Spectral unmixing versus spectral angle mapper for land degradation assessment a case study in southern spain (2)

In this study, we compare linear unmixing and spectral angle matching techniques to assess the classification performance for identifying and mapping ‘desert like’ surface features in so

Spectral unmixing versus spectral angle mapper for

land 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, 7500

AA Enschede, The Netherlands

(2) Bureau of Soils and Water Management, Quezon City, Philippines

(3) Forest Science Institute, Hanoi, Vietnam

Abstract

Unlike 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 systems that acquire data in many narrow-wavelength bands allows the use of almost continuous reflectance data in studies of the Earth’s surface This not only produces laboratory-like reflectance spectra with absorption bands specific to object properties, but also helps increase accuracy of mapping surface features Classification by means of spectral matching thus becomes more feasible With so much information, the well-known problem of mixed pixels can be solved by a mixture model, which is commonly assumed to occur in a linear fashion

In this study, we compare linear unmixing and spectral angle matching techniques

to 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 pixel

to a dominant class, the data is affected by illumination variations caused by topography, so that selection of end member can be biased By comparison, the spectral angle matching technique compares only the angle between known and unknown spectra, which uses only the direction and not the length of the spectral vector It is therefore insensitive to the gain factor caused by surface illumination conditions and thus more suitable in areas with high illumination differences On the other hand, linear unmixing calculates, for each pixel, the abundance of pixel components Present study shows that linear unmixing seems to provide more realistic results for mapping “desert like” surface features as compared to spectral angle mapper

Keywords: hyperspectral, linear unmixing, spectral matching, spectral angle_desert

like_surface features

Introduction

The concept of desertification, considered a severe stage of land degradation, is responsible for the manifestation of “desert-like” conditions especially in dryland areas outside the desert boundaries (Rapp, 1986) Climatic conditions together with geomorphologic processes help in molding the so-called desert-like soil surface

features The identification of these soil features serves as a useful input in assessing the process 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 not

in general provide satisfactory results in mapping soil properties, because their bandwidth of 100 to 200 µm cannot resolve diagnostic spectral features of terrestrial materials (De Jong, 1994) Hyperspectral data provide greater classification accuracies

as compared to broadband instruments (Pieters and Mustard, 1988; Kruse, 1989; Clark

et al., 1990) Increased spatial resolution also facilitates detailed surficial mapping.

However, analytical techniques developed for analysis of broadband spectral data are incapable of taking advantage of the full range of information present in hyperspectral remote sensing imagery (Cloutis, 1996) Since hyperspectral data allows the use of almost continuous reflectance data in studies of the Earth’s surface, analysis of reflectance spectra with absorption bands specific to object properties can be carried out

Study area

The 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 airborne hyperspectral image, with its flight line starting at 37o02’32” N and 2o30’14” W and ending at 37o04’25” N and 2o16’40” W The Tabernas basin is a structural depression in the Alpine nappes of the Betic Cordilleras of southern Spain, which is bounded by major strike-slip fault (Kleverlaan, 1989) The terrain is relatively rugged with very sparse vegetation The mountain ridges on north and south sides of the basin act as main barriers for precipitation and have lead to pronounced dry conditions leading to desertification The climate is characterised as semi-arid with long hot summers Annual precipitation 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.

The soils, in general, are shallow (less than 50 cm depth), except in the valleys and occasionally on the piedmonts On the steeper slopes they are mostly derived from the weathering of the exposed bedrock, while in the valleys they consist of irregular deposits of materials coming from the surrounding mountains and hillands brought down by flash floods Soil texture is commonly sandy loam to loamy sand with more than 40% coarse fragments on the surface Saline soils occur in the valleys with electrical conductivity values of more than 2 dS m-1 Surface crusting is common particularly in saline areas Most of the soils are strongly calcareous with calcium carbonate content ranging from 2-31% Generally, soils in the hillands and piedmonts are classified as Lithic Torriorthents and the deeper soils are Typic Torriorthents according to the USDA Soil Taxonomy (1998) In the valleys, soils are classified as Fluventic Haplocambids and towards the upper terraces, they are classified as Typic Haplocambids

