a higher fraction. It is noticeable that the fraction images of all classes have a similar

grey level. These results may be attributed to the spectral similarity among the six

classes. The most obvious misinterpretation is the confusion between transportation

and commercial/industrial area in the central part of the study area. Therefore, the

linear SMA would result in substantial misinterpretation due to the spectral

similarity among classes.

The fraction images derived from the partial-fuzzy method (figure 7) present a

more obvious pattern than the linear SMA. Particularly, fractions of the

commercial/industrial area and the residential area have been refined. The bright

pixels in the two-fraction images correspond well to the known impervious area

within the original ETM + image. Moreover, the woodland fraction image concurs

with the field woodland distribution, i.e. almost zero in the CBD and ranging

between 60–80% in the residential areas.

The fraction images from the fuzzy-SMA model achieved a remarkable

improvement compared to both linear SMA and partial-fuzzy methods. In figure 8,

the brightest spot, as an indicator of high proportion for the commercial/industrial

fraction image, is located in the central area of the study area. The residential

fraction is near zero in the high-density commercial or industrial area, while it

4054 J. Tang et al.


gradually increases to 10–50% in the transition zone between the industrial area and

residential area, and approaches 90% in the high-density residential area. The

transportation fraction image is also consistent with its actual distribution, showing

an interlaced pattern. Most grassland is located in the south-eastern corner and

peaks at almost 100% in the park area. The woodland has the least fraction in the

central area of Houston, ranging between 10 and 30%. The brightest spot of the

woodland is found in the known woodland area, the north-eastern area of Houston.

The fact that fuzzy-SMA performed better than the linear SMA can be attributed to

the incorporation of fuzzy mean and fuzzy variance, with which the spectral

overlaps between the endmembers has been significantly reduced.

Table 1 shows the accuracy indices (MAE) and the cross-tabulation matrix for the

fuzzy-SMA, partial-fuzzy, linear SMA and MLC. In table 1, a smaller index denotes

a better classification result. From this table we can easily find that the fuzzy-SMA

performed better than the other two methods since it has the smallest MAE (0.35). A

detailed examination with the MAE shows that fuzzy-SMA performed well with the

impervious surface, e.g. the commercial or industrial area (0.06), residential area

(0.05) and transportation area (0.09). The best fraction is associated with the barren/

soil category, having the smallest MAE (0.01). A possible explanation could be that

most of the training samples for barren/soil are mixed with vegetation, especially for

the ‘fragmentized’ grassland. The fuzzy-SMA accounts for the fractions in dealing

with the training samples, thus reducing the signature confusion between the

vegetation and soil.

Figure 6. Fraction images generated by the linear spectral mixture analysis (linear SMA)model.



Table 2 shows the cross-tabulation matrix for the MLC, linear SMA, partial-fuzzy

and fuzzy-SMA. The diagonal numbers in the matrix were underlined to highlight

the agreement between the classified results and empirical map. Evidently, fuzzy-

SMA showed an obvious improvement in the results with the highest overall

accuracy (82.11%) and Kappa (77.33%). In particular, fuzzy-SMA has the highest

agreement in the commercial/industrial area (11.63%), transportation (26.83%) and

woodland (16.40%).

Further analysis on the cross-tabulation matrix suggests that there are still some

drawbacks with the sub-pixel classification methods. In the cross-tabulation matrix,

the improvement from the MLC to the linear-SMA can mainly be found in the

transportation (from 6.02 to 12.12%), grassland (from 6.73 to12.36%) and barren/

soil (from 0.57 to 1.71%). These classes usually have a distinct spectral

characteristic. Other classes, such as the residential and commercial/industrial, due

to the spectral confusion, generated even worse results with linear-SMA.

A further comparison was carried out between the actual class fractions and

estimated fractions for the three models (figures 9–12). The distance that the test

samples deviate from the line y5x was then used to assess the closeness between the

actual proportions and estimated proportions of each class. The total distance (SD)

for each class was also shown in each plot. The closer the test samples to the line

y5x, the better the estimated result will be. In the one-to-one relationships observed

in the MLC model (figure 9), a number of fractions of landscape classes are

estimated as either 0 or 1, especially for the commercial/industrial and transporta-

tion, which indicates that the conventional ‘hard’ MLC approaches are ineffective

Figure 7. Fraction images generated by the partial-fuzzy method.

