**C.S.Wu, C.F. Chen, K.S. Chen and A.J. Chen**

Center for Space and Remote Sensing Research

National Central University, Chung-Li, TAIWAN, R.O.C.

Abstract

An automatic method is developed to extract oceanic wave length and direction of major wave pattern near the coastal water from SPOT image. The process consists of three step: preprocessing, two-dimensional Fourier transformation, and wave detection. At first step, the wave appearance in the image is separated from the background in the image. Since the typical surface waves in boundaries are always found in the image due to the different water colors. The separation of wave patterns from the background becomes very important in the and unrelated linear features in the image, and then the probabilistic relaxation is image. At second step, fourier transform is utilized to transform the binary image from the spatial domain into the frequency domain for spectrum analysis. At the final step, the wave spectrum image in the frequency domain is analyzed by using filtering and clustering approach to detect the location of the governing power in the image. Finally, the length and direction of dominant ware is derived from frequency analysis. The method is tested by using 1993/12/8 SPOT PLA image along the coast of Tai-Chung Harbor, Western Taiwan. The wave lengths and directions vary from 70m to 66m and from 86o to 103o, respectively, result demonstrates that the trend of detected wave lengths and directions are consistent with the variation of ocean current and shoreline topography.

**1. Introduction**

It is apparent that the oceanic wave length and direction are two important ocean parameters in the oceanography. Conventionally, these data are collected by point-sampling from research vessel or moored buoys. These are time-consuming, costly and sometimes are dangerous. Satellite remote sensing presents a two-dimensional synoptic view and has the ability to provide a large-scale and long-period spatial-sampling data. However, the data volume being collected must be many order of magnitude greater than those being collected by traditional methods. Thus, an automatic detection system for remote sensing image will be of great help to the oceanographer.

In this paper, we propose a method which can automatically detect oceanic wave length and direction form SPOT image (The system diagram is shown in Fig. 1). The proposed method is divided into three stages : preprocessing, fourier transformation and wave detection. Because the wave phenomena captured by visible wavelength sensors, such as SPOT, is usually disturbed by the change of water color, or is obscured by the solar reflectance of ocean surface; the typical surface waves in the remotely sensed image normally appear to be dim and blurry and, moreover, the linear boundaries are always found in the image due to the different water colors. The separation of wave patterns from the background becomes very important in the first stop. This study uses the mathematical morphology to reduce the noise and unrelated linear features in the image, and then the probabilistic relaxation is employed to classify the wave patterns and transform the image into a binary image. At second step, the fourier transform is utilized to transform the binary step, the wave spectrum image in the frequency domains analyzed by using filtering and clustering approach to detect the location of the governing power in the image. As a result, the wave length and direction of dominant wave is derived wave is derived from frequency analysis.

** Figure 1 The flow chart of the proposed system **

In the next section, we present the details of our algorithm. Section 3 and 4 give experimental results and conclusions, respectively.

**2 Method**

**2-1 Top-hat transformation**

Because the remotely sensed image is the snapshot of ocean surface when the satellite passes over the sea, the wave pattern in the image is disturbed by the variations in scene illumination conditions, the change of water color and other effects. To correctly compute wave length and direction, the wave pattern must be separated from other phenomenon in the image. Top-hat transformation [1] is used to extract wave pattern from background, the original gray scale image f is first opened by a cylinder structuring element B with a radius of 10 pixels. The resultant image is then subtracted from the original, producing a different image Y which retains wave information. The process can be expressed as follow.

Y = f – (f° B) (1)**2.2 Probabilistic Relaxation**

Since the wave information contained in the difference image is, to some extent, obscure, it is difficult to determine the wave length and direction from its spectrum. Thus, a probabilistic relaxation scheme is used to classify the wave information contained in the different image.

Probabilistic relaxation is an iterative algorithm to reduce the ambiguity in local pixel assignment by means of the contextual information. In probabilistic relaxation, must be defined first. Several methods have been reported for defining the compatibility coefficient process and parameter settings are based on the scheme proposed by Danker et al [4]. Since the relaxation process can converge to a good classification result at the early iteration of the process [5], the process is controlled to iterate ten times for the reason of efficiency.

**2-2 Automatic thresholding**

After the probabilistic relaxation classification process, the histogram of wave pattern image has been transformed to bimodal. It is easy to obtain a binary image by using a thresholding method. The algorithm based on the moment-preserving concept proposed by Tsai [6] was then applied to obtain a binary image.

**2-3 Extend Image**

Obviously, If the resolution in frequency domain is not high enough to discriminate the change of wave length and direction, it is impossible to identify the variation of these Parameters. To get higher resolution in frequency domain, and to compute wave parameters more a accurately, the binary wave-pattern image is placed is placed at the center of a 51.2 x 512 black image (a image with gray value 0 only). This extended image is then used as input of a two -dimensional fast fourier transformation algorithm. The reason behind this is that the frequency domain resolution Df and the spatial domain resolution Dx is related by (2)

Where N is the sample size per line.

**2-4 Power spectrum rank filtering**

Generally, the main surface waves must have large support in the frequency domain, while the support of noise in the frequency domain is small. Consequently, to reduce the impact of image extension, extension, a rank filter is designed to remove noise from the spectrum. The principle of designed rank filtering the fit of a probe in a shape, it is superior to the traditional morphological filter in the sense of noise insensitively. The rank filter in this research is represented as follows.

where Y(x) and X(x) represent the filtered and the original power of point x in the spectrum, respectively. L = ||A||, A= x|X(x-u) > mean of X, “u ieB. B is a disk mask and T is a threshold value.

**2-5 Power spectrum band -pass filtering**

For most surface waves, the value of wave length is always in the range of [0.05m, 500m] (excluding capillary wave)]. This suggests that a band-pass filtering may be used to remove the undesirable power in the frequency domain. Let x = (nx,ny) denote a point in the spectrum (where nx and ny represent x and y coordinate of x in the spectrum, respectively.), the band-pass filter used here can be represent as follows.

**2-6 Cluster center of spectrum **

The cluster center C = (Cnx, Cny) of a N x N image spectrum

X = {X(xi),| xi e W1 £ i £ N2}, W = {(nx,ny) | 1 £ nx, ny £ N} is obtained by weighting average method, with symmetric property understood, as follows.

**2-7 Wave length and direction**

The wave length and direction of main surface waves is computed by (7) and (8).

wave direction = tan-1 Cnx/Cny (8)

where Dx = 6.25m for SPOT PLA image.

**3. Experimental results**

The method was tested by using 1993/12/8 SPOT PLA image (Fig.2) along the coast of Tai-Chung Harbor, Western Taiwan. The wave lengths and directions computed vary from 70m to 66m and from 86o to 103o, respectively, when a series of subimages cover from open sea to shore water was inspected. This result demonstrates that the trend of detected wave lengths and direction are consistent with the variation of ocean current and shoreline topography.

** Figure 2 Algorithm derived wave field of SPOT PLA image (window size 256*256) **

In this paper, an automatic detection algorithm have been proposed to compute the wave length and direction of ocean surface waves, the proposes algorithm has the following advantages. First of all, the interference of irrelevant ocean phenomenon has been suppressed by top-hat transformation and probabilistic relaxation process. Secondly, the image extension process enhances the frequency domain resolution, and the detection accuracy has been increased. Finally, being taking account of real-world wave behavior, the rank filter and the band-pass filter have been designed to remove the noise in the frequency domain. Further research will be made to extend the capability of the algorithm to detect multiple wave system in the spectrum.

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