Primary Study of Fourier Spectrum Feature Extraction for HyperSpectral Image
Data in the images space directly offer a visual way to understand the spatial variation of the scene and the relationship between an individual pixel and the land cover class it belongs to Tasks of manual image interpretation are usually carried out in the image space. Spectral space shows the spectral variation of pixels respectively. Each curve shown in the spectral space can be thought as a response function of wavelength. Theoretically each class related to the Composition of different material has its own shape and variance of the spectral curve. Some methods like "spectral matching" or "spectral angle mapper" use this property to distinguish the unknown spectral curve comparing with a series of pre-labeled spectral curve. In feature space, a pixel with n-band measurement is viewed as a point, i.e., a vector in an n-dimensional space, and the sets of the n-band measurements within a class is considered as a pattern. The characteristics of classes are modeled base on the stochastic or random process approach. During the past three decades, "pattern recognition" based on the statistic approach has been used successfully in the classification of multispectral data (Swain and Davis, 1978). However, the existing statistic approach to classifying hyperspectral data often brings the consequence of failures to achieve satisfactory results. This reveals that extracting substantial information from hyperspectral data is critical in the study of hyperspectral data. The feature space provides the mathematical basis for information extraction.
Image Space
Spectral Space
Feature Space
Figure 1. Three forms for representing multispectral data
The analysis of spectral difference in spectral space
The spectral response of a material can be defined as a spectral signature (Schowengerdt, 1997) by the reflectance or radiance as a function of wavelength. Theoretically, different types of materials can be distinguished on the basis of differences in their spectral signature. However, the difference is often not distinguishable due to some factors, including the variation of the sensor, the atmospheric scattering the nature variability for a given material type, etc. Objects of a certain class may not reflect incident light identically. Figure 2(a) shows the spectral variation of alfalfa. Some fundamental statistics can be used to describe the characteristics of the spectral variation. In Figure 2(b), the mean curve represents the trend of the spectral variation. The standard deviations show the scattering to the mean. And the maximum and the minimum values present the range of variation One can discover that two different object classes may have very similar mean, but present very different standard deviation, maximum and minimum values. Therefore, it is important to inspect every aspect of spectral variation. In order to view the spectral variation in the frequency domain, we transform spectral curve to the space of the Fourier power spectrum as show in figure 2(d).
In order to quantify the difference of two spectral curves, the Euclidean distance and spectral angle between two different vectors in feature space are calculated. In figure 3(a), we can see that the distance between two pixels of wheat and oats increase as the number of
Spectral bands increase. This phenomenon will be discussed in feature space later. Figure 3(b) show the Euclidean between two alfalfa samples.
Figure 2. The variability of a spectral curve.
Figure 3. The Euclidean distance between the wheat and oats classes
Features of Fourier spectrum
As described above, hyperspectral data potentially contain more information than multispectral data because the higher spectral resolution, but the traditional classification techniques can not provide better result when the number of spectral bands increases. The key problem is that the accuracy of parameters estimation of stochastic models depends substantially on the ratio of the number of training samples to the dimensionality of the feature space (P-Fuei Hsien, 1998). There are two possible ways to resolve the problem, one is to increase the number of training samples needed to characterize the classes increase as well, and another is to find the lowest dimensional subspace to use for classification purposes. The former time-wasting and unpractical, the later which is called "feature extraction" is generally though as the way to use hyperspectral data efficiently.