4056 J. Tang et al.


for mapping urban internal structures, especially when using the coarse resolution

image.

In contrast to the MLC method, the linear SMA has largely alleviated the extreme

situation of having either ‘0%’ or ‘100%’ fractions. A much clearer correlation can

be discerned between the estimated and actual fractions (figure 10) though most

observed points do not distribute along the y5x line. As previously discussed, such a

situation may be a result of the spectral similarity among urban landscape classes.

Although many researchers have found that SMA is an effective approach in

characterizing urban landscape (Lu and Weng 2004, Wu 2004), few endmembers

(e.g. three or four surface covers) were usually the cases in their studies. When more

Figure 8. Fraction images generated by the fuzzy-spectral mixture analysis (fuzzy-SMA)model.

Table 1. Comparisons of mean absolute error (MAE) for fuzzy-spectral mixture analysis(fuzzy-SMA), linear SMA and Maximum Likelihood Classification methods.

Accuracyassessment

Residen-tial

Commercial/industrial

Transport-ation

Grass-land

Wood-land

Barren/soil

Total

MAE MLC 0.48 0.08 0.25 0.17 0.12 0.04 0.58Linear

SMA0.15 0.17 0.20 0.17 0.13 0.14 0.48

Partial-Fuzzy

0.13 0.10 0.28 0.17 0.14 0.46 0.64

Fuzzy-SMA

0.05 0.06 0.09 0.06 0.08 0.01 0.18



Table 2. Cross-tabulation matrix (%) for the Maximum Likelihood Classification, linear spectral mixture analysis (linear SMA), partial-fuzzy and fuzzy-SMA methods. Maximum Likelihood Classification is given in roman, the linear SMA is given in bold, the partial-fuzzy method is given in italics and the

fuzzy-SMA is given in bold italics. The underlined value is the agreement between the classified results and empirical map.

Empirical map

Classifiedresult

Residential Commercial/industrial

Transportation Grassland Woodland Barren/soil Total

Residential 17.77 3.73 20.30 8.77 15.90 0.70 67.1711.84 1.71 3.86 1.83 1.51 0.11 20.86

9.15 0.25 2.28 1.37 0.66 0.01 13.7216.17 0.07 0.37 1.35 1.09 0.09 19.14

Commercial/industrial

0.13 6.20 1.48 0.38 0.29 0.54 9.022.05 5.26 3.30 1.71 3.69 0.03 16.040.01 3.51 0.89 0.35 0.09 0.00 4.850.45 11.63 1.78 2.19 0.92 0.26 17.23

Transportation 0.00 1.53 6.02 0.64 0.13 0.17 8.490.23 0.70 12.12 0.72 1.33 0.13 15.230.01 0.37 1.39 0.10 0.02 0.00 1.890.98 0.26 26.83 2.81 1.98 0.47 33.33

Grassland 0.03 0.01 0.34 6.73 1.07 0.15 8.331.20 0.98 2.32 10.36 2.18 0.04 17.080.07 0.03 0.44 4.04 0.22 0.00 4.800.10 0.00 0.03 10.07 0.71 0.14 11.05

Woodland 0.00 0.00 0.00 0.00 3.48 0.00 3.480.73 1.61 2.32 0.64 9.35 0.13 14.782.05 0.40 4.52 4.31 14.68 0.11 26.070.31 0.01 0.40 0.85 16.40 0.10 18.07

Barren/soil 0.05 0.63 1.27 0.77 0.24 0.57 3.531.96 1.82 5.52 1.96 3.07 1.71 16.046.77 7.53 19.85 7.08 5.41 2.04 48.680.00 0.06 0.00 0.07 0.03 1.02 1.18

Total 17.98 12.01 29.41 17.29 21.11 2.13 10018.01 12.08 29.44 17.22 21.13 2.15 10018.06 12.09 29.37 17.25 21.08 2.16 10018.01 12.03 29.41 17.34 21.03 2.08 100

Overall accuracy: MLC (40.77); linear-SMA (50.65); partial-fuzzy (34.81); fuzzy-SMA (82.11)Kappa: MLC (27.85); linear-SMA (40.82); partial-fuzzy (26.76); fuzzy-SMA (77.33)

40

58

J.

