Symposium no. 52 Paper no. 1141 Presentation: oral

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Spectral unmixing versus spectral angle mapper forland degradation assessment: a case study

in Southern Spain

SHRESTHA D.P. (1), MARGATE D.E. (2), ANH H.V. (3) and Van DER MEER F.(1)

(1) International Institute for Aerospace Survey and Earth Sciences, P O Box 6, 7500AA Enschede, The Netherlands

(2) Bureau of Soils and Water Management, Quezon City, Philippines(3) Forest Science Institute, Hanoi, Vietnam

AbstractUnlike conventional sensor systems such as Landsat-TM, Spot-MX or IRS-LISS,

which acquire data in only a few spectral bands, the development of scanner systemsthat acquire data in many narrow-wavelength bands allows the use of almost continuousreflectance data in studies of the Earth’s surface. This not only produces laboratory-likereflectance spectra with absorption bands specific to object properties, but also helpsincrease accuracy of mapping surface features. Classification by means of spectralmatching thus becomes more feasible. With so much information, the well-knownproblem of mixed pixels can be solved by a mixture model, which is commonlyassumed to occur in a linear fashion.

In this study, we compare linear unmixing and spectral angle matching techniquesto assess the classification performance for identifying and mapping ‘desert like’surface features in southern Spain. These features include desert pavements, calcareous,gypsiferous and saline surface soils. Although spectral unmixing helps to assign a pixelto a dominant class, the data is affected by illumination variations caused bytopography, so that selection of end member can be biased. By comparison, the spectralangle matching technique compares only the angle between known and unknownspectra, which uses only the direction and not the length of the spectral vector. It istherefore insensitive to the gain factor caused by surface illumination conditions andthus more suitable in areas with high illumination differences. On the other hand, linearunmixing calculates, for each pixel, the abundance of pixel components. Present studyshows that linear unmixing seems to provide more realistic results for mapping “desertlike” surface features as compared to spectral angle mapper.

Keywords: hyperspectral, linear unmixing, spectral matching, spectral angle_desertlike_surface features

IntroductionThe concept of desertification, considered a severe stage of land degradation, is

responsible for the manifestation of “desert-like” conditions especially in dryland areasoutside the desert boundaries (Rapp, 1986). Climatic conditions together withgeomorphologic processes help in molding the so-called desert-like soil surface

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features. The identification of these soil features serves as a useful input in assessing theprocess of desertification and land degradation as a whole.

Hyperspectral remote sensing provides a different approach to image processing.Conventional broadband sensors such as SPOT, Landsat MSS and Landsat TM do notin general provide satisfactory results in mapping soil properties, because theirbandwidth of 100 to 200 µm cannot resolve diagnostic spectral features of terrestrialmaterials (De Jong, 1994). Hyperspectral data provide greater classification accuraciesas compared to broadband instruments (Pieters and Mustard, 1988; Kruse, 1989; Clarket al., 1990). Increased spatial resolution also facilitates detailed surficial mapping.However, analytical techniques developed for analysis of broadband spectral data areincapable of taking advantage of the full range of information present in hyperspectralremote sensing imagery (Cloutis, 1996). Since hyperspectral data allows the use ofalmost continuous reflectance data in studies of the Earth’s surface, analysis ofreflectance spectra with absorption bands specific to object properties can be carriedout.

Study areaThe study area is located in the surroundings of Tabernas in the province of

Almeria (Figure 1). The exact site corresponds to the coverage of the HYMAP airbornehyperspectral image, with its flight line starting at 37o02’32” N and 2o30’14” W andending at 37o04’25” N and 2o16’40” W. The Tabernas basin is a structural depression inthe Alpine nappes of the Betic Cordilleras of southern Spain, which is bounded bymajor strike-slip fault (Kleverlaan, 1989). The terrain is relatively rugged with verysparse vegetation. The mountain ridges on north and south sides of the basin act as mainbarriers for precipitation and have lead to pronounced dry conditions leading todesertification. The climate is characterised as semi-arid with long hot summers. Annualprecipitation ranges from 115 mm to 431 mm, with rainy days varying from 25 to 55.

