Good morning, ladies and gentlemen. I am LI Yanghuan. Thank you for allowing me to introduce the work of DUAN Chongwen at this place. The title of the paper is ‘SAR Image Based Geometrical Feature Extraction of Ships’.
Before we start, I’d like to show you the outline of the report. In the first place, I’ll introduce the background of the research and the source of the paper’s idea. After that, the three-dimensional geometrical feature extraction algorithm is illustrated. Some details of the algorithm are also explained. As a conclusion, some experiment results are given in the end.
In a SAR image, the down and cross range resolution are realized respectively through the pulse compression and the coherent processing of consecutive echoes. [Mouse Click] As a result, the scattering centers distribute in a way of orthographic projections on the imaging plane. With SAR images, several kinds of features are extracted for the sake of object recognition. [Mouse Click] Geometrical features are one of the mostly used ones.
The geometrical features mentioned here includes the shape parameters of the object, for example, the length, width, the Length-to-Width Ratio, and even the height if possible. It also includes the relative angles with radar, such as the pose angle for 2-dimensional condition, and the azimuth and elevation for 3-dimensional case. [Mouse Click] However, considering the orthographic projection mechanism, 2-dimensional features are sometimes ambiguous and the 3-dimensional ones are preferred. [Mouse Click] Here we are trying to extract the 3-dimensional geometrical features of a ship from its SAR images. Present techniques on this subject can be classified into two sorts.
The signal processing techniques need a careful examination on the phase differences between each echoe. [Mouse Click] While the optical image processing methods operate with the amplitude images, and bring in the algorithms in the computer vision field. [Mouse Click] All these techniques focus on the 3-dimensional coordinate estimation of scattering centers. However, one of the key steps, namely, the match of scattering centers between the images, is difficult to carry out, [Mouse Click] as SAR images are seriously blurred by the unfocused distortion caused by wave movements, [Mouse Click] and the scattering scintillation during observing intervals.
Here we see some SAR images of ocean ships. As the blurs occur, it is difficult to carry out the scattering center matching work with these images. Fortunately, all the ships are found to have an outline that can be approximated by an ellipse. And we know that the body of a ship resembles an ellipsoid to some extent. We are going to utilize this advantage to achieve our goal in the following.
Here is the main process of our algorithm. Having several SAR images of the same ship at hand, [Mouse Click] the elevations of the radar are supposed to be known, while the azimuths are not. We firstly preprocess the images to suppress noises and sea clutters, so that object segmentation and pose estimation can be achieved with higher accuracy. After that, feature extraction is carried out on the ship region to get the projected ellipse parameters. In the third step, the azimuths of each image is estimated through a nonlinear Least Square estimation. And the geometrical features of the ellipsoid, thus the ship, is extract as a result.
In the preprocessing, the Minimum Variance Method is selected. The MVM does a good work in the suppression of noises, sidelobes and sea clutters. This example shows how MVM improves the interpretability of a ship image. The original data is from electromagnetic calculations. The three images in the upper are generated by Fourier Transform, Hanning windowed Fourier, and MVM. The three below are ship region segmented. Apparently, the ship in the MVM image is the most clear to identify. [Mouse Click] The projected ellipse is then extracted, as shown with the dotted yellow line.
In a matter of fact, if given both the elevation and azimuth angles, the parameters of an ellipsoid can be fixed by any of its projected ellipse. So does the inversion. As the formula listed here, ‘theta’ and ‘phi’ are the radar azimuth and elevation angle. [Mouse Click] ‘a’, ‘b’, and ‘c’ respectively stand for the half-axis length of the ellipsoid in the length, width, and height directions. [Mouse Click] And ‘a11’, ‘a12’, and ‘a22’ are functions of the ellipse parameters. [Mouse Click] However, considering the absence of radar azimuths and the estimation errors in the ellipse parameters, the equations seldom meet. As result, at least two ellipses are required. And a robust algorithm should be constructed.
With totally N images preprocessed, the group of ellipse parameters, ‘An’, ‘Bn’, and ‘gamma_n’, are figured out. [Mouse Click] Setting ‘Fa_n’, ‘Fb_n’, and ‘Fc_n’ with these parameters, we expect that all ‘Fa’s be close to each other, so that they equal to the square of the longest half axis. Similar expectations are posed for ‘Fb’s and ‘Fc’s. This consideration comes to the formation of a nonlinear Least Square estimation, through which the radar azimuth of each view is estimated.
The object function to be minimized are composed of four parts, [Mouse Click] which are all functions of the tangents and cotangents of the azimuths. The first three parts, ‘J1’s, ‘J2’s, and ‘J3’s, intend to minimize the axis length estimation differences between each view. The ‘J4’ terms are based on the fact that multiplication of tangent and cotangent of the same angle equals to one. These terms are introduced for the robustness consideration. Moreover, the regularization parameters, ‘lambda_i’s, make sure that the terms are all in the similar scale. The prior information about the ship dimensions would facilitate the choice of them. With the azimuths estimated, the axis lengths of the ellipsoid are easy to calculate. And finally we get the length, width, and height of the ship.
In the following, I am going to illustrate the validity of the algorithm with two experiments. In the first experiment, electromagnetic calculations provide three SAR images of a fishing ship located on a rough surface. The azimuths are 30, 50, and 70 degrees respectively, and the elevations are all 45 degrees. [Mouse Click] The ship regions are shown below, [Mouse Click] as well as the approximated ellipses. Again, we find it difficult to match the scattering centers in each image.
However, with algorithms mentioned above, the azimuth for each view is estimated in a pretty well accuracy. Furthermore, the size of the ship in each dimension is also given. Compared with the real values, the length of the ship is estimated precisely, while the errors for the other two dimensions are a bit large. Our present work is aimed at the improvement of these parameters.
In the second experiment, the Monte Carlo technique is introduced to analyze the performance of the algorithm. Given an ellipsoid with size 180*25*25, the parameters of projected ellipses are firstly calculated under view angles the same with the first experiment. After that, zero-mean Gaussian noises of different levels are added into these values. The ellipsoid is then reconstructed with these parameters. With the noise level of 1, the noise deviations for ‘A’ and ‘B’ are 1m each, while the deviation for ‘gamma’ is 1°. [Mouse Click] A set of 1000 simulations are carried out at each noise level. The means and error bars for the length, width, and height estimations are drawn below. As the noise level goes from 0 to 6, all the means deviates slightly, while the error bars widen in quite a different way. For length, it changes in the same pace as the adding noise. However, they are a bit large for the other two dimensions, especially considering the relative smallness of these values.
Here comes the conclusion of this report. In the SAR application of ship recognition, geometrical features are the very important attributes of interest. It is shown in this work that the ellipsoid-ellipse simplification can effectually help the 3-dimensional geometrical feature extraction of the ocean ship. In the process of the algorithm, a proper preprocessing of the image is necessary, which facilitates the estimation of the projected ellipses. Though the azimuths and length estimation is pretty satisfied, more efforts are required to reduce the variances of the width and height estimations. And this is just our present work.
Well, that’s the end of the report. Thank you for your attention. [Mouse Click] The author has left her email address, hoping to help anyone with any interests on this report.
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