Desert-like soil surface features are common in the area The abundance of uncovered loose materials is readily available for transport either by wind or water leaving 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 high evaporation rates, lack of leaching and percolation to deeper horizons, many low-lying areas are saline and alkaline Calcium carbonate and gypsum are often present in abundance, forming hard pans and contributing to the formation of surface crust

Methods and Techniques Applied Data collection

An 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 was available Data were collected in the field during September/October 1999 and September 2000 (1) to characterize desert-like surface features, (2) to find characteristic reflectance spectra of endmembers, and (2) to collect ground truth data for accuracy assessment Little change of land cover/use was found between these two fieldwork periods

Field observations were sampled using stratified random method The thematic strata are geomorphic units, which were delineated using geopedologic photo interpretation approach (Zinck, 1988) Each observation point covers an area of 10 by

10 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 soil properties (percent gravel cover, Munsell soil colour, soil texture, calcareousness test with 10% HCl, pH measurement and field electrical conductivity test) and land use/cover information The coordinates of the observation points were taken with a GPS receiver (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 was measured by comparing the radiance of the target with the radiance of a reference panel made of BaSO4 In addition, reflectance was measured in the laboratory The measured spectra in the field and in laboratory were resampled to match the response of the HYMAP scanner For selecting endmembers two techniques were adopted: (1) use of portable spectrometer in field and in laboratory, and (2) deriving endmembers from the

purest pixels in the image The identification of the endmembers is the most important step in hyperspectral image classification, since entering a wrong endmember would

strongly affect the result of classification Boardman et al (1995) explain a procedure to

find endmembers using n-dimensional scatter plot, where n is the number of bands To find the purest pixels, the data are first transformed using Maximum Noise Fraction (MNF) algorithm resulting in MNF images with decreasing signal-to-noise ratio, they

contrast to the principal component transformation which maximises variance (Green et

al., 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 each projection are recorded and the total number of times each pixel is marked as extreme is noted By looking at these extreme pixels and comparing against the target spectra taking into account the field data, characteristic spectral curves (endmembers) were established for each of the surface features (Figure 2)

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

Hyperspectral image classification

The study aims to identify and determine the spatial distribution of the so-called

“desert-like” soil surface features by applying hyperspectral image classification Two classification 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 dimensionality

equal 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 the unknown gain factor, thus avoiding requirement for any preprocessing technique such

as normalization of data for uniform intensity (Shrestha and Zinck, 2001)

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

function

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

t

which can be written as:



















































∑

=

=

=

−

5 0 n

1 i

2 i

5 0 n

1 i

2 i

n

1 i i i 1

r t

r t

For each reference spectrum chosen in the analysis of a hyperspectral image, the

spectral angle, between the two spectra as calculated for each channel, i, is determined

for every image spectrum (pixel) This value, in radians, is assigned to the corresponding pixel in the output SAM image, one output image for each reference spectrum The derived spectral angle maps form a new data cube with the number of bands equal to the number of reference spectra used in the mapping

On the other hand, it is well known that ground surfaces constituting individual pixels of remotely sensed imagery often contain more than one land cover type, each type contributing to the overall spectral response (spectral mixing) to that pixel Spectral mixing 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 review

of 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 linear model, the reflectance ri, of a pixel in ith band is given by Smith et al (1985) as follows:

( ) i n

1 j

ij j

Where: i =1, ,m and j=1, ,n

Ri is the reflectance of the mixed spectrum in image band i for each pixel

Fj is the fraction of each endmember j calculated by band,

REij is the reflectance of endmember spectrum j in band i

i is the band number

j is each of the endmembers and ε is the residual error

m represents the number of spectral bands while n stands for the number of components in the pixel

Each classification algorithm results in so-called rule images or endmember images, their values indicates spectral angle in case of SAM and abundance in case of linear 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 was selected for linear unmixing

Results and discussions

The results (Figure 4 and Table 1) show that area classified as calcareous and gypsiferous soils are similar in both the classifications Linear unmixing shows slightly more area (1113 ha) under desert pavement as compared to SAM classification SAM result 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 is 36% in linear unmixing The unknown pixels are the ones which fall beyond the threshold limits Both techniques show classification problems SAM classification result shows the occurrence of saline soils in all the geomorphic units (Table 2) Since the development of salinity in Tabernas area is due to the evaporation of ground water which comes to the surface by capillary rise, it is very unlikely that salinity can develop

in the hills or piedmonts On the other hand, classification by linear unmixing under-estimates the salinity problem in the area

Figure 4 Classification results.