Figure 1 Location map of the study area at Tabernas, Almeria, Spain.

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The soils, in general, are shallow (less than 50 cm depth), except in the valleys andoccasionally on the piedmonts. On the steeper slopes they are mostly derived from theweathering of the exposed bedrock, while in the valleys they consist of irregulardeposits of materials coming from the surrounding mountains and hillands broughtdown by flash floods. Soil texture is commonly sandy loam to loamy sand with morethan 40% coarse fragments on the surface. Saline soils occur in the valleys withelectrical conductivity values of more than 2 dS m-1 Surface crusting is commonparticularly in saline areas. Most of the soils are strongly calcareous with calciumcarbonate content ranging from 2-31%. Generally, soils in the hillands and piedmontsare classified as Lithic Torriorthents and the deeper soils are Typic Torriorthentsaccording to the USDA Soil Taxonomy (1998). In the valleys, soils are classified asFluventic Haplocambids and towards the upper terraces, they are classified as TypicHaplocambids.

Desert-like soil surface features are common in the area. The abundance ofuncovered loose materials is readily available for transport either by wind or waterleaving behind desert pavements, which are continuous layer of gravel and small stones.They are usually formed on the surfaces of the pediments, fans and plains. Due to highevaporation rates, lack of leaching and percolation to deeper horizons, many low-lyingareas are saline and alkaline. Calcium carbonate and gypsum are often present inabundance, forming hard pans and contributing to the formation of surface crust.

Methods and Techniques Applied

Data collectionAn airborne hyperspectral data set (HYMAP) of the study area, acquired on 2 June

1999, with spatial resolution of 5 m and covering 4 km width and 20 km length wasavailable. Data were collected in the field during September/October 1999 andSeptember 2000 (1) to characterize desert-like surface features, (2) to find characteristicreflectance spectra of endmembers, and (2) to collect ground truth data for accuracyassessment. Little change of land cover/use was found between these two fieldworkperiods.

Field observations were sampled using stratified random method. The thematicstrata are geomorphic units, which were delineated using geopedologic photointerpretation approach (Zinck, 1988). Each observation point covers an area of 10 by10 m, to make sure that at least one pixel of HYMAP falls within each observation area.Observation in each point included information on geomorphic unit, surface soilproperties (percent gravel cover, Munsell soil colour, soil texture, calcareousness testwith 10% HCl, pH measurement and field electrical conductivity test) and landuse/cover information. The coordinates of the observation points were taken with a GPSreceiver (Garmin 12XL).

At each observation point, reflectance was measured using a field spectrometer(GER 3700) with full real-time data acquisition from 350 to 2,500 nm Reflectance wasmeasured by comparing the radiance of the target with the radiance of a reference panelmade of BaSO4. In addition, reflectance was measured in the laboratory. The measuredspectra in the field and in laboratory were resampled to match the response of theHYMAP scanner. For selecting endmembers two techniques were adopted: (1) use ofportable spectrometer in field and in laboratory, and (2) deriving endmembers from the

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purest pixels in the image. The identification of the endmembers is the most importantstep in hyperspectral image classification, since entering a wrong endmember wouldstrongly affect the result of classification. Boardman et al. (1995) explain a procedure tofind endmembers using n-dimensional scatter plot, where n is the number of bands. Tofind the purest pixels, the data are first transformed using Maximum Noise Fraction(MNF) algorithm resulting in MNF images with decreasing signal-to-noise ratio, theycontrast to the principal component transformation which maximises variance (Green etal., 1988). The Purest Pixel Index (PPI) is then computed by repeatedly projecting n-dimensional scatter plots onto a random unit vector. The extreme pixels in eachprojection are recorded and the total number of times each pixel is marked as extreme isnoted. By looking at these extreme pixels and comparing against the target spectrataking into account the field data, characteristic spectral curves (endmembers) wereestablished for each of the surface features (Figure 2).

Figure 2 Established image spectra of the identified “desert-like” soil.

