Spectrum Representation
In this chapter, we provide an overview of spectrum representation methods. Along these lines, we review compact representations of the spectrum commonly used in the literature. These representations include those that view the spectra as a mixture, those
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Spectrum Representation
Due to the high-dimensional nature of spectral data, many classical algorithms in pattern recognition and machine learning have been naturally borrowed and adapted to perform feature extraction and classification (Landgrebe 2002). Dimensionality reduction techniques such as principle component analysis (PCA) (Jolliffe 2002), linear discriminant analysis (LDA) (Fukunaga 1990), projection pursuit (Jimenez and Landgrebe 1999) and its variants mitigate the curse of dimensionality by treating raw spectra as input vectors in a high-dimensional space, where the dimensionality is given by the number of bands. However, these methods are not able to interpolate reflectance and radiance values over the full spectrum. This is further exacerbated by the fact that spectra acquired with different sensors are often sampled at disparate spectral resolutions and noise levels. Further, the features extracted from reflectance spectra can be mapped to a low-dimensional space using kernel-based classifiers such as support vector machines (SVMs). This, is often found to be more effective than dimensionality reduction techniques (Fu et al. 2006a; Shah et al. 2003), which is not surprising since dimensionality reduction may potentially result in a loss of discriminant information, whereas the mapping from an input feature space to a kernel space can be viewed as an implicit feature selection. An alternative to raw reflectance spectra as a means towards classification and recognition is the use of a reflectance descriptor, robust to changes in illumination, noise, geometric and photometric effects. Nayar and Bolle (1996) have proposed a method of object recognition based on the reflectance ratio between object regions. Dror et al. (2001) described a vision system that learnt the relationship between surface reflectance and certain statistics computed from grey-scale images. Slater and Healey (1997) used a set of Gaussian filters to derive moment invariants for recognition. Jacobs et al. (1998) employed image ratios for comparing images under variable illumination. Lin and Lee (1997) used an eigenspace of chromaticity distribution to obtain illumination direction, illumination colour and specularity invariance for three-dimensional object recognition. Lenz et al. (2007) used perspective projections in the canonical space of colour signals to separate intensity from chromaticity so as to recover a three-dimensional colour descriptor. More recently, A. Robles-Kelly, C.P. Huynh, Imaging Spectroscopy for Scene Analysis, Advances in Computer Vision and Pattern Recognition, DOI 10.1007/978-1-4471-4652-0_7, © Springer-Verlag London 2013
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Spectrum Representation
Chang et al. (2009) developed a coding scheme for the spectral variation of hyperspectral signatures by means of spectral derivatives.
7.1 Compact Representations of Spectra The main bulk of work on spectrum representation so far has concentrated on modelling spectra as a linear combination of a predetermined basis. Maloney (1986) validated the use of l
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