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Using Stationary Wavelet Transform in the Classification of Sar Images

ACRS 1998

Poster Session 1

Using Stationary Wavelet Transform in the Classificationof Sar Images

Warin Chumsamrong, Punya Thitimajshima, and Yuttapong Rangsanseri

Department of Telecommunications Engineering,

Faculty of Engineering
King Mongkut’s Institute of Technology Ladkrabang,
Bangkok 10520, Thailand
[email protected],
[email protected]
Charnchai Pienvijarnpong
Remote Sensing Ground Station, National Research Council of Thailand
Chalongkrung Rd., Ladkraband, Bangkok 10520, Thailand


Abstract

In this paper, a novel method for SAR image classification based on stationary wavelet transform will be described. First, a SAR image is decomposed into 4 subbands using stationary wavelet transform. Each pixel is then represented by a 4-dimension vector whose components are taken from the wavelet subbands. The pixels are finally classified into a small set of categories by using parametric supervised classification algorithm. The classification using this wavelet was successfully applied to a JERS-1/SAR image.


1 Introduction

Remote sensing image data of the earth’s surface from the earth resources satellite i.e. ERS-1, JERS-1 or Landsat can be divided into two categories: multispectral image and SAR image. The classification of these images. Applied for studying a change of the earth resources, can be performed by various algorithms i.e. Maximum Likelihood Classification, Minimum Distance Classification, Parallelepiped Classification or Table Look up Classification [1].

In the case of multispectral images, they are consistered of several sub-images or bands and each band is contained with the gray value data. These gray value data are then represented by an N-dimension vector and can be directly classified for such any desired purpose. While SAR images are the single band image which is contained with the multiresolution texture data due to the non-station of microwave’s reflection on the ground. The classification of these images without any preliminary analysis usually result in high error rate.

Wavelet transform [2] has been attracting attention in diverse areas such as signal processing and image processing. In this paper, we present a texture classification result utilizing the characteristics of the wavelet transform.


Figure 1: Two-level discrete wavelet tranform.


2 Discrete wavelet transform

The discrete wavelet transform is the most useful technique for frequency analysis of signals that are localized in time of space. It decomposes signals into basis functions that are dilations and translations of a single prototype wavelet function :

Where
Ym,n(x)=2-m/2Y(2-mx-n), are obtained by translates and dilates of the wavelet function
Y(x). The discrete wavelet transform coefficients
Cmn can be calculated by the inner products
(Ym,n(x), f(x)) which are the estimation of signal components at (2-mn, 2m) in the Time-Frequency plance.

Actually, the discrete wavelet transform [3] corresponds to multiresolution approximation expressions. This method permits the analysis of the signal in many frequency bands or at many scales [4] [5]. In practice, mutiresolution analysis is carried out using 2 channel filter banks composed of a low-pass (G) and a high-pass (H) filter and each filter bank is then sampled at a half rate (1/2 down sampling) of the previous frequency. By repeating this procedure, it is possible to obtain wavelet transform of any order. The down sampling procedure keeps the scaling parameter constant (n=1/2) throughout successive wavelet transforms so that it benefits for simple computer implementation. In the case of an image, the filtering is implemented in a separable way by filtering the lines and columns. An example can be illustrated in Figure 1.

According to this procedure, the original image can be transformed into four sub-image, namely:

  • LL sub-image: Both horizontal and vertical directions have low-frequencies.
  • LH sub-image: the horizontal direction has low-frequencies and the vertical one has high-frequencies.
  • LH sub-image: The horizontal direction has high-frequencies and the vertical one has low-frequencies.
  • LH sub-image: Both horizontal and vertical directions have high-frequencies.


3 Stationary wavelet transform

The discrete wavelet transform provides the information useful for texture analysis in the image. Its fast implementation is usually performed by using multiresolution analysis. The wavelet coefficients are sampled based on the Nyquist criteria. The representation is accordingly non-redundant and the total number of sample in the representation is equal to the total number of the image pixels. The major inconvenience of this representation is that it does not conserve an essential property in image processing, which is the invariance by translation. Thus pyramidal multiresolution analysis is not desirable for estimation/detection problems. In order to preserve the invariance by translation, the down sampling operation must be suppressed and the decomposition obtained is then redundant and is called a stationary wavelet transform [6]. In practice, the structure in cascade of the filter bank does not change, the only operation of down sampling are suppressed.


4 The proposed algorithm

The technique used here for SAR image classification is based on wavelet feature input to a minimum distance classifier, as shown in Figure 2. First, a SAR image is transformed into 4 sub-images using stationary wavelet transform. Each pixel at the same position of these wavelet sub-images in then represented by a feature vector x = [x1x2x3x4]t where t represents transpose. Then, the pixels are classified into a small set of categories by using a parametric supervised classification algorithm.


Figure 2: Overall scheme of the proposed algorithm.

The classification algorithm used in our research is based on the minimum distance method. Mahalanobis distance is the most commonly used in remote sensing. The distance measure is defined as:

d(x,mi)2 = (x-mi)tS-1 (x-mi) (2)

where the subscript I indicates the number of category to be classified, mi the mean vector of the data in class I, and