Spectral Angle Mapper Classification

The Spectral Angle Mapper Classification (SAM) is an automated method for directly comparing image spectra to a known spectra (usually determined in a lab or in the field with a spectrometer) or an endmember. This method treats both (the questioned and known) spectra as vectors and calculates the spectral angle between them. This method is insensitive to illumination since the SAM algorithm uses only the vector direction and not the vector length. The result of the SAM classification is an image showing the best match at each pixel. This method is typically used as a first cut for determining the mineralogy and works well in areas of homogeneous regions. The USGS maintains a large spectral library, mostly composed of mineral and soil types, which image spectra can be directly compared.

Spectral Unmixing/Matched Filtering

Most surfaces on the earth, geologic or vegetated, are not homogeneous which results in a mixture of signatures characterized by a single pixel. Depending on how the materials are mixing on the surface results in the type of mathematical models capabale of determining their abundances. If the mixing is rather large, than the mixing of the signatures can be represented as a linear model. However, if the mixing is microscopic, then the mixing models become more complex and non-linear.

The first step to determining the abundances of materials is to select endmembers, which is the most difficult step in the unmixing process. The ideal case would consist of a spectral library which consists of endmembers when linearily combined can form all observed spectra [Kruse et. al, 1997]. A simple vector-matrix multiplication between the inverse library matrix and an observed mixed spectrum gives an estimate of the abundance of the library endmembers for the unknown spectrum.

N-Dimensional visualization techniques can be used to select endmembers within a scene. The image below represents a 2-Dimensional representation of endmember selection using ENVI. Extreme pixels which ultimately correspond to endmembers can be determined by rotating this scatter plot in n-dimensions.

2-Dimensional scatter plot of Eigenvectors 1 & 2.

Matched filtering is based on a well known signal processing method and creates a quick means of detecting specific minerals based on matches to specific library or endmember spectra. The matched filtering algorithm maximizes the response of a known endmember while supressing the response of the background. The result of the matched filtering resembles the results from the linear unmixing methods and are usually represented as a greyscale image with values ranging from 0 to 1 which corresponds the the relative degree of the match.

Classified image of 1995 AVIRIS frame over Cuprite, Nevada using Spectral Unmixing Techniques

Other Classification Techniques

Classification and feature extraction methods have been commonly used for many years for the mapping of minerals and vegetative cover of multispectral data sets. However, conventional classification methods, such as a Gaussian Maximum Likelihood algorithm, cannot be applied to hyperspectral data due to the high dimensionality of the data.

The difficulty in using many classification methods based upon conventional multivariate statistical approaches, is that many of these methods rely on having a non-singular class-specific covariance matrices for all classes [Benediktsson et. al, 1995]. When working with high-dimensional data sets, it is likely that the covariance matrices will be singular when using a limited (with respect to the number of input bands) amount of training samples.

A nonparametric classifier, such a neural network, and other feature extraction methods can be used to accurately classify a hyperspectral image. Feature extraction methods, such as the decision boundary feature extraction (DBFE) can extract the features necessary to achieve classification accuracy while reducing the amount of data analyzed in feature space.