Material Discovery
In this chapter, we treat scenes as being composed of a tapestry of materials which can then be unmixed into end members. This leads to a treatment by which materials are intrinsic to the scene. Subsequently, we elaborate on how consistency may be imposed
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Material Discovery
For spectral image classification, each pixel is associated with a spectrum which can be viewed as an input vector in a high-dimensional space. Thus algorithms from statistical pattern recognition and machine learning have been adopted to perform pixel-level feature extraction and classification (Landgrebe 2002). These methods either directly use the complete spectra, or often make use of preprocessing and dimensionality reduction steps at input and attempt to recover statistically optimal solutions. Linear dimensionality reduction methods are based on the linear projection of the input data to a lower dimensional feature space. Typical methods include principal component analysis (PCA) (Jolliffe 2002), linear discriminant analysis (LDA) (Fukunaga 1990) and projection pursuit (Jimenez and Landgrebe 1999). Almost all linear feature extraction methods can be kernelised, resulting in kernel PCA (Schölkopf et al. 1999), kernel LDA (Mika et al. 1999) and kernel projection pursuit (Dundar and Landgrebe 2004). These methods exploit non-linear relations between different segments in the spectra by mapping the input data onto a highdimensional space through different kernel functions (Scholkopf and Smola 2001). From an alternative viewpoint, features of the absorption spectrum can be used as signatures for chemicals and their concentrations (Sunshine et al. 1990). Absorption and reflection are two complementary behaviours of the light incident on the material surface. Absorptions are inherently related to the material chemistry as well as other physical properties such as surface roughness (Hapke 1993). Therefore, the presence of an absorption at a certain spectral range is a “signature”, which can be used for identification and recognition purposes.
8.1 Scenes in Terms of Materials Up to this stage, we have elaborated on the invariance or representation problems related to imaging spectroscopy devoid of subpixel information. The use of imaging spectroscopy for scene analysis also permits the representation of a scene in terms of materials and their constituents. Note that the problem of decomposing a surface A. Robles-Kelly, C.P. Huynh, Imaging Spectroscopy for Scene Analysis, 141 Advances in Computer Vision and Pattern Recognition, DOI 10.1007/978-1-4471-4652-0_8, © Springer-Verlag London 2013
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Material Discovery
material into its primordial constitutive material compounds is a well-known setting in geoscience. This “unmixing” of the spectra is commonly stated as the problem of decomposing an input spectrum into relative portions of known spectra of end members. These end members are often provided as input in the form of a library and can correspond to minerals, chemical elements, organic matter, etc. The problem of unmixing applies to cases where a capability to provide subpixel detail is needed, such as geosciences, food quality assessment and process control. Moreover, unmixing is not exclusive to subpixel processing but can be viewed as a pattern recognition task related to soft cluster
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