Table 1 Classification results.

SAM classification Result Linear Unmixing classification

Result Classes

Area (ha) Percentage Area (ha) Percentage Desert pavement 805 10 1113 14

Saline soil 1247 16 2 <1

Calcareous soil 2827 36 2610 34

Gypsiferous soil 1204 16 1252 16

Table 2 Classification of features by geomorphic unit

Landscape SAM result Desert-like

features

ha Linear unmixing result

Desert-like features

ha

Desert pavement 148 Desert pavement 252

Calcareous soils 1412 Calcareous soils 1447 Gypsiferous soils 743 Gypsiferous soils 673 Hills

Desert pavement 126 Desert pavement 171

Calcareous soils 673 Calcareous soils 599 Gypsiferous soils 126 Gypsiferous soils 91 Piedmont

Desert pavement 509 Desert pavement 689

Calcareous soils 749 Calcareous soils 554 Gypsiferous soils 321 Gypsiferous soils 485 Valley

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









−−

=

c

c o

p 1

p p

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

N

X p

r

1 i ii o

∑=

r

1 i

i i c

N

X X

p ∑= + +

where, Xi+ is the sum of the ith row and X+I is the sum of the ith column, and N is the total number of observations The error matrices are shown in Table 3 and 4 Overall accuracy of linear unmixing seems to be better (0.75) as compared to SAM (0.60) The kappa value, which takes into account not only complete agreement between the ground truths but also the agreements by chance, shows that a large portion of the class agreement for SAM could be due to chance agreement since its kappa value is 0.44 which 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

Desert pavement

Saline soils

Calcareous soils

Gypsiferous soils

Test pixels

Unknown Total test

pixels Desert

pavement

149 (0.6) 65 33 2 249 0 249 Saline soils 28 29

(0.48) 4 0 61 0 61 Calcareous

soils 17 26

59 (0.56) 4 106 24 130 Gypsiferous

soils 0 7 38

95 (0.68) 140 16 156 Reliability 0.77 0.23 0.44 0.94

Average accuracy = 0.58 Average reliability = 0.59

Overall accuracy = 0.60 Kappa value (k) = 0.44

Table 4 Error matrix for linear unmixing classification result

Ground truth (test pixels) Desert

pavement

Saline soils

Calcareous soils

Gypsiferous soils

Test pixels

Unknown Total test

pixels Desert

pavement

152 (0.95) 0 7 0 159 90 249 Saline soils 33 1

(0.03) 2 0 36 25 61 Calcareous

soils 25 0

63 (0.71) 1 89 41 130 Gypsiferous

soils 5 3 28

98 (0.73) 134 22 156 Reliability 0.71 0.25 0.63 0.99

Average accuracy = 0.61 Average reliability = 0.64

Overall accuracy = 0.75 Kappa value (k) = 0.63

To test whether the two classification results were significantly different, the method 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 (σ ,2 1 σ ) as follows:2 2

2 2 1 2 2

k z

σ

− σ

−

With k1 = 0.44, k2 = 0.63,

1

σ = 0.0259 and σ = 0.0338 we find that z = 4.6 This2 value substantially exceeds zt= 1.96 (at ∀ = 0.05) Thus we can conclude that there is a significant difference between the two classification results

Conclusion

Selection of the endmembers is of utmost importance for hyperspectral classification since choosing a wrong one can make great difference in classification result Although the result given by linear unmixing seems to be more realistic as compared to SAM, one has to be very careful in applying the technique since unmixing

is purely based on the number of endmembers decided by the user The use of ancillary data such as geomorphic map of the area can prove to be useful in interpreting the results

Acknowledgements

David Rossiter reviewed this paper His comments are duly acknowledged

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