Multiresolution representation of images using the wavelet transform is a new approach for the analysis of image information content. The transform can be computed efficiently by a pyramidal algorithm based on convolution with quadrature mirror filters. The result is a set of subband images which consists of a lower resolution version of the original image and a sequence of detail images containing higher frequency spectral information. We used this representation for the supervised segmentation of polarimetric SAR images of the San Francisco Bay area acquired by the airborne JPL system for identifying various terrain covers. Since the wavelet transform generates the localized spatial and spectral information simultaneously, detailed knowledge of the texture variations within an image can be extracted from the data in the spectral subbands. The segmentation algorithm developed in this paper is formulated by taking into consideration both the intensity and the texture information. For polarimetric SAR images, the classification accuracy can be enhanced, if the combined data from copolarized and cross-polarized images are used in the discrimination process. In contrast to other texture segmentation approaches, this algorithm does not require extensive calculations. 0 1993 John Wiley 8 Sons, Inc.
1. Introduction
The wavelet transform is of great interest for the analysis of nonstationary signals [ 11. A nonstationary signal is transformed into a representation which is localized in both time and frequency. Unlike the Fourier transform which is not suitable for obtaining frequency content localized in time, the wavelet transform produces the time evolution of frequency. Short time Fourier and Gabor transforms have also been proposed [ 1,2]. The basic difference is that a fixed window size is used for the short time Fourier and Gabor transforris, while the wavelet transform uses short windows at higher frequencies and long windows at low frequencies. Thus. the wavelet transform can achieve greater accuracy in timefrequency analysis. Remotely sensed images, such as synthetic aperture radar (SAR) images contain scenes of natural terrain and manmade objects. The signal is nonstationary in nature, and texture in images is difficult to quantify with the Fourier transform. The wavelet transform seems to be an ideal tool for analyzing this type of imagery. I t has been applied for edge detections [3,4]. data compression and image coding [5,6]. We apply it to the segmentation of polarimetric SAR images.
Grossmann and Morlet 171 first introduced the wavelets as functions whose translations and dilations can be used for the Keceived 18 August 1092: revised manuscript received