Primary Study of Fourier Spectrum Feature Extraction for HyperSpectral Image
Pai-Hui Hsu , Yi-Hsing Tseng
Deparatment of Surveying Engineering, National Cheng-Kung University
No. 1 University Road, Tainan, Taiwan, R.O.C.
Tel: +886-6-2370876 Fax: + 886-6-2375764
E-mail : p6885101@sparcl.cc.ncku.edu.tw
Key words: hyperspectral data, spectral analysis, feature extraction, class separability
Abstract
Recently due to the advance of image scanning technology, hyperspectral image scanners which have tens or even hundreds spectral bands have been invented. Comparing to the traditional multispectral images, hyperspectral images include richer and finer spectral information than the images we can obtain before. Theoretically, using hyperspectral images should increase our abilities in classifying land use/cover types. However, when traditional classification technologies are applied to process hyperspectral images, people are usually disappointed at the consequences of low efficiency, needing a large amount of training data, and hard improvement of classification accuracy. In order to solve this problem, technologies of hypersepctrial data analyses and processes must be developed. First, this paper illustrates the characteristics of three different spaces (Images, Spectral and Feature) in which hypersectral data can be inspected. Then, some fundamental statistical theories and graphical presentations of the statistics for hyperspectral images are introduced and spectral differences are analyzes in difference spaces. Two methods of data transformation for feature extraction are discussed in this paper. In addition to spectral to spectral differences, differences between two hyperspectral data classes are also analyzed.
Introduction
In the past two decades, multispectral sensors have been widely used to investigate various phenomena on the earth surface. Image data obtained by such sensors traditionally have the number of spectral bands less than 20. Recently, due to the advance of imagery technology, the new generation of remote sensors, referred as imaging spectrometers or hyperpectral images with hundreds of contiguous narrow spectral bands, These images are commonly referred as hyperspectral images.
As featured in high spectral resolution, fine spatial resolution, and a large dynamic range, hyperspectral images have led to the hope in increasing our abilities of exploring, investigating, and identifying subtle phenomena displayed on the earth surface. However, by extending the data analysis approaches, which have been successfully applied to multispectral images, to Hyperspectral data analysis, one would commonly be disappointed at not obtaining better results and the low efficiency of data processing. In order to explore the power of hyperspectral images, this problem has to be investigated and analyzed.
This paper will first study the spectral difference between two image pixels. By using the distance between two points in the feature space formed by spectral bands as the quantification of the spectral difference, the variation of the spectral differences subject to the changes of dimensionality is investigated. Similarly the characteristics of the spectral difference between two classes of pixels, referred as class separability, are also analyzed. Based on this study, one can easily discover that the class separability among a set of spectral data will become more and more indistinguishable when the number of the dimension of the feature space is increasing. The phenomenon explains the problem mentioned above and leads us to develop a favorable method that can reduce the dimensionality and maintain the class separbility for hyperspectral data by extracting features from the original data.
Coinciding with our discovery, many articles indicate that the traditional classification techniques can be retrained if hyperspectral data are preprocessed properly in advance. However, a linear transformation performed in the feature space, such as Principal component Transformation (PCT), is usually applied to extracted features. Although this method can effectively provide good classification accuracy when number of dimension is reduced, it is sensitive to noise and has to be performed with the whole data set. As opposed to a liner transformation, this paper proposes a nonlinear transformation that is Fourier Spectrum Transformation (EST) of the spectral data for each pixel. Therefore, it is named Fourier Spectrum Feature Extraction (FSFE), in this paper. This transformation is featured in the use of the frequency characteristics of the spectral data. The new feature space formed by the Fourier spectrum is expected to more meaningful and more stable than that formed by PCT. Finally, a 220-band AVIRIS data are analyzed to illustrated our discovery and tested to show the efficiency of SEF.
The representation of hyperspectral data
For the convenience of analyzing and quantifying the characteristics of hyperspectral data, it is necessary to define mathematically and conceptually some representation space inspect the data variations from some aspects. Landgrebe (1997) illustrated that there have been three principle ways in which multispectral data are represented quantitatively and visualized. See Figure 1. The same representations are still convenient for hyperspectral data.