Ta

ng

eta

l.


endmembers are designated within the urban area category, the method will easily

reach its limit due to the spectral closeness and overlap. The correlation between the

estimated fraction using the partial-fuzzy and actual fraction from the IKONOS is

shown in figure 11. Although the partial-fuzzy method has advantages over the

MLC method, most classes still have zero fractions in several test plots. Therefore,

we can conclude that from the MLC to the partial-fuzzy method, there is little

improvement for the urban landscape classification.

Figure 9. Relationships for the 30 test samples between the estimated fraction usingMaximum Likelihood Classification and the ‘actual’ fraction digitized from the IKONOSimage.

Figure 10. Relationships for the 30 test samples between the estimated fraction using linearspectral mixture analysis (linear SMA) and the ‘actual’ fraction digitized from the IKONOSimage.



Compared to the MLC, linear SMA and partial-fuzzy methods, fuzzy-SMA has

achieved a promising result with the smallest overall distance to the y5x line

(figure 12). The best classification result using fuzzy-SMA was observed in the

barren/soil and residential area, with distances of 1.27% and 4.66%, respectively.

The test samples were much closer to the y5x line in the fuzzy-SMA, indicating that

the fuzzy-SMA method gives the most accurate estimation of the landscape

composition in this study area.

Figure 11. Relationships for the 30 test samples between the estimated fraction usingpartial-fuzzy method and the ‘actual’ fraction digitized from the IKONOS image.

Figure 12. Relationships for the 30 test samples between the estimated fraction using fuzzy-spectral mixture analysis (fuzzy-SMA) and the ‘actual’ fraction digitized from the IKONOSimage.

4060 J. Tang et al.


5. Conclusions

Using moderate resolution satellite images, traditional ‘hard’ classification is usually

inappropriate for urban landscape analysis since multiple class memberships exist

within one pixel. In this paper, we developed a fuzzy-SMA method to estimate the

subpixel fractions for urban landscape and the performance was compared to linear

SMA, partial-fuzzy and MLC methods. The same sets of training and test samples

were used in these methods based on IKONOS data. Previous studies proved that

the SMA and partial-fuzzy methods were effective in the urban classification,

especially when addressing fuzziness in the training and testing samples. However,

the straightforward application of linear SMA was unsatisfactory when the number

of endmembers goes over four using TM images. Conversely, we propose to carry

out SMA in the first stage and serve its result in the calculation of fuzzy mean and

fuzzy covariance, followed up with a fuzzy classification to derive the final fractions.

It turns out that this fuzzy-SMA performs consistently better than the MLC, linear

SMA and partial-fuzzy methods.

For most subpixel classifications, endmember selection is still a critical step

towards the final success. Various unmixture methods are vulnerable with an

inappropriate identification of pure endmembers. This is particularly true without

having a higher spatial resolution reference image. Moreover, most SMA studies

only choose three or four endmembers, i.e. VIS models developed by Ridd (1995)

and Wu and Murray’s SMA models (2003). This circumvents a finer characteriza-

tion of the urban landscape since it usually has various surface types.

Shade, caused by tall buildings or trees, is an inevitable part of urban area,

especially in the developed areas. In this research, we classified it into barren and soil

instead of treating it as a separate endmember. This simplification adversely

influences modelling results, e.g. barren and soil area is overestimated and

commercial/industrial area is underestimated. In future research, we will incorporate

the shade as a single endmember to reduce the error within other classes.

Although in this study, the fuzzy-SMA method achieved considerable improve-

ments in the urban landscape classification, the exact location of each endmember

within one pixel is still unresolved. To locate each endmember, we could incorporate

the context information from its surrounding pure pixels. How to combine this

knowledge in a fuzzy classification to develop a more sophisticated soft method is

still an interesting research topic.

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