Hyperspectral image classificationThe study aims to identify and determine the spatial distribution of the so-called

“desert-like” soil surface features by applying hyperspectral image classification. Twoclassification algorithms, spectral angle mapper and linear unmixing, were applied.Spectral Angle Mapper (SAM) is one of the techniques to classify hyperspectral image.The technique determines the similarity between two spectral by calculating the“spectral angle” between them, treating them as vectors in a space with dimensionalityequal to the n number of bands (Kruse et al., 1993) (Figure 3). Since it uses only the"direction" of the spectra, and not their "length," the method is insensitive to theunknown gain factor, thus avoiding requirement for any preprocessing technique suchas normalization of data for uniform intensity (Shrestha and Zinck, 2001).

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Figure 3 Two-dimensional illustration on the concept of spectral angle mapperfunction.

SAM determines the similarity of an unknown spectrum t to a reference spectrum r,by applying the following equation (Kruse et al., 1993):

→→

→→−

||r

||.||t

||r

.tcos 1 (1)

which can be written as:

∑∑

∑

==

=−5.0n

1i

2i

5.0n

1i

2i

n

1iii

1

rt

rtcos (2)

For each reference spectrum chosen in the analysis of a hyperspectral image, thespectral angle, between the two spectra as calculated for each channel, i, is determinedfor every image spectrum (pixel). This value, in radians, is assigned to thecorresponding pixel in the output SAM image, one output image for each referencespectrum. The derived spectral angle maps form a new data cube with the number ofbands equal to the number of reference spectra used in the mapping.

On the other hand, it is well known that ground surfaces constituting individualpixels of remotely sensed imagery often contain more than one land cover type, eachtype contributing to the overall spectral response (spectral mixing) to that pixel. Spectralmixing is reported to occur in a linear fashion if mixing is large (Singer and McCord,1979) and non-linear for microscopic mixing (Nash and Conel, 1974). Extensive reviewof mixture models is given by Ichoku and Karnieli (1996). With so much information,the well-known problem of mixed pixels can be solved by a mixture model. In a linearmodel, the reflectance ri, of a pixel in ith band is given by Smith et al. (1985) as follows:

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( ) i

n

1jijji RF.FR ε+=∑

=

(3)

Where: i=1,..,m and j=1,..,nRi is the reflectance of the mixed spectrum in image band i for each pixelFj is the fraction of each endmember j calculated by band,REij is the reflectance of endmember spectrum j in band ii is the band numberj is each of the endmembers and ε is the residual error.m represents the number of spectral bands while n stands for the number ofcomponents in the pixelEach classification algorithm results in so-called rule images or endmember

images, their values indicates spectral angle in case of SAM and abundance in case oflinear unmixing. The rule images need to be classified to get the final result. For SAM,threshold value of 0.09 radians or less was used whereas abundance of 0.50 or more wasselected for linear unmixing.

Results and discussionsThe results (Figure 4 and Table 1) show that area classified as calcareous and

gypsiferous soils are similar in both the classifications. Linear unmixing shows slightlymore area (1113 ha) under desert pavement as compared to SAM classification. SAMresult shows 16 % of the total area under saline conditions whereas it is negligible(<1%) in linear unmixing result. The unclassified area in SAM is 22% whereas it is36% in linear unmixing. The unknown pixels are the ones which fall beyond thethreshold limits. Both techniques show classification problems. SAM classificationresult shows the occurrence of saline soils in all the geomorphic units (Table 2). Sincethe development of salinity in Tabernas area is due to the evaporation of ground waterwhich comes to the surface by capillary rise, it is very unlikely that salinity can developin the hills or piedmonts. On the other hand, classification by linear unmixing under-estimates the salinity problem in the area.

Figure 4 Classification results.

