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Unformatted text preview: . materials that are not actually present. If the best-matching reference spectrum has a sufficient fit to the image spectrum, then this material is probably the dominant one in the mixture and the pixel is assigned to this material. If no reference spectrum achieves a sufficient match, then no endmember dominates, and the pixel should be left unassigned. The result is a “material map” of the image that portrays the dominant material for most of the image cells, such as the example shown below. Sample mixed spectra can be included in the library to improve the mapping, but it is usually not possible to include all possible mixtures (and all mixture proportions) in the reference library.
Minerals Alunite Kaolinite Alunite + Kaolinite Montmorillonite Chalcedony Reflectance Mineral map for part of the Cuprite AVIRIS scene, created by matching image spectra to mineral spectra in the USGS Spectral Library. White areas did not produce a sufficient match to any of the selected reflectance spectra, and so are left unassigned. page 17 Introduction to Hyperspectral Imaging Spectral Matching Methods
The shape of a reflectance spectrum can usually be broken down into two components: broad, smoothly changing regions that define the general shape of the spectrum and narrow, trough-like absorption features. This distinction leads to two different approaches to matching image spectra with reference spectra. Many pure materials, such as minerals, can be recognized by the position, strength (depth), and shape of their absorption features. One common matching strategy attempts to match only the absorption features in each candidate reference spectrum and ignores other parts of the spectrum. A unique set of wavelength regions is therefore examined for each reference candidate, determined by the locations of its absorption features. The local position and slope of the spectrum can affect the strength and shape of an absorption feature, so these parameters are usually determined relative to the continuum: the upper limit of the spectrum’s general shape. The continuum is computed for each wavelength subset and removed by dividing the reflectance at each spectral channel by its corresponding continuum value. Absorption features can then be matched using a set of derived values (including depth and the width at half-depth), or by using the complete shape of the feature. These types of procedures have been 1.0 C organized into an expert 0.8 system by researchers at the U.S. Geological Sur0.6 B vey Spectroscopy Lab 0.4 (Clark and others, 1990).
0.2 Many other materials, A such as rocks and soils, 0 0.5 1.0 1.5 2.0 2.5 may lack distinctive abWavelength (µ m) sorption features. These spectra must be character- Reflectance spectrum for the mineral gypsum (A) with ized by their overall shape. several absorption features. Curve B shows the continuum for the spectrum, and C the spectrum after Matching procedures uti- removal of the continuum. lize full spectra (omitting noisy image bands severely affected by atmospheric absorption) or a uniform wavelength subset for all candidate materials. One approach to matching seeks the spectrum with the minimum difference in reflectance (band per band) from the image spectrum (quantified by the square root of the sum of the squared errors). Another approach treats each spectrum as a vector in spectral space and finds the reference spectrum making the smallest angle with the observed image spectrum. Reflectance page 18 Introduction to Hyperspectral Imaging Linear Unmixing
Linear unmixing is an alternative approach to simple spectral matching. Its underlying premise is that a scene includes a relatively small number of common materials with more or less constant spectral properties. Furthermore, much of the spectral variability in a scene can be attributed to spatial mixing, in varying proportions, of these common endmember components. If we can identify the endmember spectra, we can mathematically “unmix” each pixel’s spectrum to identify the relative abundance of each endmember material. The unmixing procedure models each image spectrum as the sum of the fractional abundances of the endmember spectra, with the further constraint that the fractions should sum to 1.0. The best-fitting set of fractions is found using the same spectral-matching procedure described on the previous page. A fraction image for each endmember distills the abundance information into a form that is readily interpreted and manipulated. An image showing the residual error for each pixel helps identify parts of the scene that are not adequately modeled by the selected set of endmembers. The challenge in linear unmixing is to identify a set of spectral endmembers that correspond to actual physical components on the surface. Endmembers can be defined directly from the image using field information or an empirical selection technique such as the one outlined on the next page can be used. Alternatively, endmember reflectance spectra can be selected from a reference library, but this approach requires that the image has been accurately converted to refl...
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This note was uploaded on 12/16/2010 for the course ENV 148 taught by Professor Chang during the Spring '10 term at APU Japan.
- Spring '10