Symposium no. 52
Paper no. 1141
Presentation: oral
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
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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.
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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
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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 ndimensional 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).
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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):
→ . → t r cos → || . || → || || t r
(1)
n t r ∑ i i i=1 cos −1 0 . 5 0 . 5 n n t 2 r 2 ∑i ∑ i i=1 i=1
(2)
−1
which can be written as:
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:
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R i = ∑ (Fj .RFij ) + ε i n
(3)
j=1
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 underestimates the salinity problem in the area.
Figure 4 Classification results.
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SHRESTHA ET AL Table 1 Classification results. Classes
Desert pavement Saline soil Calcareous soil Gypsiferous soil Unknown
SAM classification Result Area (ha) 805 1247 2827 1204 1732
Linear Unmixing classification Result Area (ha) Percentage 1113 14 2 <1 2610 34 1252 16 2838 36
Percentage 10 16 36 16 22
Table 2 Classification of features by geomorphic unit Landscape Hills
Piedmont
Valley
SAM result Desert-like features Desert pavement Saline soils Calcareous soils Gypsiferous soils Unknown Desert pavement Saline soils Calcareous soils Gypsiferous soils Unknown Desert pavement Saline soils Calcareous soils Gypsiferous soils Unknown
ha
Linear unmixing result Desert-like features Desert pavement Saline soils Calcareous soils Gypsiferous soils Unknown Desert pavement Saline soils Calcareous soils Gypsiferous soils Unknown Desert pavement Saline soils Calcareous soils Gypsiferous soils Unknown
148 483 1412 743 929 126 267 673 126 210 509 509 749 321 589
ha 252 2 1447 673 1341 171 0 599 91 542 689 <1 554 485 948
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: p − pc k = o 1 − pc
(4)
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: r
po =
∑X i =1
N
r
ii
and p c =
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∑X
i+
i =1
N2
X +i (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 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. Classification Desert pavement
Saline soils
Ground truth (test pixels) Calcareous Gypsiferous Test soils soils 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
140
16
156
95 (0.68) 0.23 0.44 0.94 Average reliability = 0.59
Reliability 0.77 Average accuracy = 0.58
38
Overall accuracy = 0.60 Kappa value (k) = 0.44
Table 4 Error matrix for linear unmixing classification result
Desert pavement
Desert pavement 152 (0.95)
Saline soils
Ground truth (test pixels) Calcareous Gypsiferous Test soils soils pixels
Unknown Total test pixels
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
134
22
156
Reliability 0.71 Average accuracy = 0.61
98 (0.73) 0.25 0.63 0.99 Average reliability = 0.64 28
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 kvalues (k1, k2) and their associated variance ( σ 2 k1 , σ 2 k 2 ) as follows:
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SHRESTHA ET AL z=
k1 − k 2 σ 2 k1 − σ 2 k 2
(6)
With k1 = 0.44, k2 = 0.63, σ k1 = 0.0259 and σ k2 = 0.0338 we find that z = 4.6. This 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. References Boardman, J.W., F.A. Kruse and R.O. Green. 1995. Mapping target signatures via partial unmixing of AVIRIS data. Fifth JPL Airborne Earth Science Workshop, JPL Publication, pp. 23-26. Center for the Study of Earth from Space (CSES). 1992. SIPS User’s Guide, The spectral image processing system. Vol. 1.1. University of Colorado, Boulder. 74 p. Clark, R.N., T.V.V. King, M. Klejwa, G.A. Swayze and N. Vergo. 1990. High spectral resolution reflectance spectroscopy of minerals. J. Geophys. Res. 95(12):653-680. Cloutis, E.A. 1996. Hyperspectral geological remote sensing: evaluation of analytical techniques. Int. J. Remote Sensing. 17(12):2215-2242. Cohen, J. 1960. A coefficient of agreement for nominal scales. Educational and Psychological Measurement vol. 20, pp. 37-46. De Jong, S.M. 1994. Applications of reflective remote sensing for land degradation studies in a Mediterranean environment. Netherlands Geographical Studies. KNAG, Utrecht. 240 p. Green, A.A., M. Berman, P. Switzer and M.D. Craig. 1988. A transformation for ordering multispectral data in terms of image quality with implications for noise removal. IEEE Transactions on geoscience and remote sensing 26(1):65-74. Ichoku, C. and A. Karnieli. 1996. A review of mixture modeling techniques for subpixel land cover estimation. Remote Sensing Reviews 13:161-186. Kleverlaan, K. 1989. Neogene history of the Tabernas basin (SE Spain) and its tortonian submarine fan development. Geologie Mijnbouw 68:421-432. Kruse, F.A. 1989. Spectral mapping with Landsat Thematic Mapper and imaging spectroscopy for precious metals exploration, pp. 17-28. In Proc. of the seventh thematic conference on remote sensing for exploration geology. Calgary, Alberta. 2-6 October 1989.
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Kruse, F.A., A.B. Lefkoff, J.W. Boardman, K.B. Heidebrecth, A.T. Shapiro, J.P. Barloon and A.F. Goetz. 1993. The spectral image processing system (SIPS)Interactive visualization and analysis of imaging spectrometer data. Remote sensing of environment 44:145-163. Nash, E.B. and J.E. Conel. 1979. Spectral reflectance systematics for mixtures of powdered hypersthene, labradorite, and ilmenite. Journal of Geophysical Research 79:1615-1621 Pieters, C.M. and J.F. Mustard. 1988. Exploration of crustal/mantle material for the earth and moon using reflectance spectroscopy. Remote Sensing of Environment 24:151-178. Rapp, A. 1986. Introduction to soil degradation processes in drylands. Climatic change 9, pp. 19-31. Rossiter, D.G. 2001. Assessing the thematic accuracy of area-class soil maps. Preprint submitted for publication in Geoderma. Shrestha, D.P. and J.A. Zinck. 2001. Land use classification in a mountainous areas: integration of image processing, digital elevation data and field knowledge (application to Nepal). JAG. 3(1):78-85. Singer, R.B. and T.B. McCord. 1979. Mars: Large scale mixing of bright and dark surface materials and implications for analysis of spectral reflectance. Proceedings Lunar and Planetary Science Conference, 10th, pp. 1835-1848. Skidmore, A.K. 1999. Accuracy assessment of spatial information, pp. 197-209. In A. Stein, F. van der Meer and B. Gorte (eds.). Spatial Statistics for Remote Sensing. Zinck, J.A. 1988. Physiography and soils. Lecture notes on soil survey course, subject matter: K6, ITC, Enschede, The Netherlands.
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