METHODOLOGY OF WIND FIELD RETRIEVAL
Morphological Smoothing
In image processing, smoothing is the creation an approximating function that attempts to capture important patterns (here linear features) in the image, while leaving out noise or other fine-scale structures/rapid phenomena. Smoothing is utilized to extract more information from the data as long as the assumption of smoothing is reasonable. In this paper, we apply "Opening" and "Closing" mathematical morphological operators to smooth the SAR pictures.
Eigenvectors and Eigen values
An eigenvector of a square matrix is a non-zero vector that, when multiplied by the matrix, yields a vector that differs from the original at most by a multiplicative scalar. Specifically, a non-zero column vector v is a right eigenvector of a matrix A if (and only if) there exists a number :E such that Av = :Ev. If the vector satisfies vA = :Ev instead, it is said to be a left eigenvector. The number :E is called the eigenvalue corresponding to that vector. The eigenvalue-eigenvector equation for a square matrix A can be written as:
( A ''C :E I ) x=0 , x IU 0 (1)
This implies that A ''C :E I is singular and hence that
det ( A ''C :E I ) = 0 (2)
In equation (2), :E is eigenvalues of matrix A and I is Identity matrix. Eigenvalues play an important role in many fields of data processing and Numerical analysis, situations where the matrix is a transformation from one vector space onto itself. Systems of linear ordinary deferential equations are the primary examples. The values of :E , can correspond to frequencies of vibration, or critical values of stability parameters, or energy levels of pixels in an image.
THE PROPOSED APPROACHED
Here, we propose a novel approach which, in some way, tries to exploit the advantages of Morphological Smoothing method. This method is applied to characterize the linear features in SAR images. In the aim of smoothing we use closing - opening operators with linear Structuring Element (SE) at sequential angles between 0 ° and 350° . Fig.1 schematically shows Linear Structuring Element applied to the image at various angles
As shown in Fig.1, the image P contains linear features on the slope of :Áo. Applying Morphological Smoothing with linear SE at the angle of :Áo to image P, cause linear features to be bolded and characterized. In addition, due to Closing-Opening operator properties, applying this technique at the angels except for :Áo, make linear features faded and this lead to reduce the energy level in image. This is the key factor which we used to extract the direction of linear features in SAR image.
In our proposed method a SAR image (with linear features caused by wind) is smoothed with linear SE at sequential angles between 0° and 350°. After smoothing the eigenvalues of smoothed image at each angle is computed. As previously mentioned, Eigenvalues of an image are proportional to its energy level. So, the smoothed image with linear SE at angle correspond to orientation of linear feature (wind direction) has the highest range of eigenvalues . Fig.2 shows the block diagram of proposed method.
DISCUSSION AND CONCLUSION
The proposed method has been successful for most of the images processed and has more accurate results in comparison of other spatial method (WDWaT). However, it cannot provide reliable results when the SAR images do not exhibit radar signatures referable to the wind (as, for instance, the signatures due to the ocean currents under very low wind which cause the linear features not to be visible), or the wind direction is highly variable (let us say more than 180 o) inside the imaged area. Also we have 180o direction ambiguity in this method.
The SAR data set used in this paper is not ideal to show the performances of the method, as the big deal of scenes belongs to coastal areas, where the meteorology is indeed very complicated and at the sea region linear features are not visible in most of the scene. Taking in mind all the aforementioned remarks, we could assign to the method 60%-70% of good score. Unsatisfactory performances occur when the SAR images are flat or the backscatter cells are few and the linear features are not visible as mentioned before. This method is applied on a ENVISAT Wide Swath ASAR image of the Persian Gulf. In order to evaluate the proposed method the results is compared with ECMWF model. Table 1 shows the results.
As seen in Table 1, we have more erroneous results for IMG2 and this is because the linear features in IMG2 are not as visible as IMG1.
