Subpixel analysis; Spectral mixing/unmixing; Linear spectral mixture model (LSMM)
Spectral Mixture Analysis (SMA) is a technique for estimating the proportion of each pixel that is covered by a series of known cover types - in other words, it seeks to determine the likely composition of each image pixel. Pixels that contain more than one cover type are called mixed pixels. “Pure” pixels contain only one feature or class. For example, a mixed pixel might contain vegetation, bare ground, and soil crust. A pure pixel would contain only one feature, such as vegetation. Mixed pixels can cause problems in traditional image classifications (e.g., supervised or unsupervised classification) because the pixel belongs to more than one class but can be assigned to only a single class. One way to address the problem of mixed pixels is to use SMA, (sometimes called subpixel analysis), and hyperspectral imagery.
Spectral mixture analysis (SMA) determines the component parts of mixed pixels by predicting the proportion of a pixel that belongs to a particular class or feature based on the spectral characteristics of its endmembers. It converts radiance to fractions of spectral endmembers that correspond to features on the ground.
Spectral endmembers are the ‘pure’ spectra corresponding to each of the land cover classes. Ideally, spectral endmembers account for most of the image’s spectral variability and serve as a reference to determine the spectral make up of mixed pixels. Thus the definition of land cover classes, and selection of appropriate endmembers for each of these classes, are both critical in SMA. Endmembers obtained from the actual image are generally preferred because no calibration is needed between selected endmembers and the measured spectra. These endmembers are assumed to represent the purest pixels in the image.
Selecting endmembers for natural systems can be exceedingly difficult because:
Additionally, SMA makes several assumptions in estimating the composition of each image pixel:
Process of information extraction from digital imagery using linear spectral unmixing methods:
Note that it is possible that a solution can mathematically satisfy a model, but this solution may not be physically realistic, e.g. a negative fraction for an endmember. In most practical applications of SMA, constraints, or limits, are placed on model solutions. In the Linear mixing model solutions are limited to positive numbers and component fractions sum to 1.
One alternative to linear SMA is Multiple Endmember Spectral Mixture Analysis (MESMA). The ideal condition of endmembers (from the assumptions above) is difficult to obtain. A method to address violations of the assumptions is MESMA. MESMA differs from SMA because it allows the number and the quantity of endmembers to vary pixel by pixel. This technique uses whichever model that has the smallest root mean square (rms) error when compared to spectral curve of the pixel.
Cover estimates for relevant classes.
Gross, H. N. and J. R. Schott. 1996. Hyperspectral Remote Sensing and Applications. Proceedings of Society of Photonic and Instrumentation Engineers (SPIE) v.2821, pp. 30-41. Sylvia S. Shen (ed). Applied spatial resolution enhancement and spectral mixture analysis to hyperspectral images. Combines spectral mixture analysis with spatial sharpening using step-wise unmixing.
Hostert, P., A. Roder, and J. Hill. 2003. Coupling spectral unmixing and trend analysis for monitoring of long-term vegetation dynamics in Mediterranean rangelands. Remote Sensing of the Environment 87:183-197. Evaluation of using long, time series LandSat TM and MSS to detect indicators of land degradation. Used linear spectral unmixing approach with the time series analysis of vegetation fraction images to explain changes in land cover.
Shimabukuro, Y. E. and J. A. Smith. 1991. The least-squares mixing models to generate fraction images derived from remote sensing multispectral data. IEEE Transactions on Geoscience and Remote Sensing 29(1):16-20. Proposed using the cosine of angles between candidate components as a quantitative way to measure separability of endmembers. Results suggest the uncertainty in spectral mixing and unmixing stem from inadequate reference spectra instead of the commonly used basic least-squares method itself.
Sohn, Y. and R. M. McCoy. 1997. Mapping desert shrub rangeland using spectral unmixing and modeling spectral mixtures with TM data. PERS 63(6): 707-716. Discussed method to measure the separability of potential endmembers quantitatively and subsequently derive spectral endmembers objectively. Found unmixing techniques provided moderate estimates of vegetation fractions in arid rangeland with TM data and that the degree of spectral pureness of endmembers must be consistent.