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Table 1 Classification results.SAM classification Result Linear Unmixing classification

ResultClasses

Area (ha) Percentage Area (ha) PercentageDesert pavement 805 10 1113 14Saline soil 1247 16 2 <1Calcareous soil 2827 36 2610 34Gypsiferous soil 1204 16 1252 16Unknown 1732 22 2838 36

Table 2 Classification of features by geomorphic unitLandscape SAM result Desert-like

featuresha Linear unmixing result

Desert-like featuresha

Desert pavement 148 Desert pavement 252Saline soils 483 Saline soils 2Calcareous soils 1412 Calcareous soils 1447Gypsiferous soils 743 Gypsiferous soils 673

Hills

Unknown 929 Unknown 1341Desert pavement 126 Desert pavement 171Saline soils 267 Saline soils 0Calcareous soils 673 Calcareous soils 599Gypsiferous soils 126 Gypsiferous soils 91

Piedmont

Unknown 210 Unknown 542Desert pavement 509 Desert pavement 689Saline soils 509 Saline soils <1Calcareous soils 749 Calcareous soils 554Gypsiferous soils 321 Gypsiferous soils 485

Valley

Unknown 589 Unknown 948

For classification accuracy assessment, an error matrix or contingency table wasconstructed and the estimate of a measure of overall agreement between classificationresult and ground truth data was carried out by kappa statistics (Cohen, 1960). Kappa iscomputed as follows:

−−

=c

co

p1ppk (4)

where, po is the proportion of units in which there is agreement between groundtruth and the classification result, and pc is the proportion for which agreement isexpected by chance. Po and pc can be calculated using the observation numbers in therow and columns from the error matrix as follows:

N

Xp

r

1iii

o

∑== and 2

r

1iii

c N

XXp

∑=

++

= (5)

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where, Xi+ is the sum of the ith row and X+I is the sum of the ith column, and N is thetotal number of observations. The error matrices are shown in Table 3 and 4. Overallaccuracy of linear unmixing seems to be better (0.75) as compared to SAM (0.60). Thekappa value, which takes into account not only complete agreement between the groundtruths but also the agreements by chance, shows that a large portion of the classagreement for SAM could be due to chance agreement since its kappa value is 0.44which is lower than the overall accuracy. For linear unmixing the kappa value is higher(0.63).

Table 3 Error matrix for SAM classification result.Ground truth (test pixels)Classification

Desertpavement

Salinesoils

Calcareoussoils

Gypsiferoussoils

Testpixels

Unknown Total testpixels

Desertpavement

149(0.6)

65 33 2 249 0 249

Saline soils 2829(0.48)

4 0 61 0 61

Calcareoussoils 17 26

59(0.56)

4 106 24 130

Gypsiferoussoils 0 7 38

95(0.68)

140 16 156

Reliability 0.77 0.23 0.44 0.94Average accuracy = 0.58 Average reliability = 0.59

Overall accuracy = 0.60Kappa value (k) = 0.44

Table 4 Error matrix for linear unmixing classification resultGround truth (test pixels)

Desertpavement

Salinesoils

Calcareoussoils

Gypsiferoussoils

Testpixels

Unknown Total testpixels

Desertpavement

152(0.95)

0 7 0 159 90 249

Saline soils 331(0.03)

2 0 36 25 61

Calcareoussoils 25 0

63(0.71)

1 89 41 130

Gypsiferoussoils 5 3 28

98(0.73)

134 22 156

Reliability 0.71 0.25 0.63 0.99Average accuracy = 0.61 Average reliability = 0.64

Overall accuracy = 0.75Kappa value (k) = 0.63

To test whether the two classification results were significantly different, themethod described by Cohen (1960) and elaborated by Skidmore (1999) and Rossiter(2001) were used. The method uses the normal curve deviate statistics (z) and the k-values (k1, k2) and their associated variance ( 1k

2σ , 2k2σ ) as follows:

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2k2

1k2

21 kkzσ−σ

−= (6)

With k1 = 0.44, k2 = 0.63, 1kσ = 0.0259 and

2kσ = 0.0338 we find that z = 4.6. Thisvalue substantially exceeds zt= 1.96 (at ∀ = 0.05). Thus we can conclude that there is asignificant difference between the two classification results.

ConclusionSelection of the endmembers is of utmost importance for hyperspectral

classification since choosing a wrong one can make great difference in classificationresult. Although the result given by linear unmixing seems to be more realistic ascompared to SAM, one has to be very careful in applying the technique since unmixingis purely based on the number of endmembers decided by the user. The use of ancillarydata such as geomorphic map of the area can prove to be useful in interpreting theresults.

AcknowledgementsDavid Rossiter reviewed this paper. His comments are duly acknowledged.

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