Nielson, A. A. 2001. Spectral Mixture Analysis: Linear and Semi-parametric Full and Iterated Partial Unmixing in Multi- and Hyperspectral Image Data 2001. Journal of Mathematical Imaging and Vision. 15(1-2):17 – 37. As a supplement or an alternative to classification of hyperspectral image data linear and semi-parametric mixture models are considered in order to obtain estimates of abundance of each class or end-member in pixels with mixed membership.
Williams, D. and W. Kepner. 2002. Imaging Spectroscopy for Determining Rangeland Stressors to Western Watersheds: Pollution Prevention and New Technology. United States Environmental Protection Agency. EPA/600/R-01/004. Used imagery to assess vegetation and soil of rangelands in the western U.S. in order to develop indicators of rangeland quality.
Adams, J. B., D. E. Sabol, V. Kapos, R. A. Filho, D. A. Roberts, M. O. Smith, and A. R. Gillespie. 1995. Classification of multispectral images based on fractions of endmembers: Application to land-cover change in the Brazilian Amazon. Remote Sensing of Environment, 52, 137−154.
Carvalho, Jr., O. A. and R. F. Guimarães. Employment of the Multiple Endmember Spectral Mixture Analysis (MESMA) Method in Mineral Analysis. 11th JPL Airborne Geoscience Workshop, JPL, 4-8 March, 2002.
Center for Remote Imaging, Sensing, and Processing (CRISP). http://www.crisp.nus.edu.sg/~research/tutorial/image.htm accessed 28Jan10
Hostert, P. A. Roder, and J. Hill. 2003. Coupling spectral unmixing and trend analysis for monitoring of long-term vegetation dynamics in Mediterranean rangelands. Remote Sensing of the Environment 87:183-197.
ERDAS Imagine Spectral Analysis User’s Guide, September 2008.
Gross, H. N. and J. R. Schott. 1996. Hyperspectral Remote Sensing and Applications. Proceedings of Society of Photonic and Instrumentation Engineers (SPIE), 2821:30-41. Sylvia S. Shen (ed).
Lillesand, T. M. and R. W. Kiefer, 2004. Remote sensing and image interpretation, 5th ed. John Wiley and Sons Inc, New Jersey.
Lu, D. and Q. Weng. 2006. Spectral mixture analysis of ASTER images for examining the relationship between urban thermal features and biophysical descriptors in Indianapolis, Indiana, USA Remote Sensing of Environment 104: 157–167.
Mustard, J. F. and J. M. Sunshine. 1999. Spectral analysis for earth science: Investigations using remote sensing data. In A. N. Rencz (Ed.), Remote sensing for the earth sciences: Manual of remote sensing, vol. 3 (3rd ed.) New York: John Wiley and Sons.
Nielsen, A. A. 2001. Spectral Mixture Analysis: Linear and Semi-parametric Full and Iterated Partial Unmixing in Multi- and Hyperspectral Image Data J of Math Imaging and Vision. International Journal of Computer Vision. 42(1-2):17 – 37.
Rashed, T. et al. 2001. Revealing the anatomy of cities through spectral mixture analysis of multispectral satellite imagery: a case study of the Greater Cairo Region, Egypt. Geocarto International 16(4): 4-15.
Shimabukuro, Y. E. and J. A. Smith. 1991. The least-squares mixing models to generate fraction images derived from remote sensing multispectral data. IEEE Transactions on Geoscience and Remote Sensing 29(1):16-20.
Smith, M. O., S. L. Ustin, J. B Adams, and A. R. Gillespie. 1990. Vegetation in Deserts: I. A regional measure of abundance from multispectral images. Remote Sensing of Environment, 31:1−26.
Sohn, Y. and R. M. McCoy. 1997. Mapping desert shrub rangeland using spectral unmixing and modeling spectral mixtures with TM data. PERS 63(6): 707-716.
Williams, D. and W. Kepner. 2002. Imaging Spectroscopy for Determining Rangeland Stressors to Western Watersheds. Pollution Prevention and New Technology. United States Environmental Protection Agency. EPA/600/R-01/004.
SMA requries image analysis software such as:
ERDAS: Subpixel Classifier http://www.erdas.com/Homepage.aspx
ENVI image analysis http://www.exelisvis.com/ProductsServices/ENVI/Capabilities.aspx
Applied Analysis Inc.: Subpixel Classifier http://www.discover-aai.com/
Viper Tools http://www.vipertools.org
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