Xiukun Li, Mingye Liuand Shu Jiang

1. Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China

2. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Morphological Research on
Geometrical Scattering Waves of an Underwater Target

Xiukun Li1,2*, Mingye Liu1,2and Shu Jiang1,2

1. Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China

2. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

In this paper, a new method based on morphologic research named reconstruction cross-component removal (RCCR) is developed to analyze geometrical scattering waves of an underwater target. Combining the origin of the cross-component in Wigner-Ville distribution, the highlight model of target echoes and time-frequency features of linear frequency-modulated signal can remove cross-components produced by multiple component signals in Wigner-Ville distribution and recover the auto-components of output signals. This method is used in experimental data processing, which can strengthen the real geometric highlights, and restrain the cross components. It is demonstrated that this method is helpful to analyze the geometrical scattering waves, providing an effective solution to underwater target detection and recognition.

underwater target detection; geometrical scattering waves; Wigner-Ville distribution; morphology; reconstruction cross-component removal (RCCR)

1 Introduction1

Underwater target detection and recognition technology is one of the current research focuses in underwater acoustic field. For bottom and buried targets, detection and recognition technology is mostly based on active sonar. With the development of electronic and information processing technology, feature extraction, feature fusion and classification decision based on signal space become three core techniques of active sonar detection and recognition (Li and Xia, 2013). Currently, researches in this field focus on physical characteristics and signal features of target, reverberation field and anti-reverberation techniques. Because of the important theoretical and practical value of target echo, many scholars have conducted wide and deep studies on it. Target echo is also known as monostatic scattering, it refers to the reverse scattering wave from the target. Fan (2001) studied the echo characteristics of underwater complex targets. Fan et al. (2010) studied the scatting sound field structure of water-filled cylindrical shell.The acoustic scattering from a finite periodically or quasi-periodic bulkhead cylindrical shell was studied by Pan et al. (2012, 2013a, 2013b, 2014). Besides, the scattering of obliquely incident plane waves by cylindrical shells immersed in water was measured by Scot et al. (1997) and the ray methods (Florian and Philip, 2002) was developed to model and interpret those responses. Ying et al. (2003) investigated the circumferential resonance modes in such condition. The resonance scattering theory can provide the physical explanations for observations (Mitri, 2010; Farhang et al., 2011). Williams et al. (2010) researched the sound scatting of a solid cylinder half-buried in sand. The scattering of fully buried target was studied by Waters et al. (2012). These work illustrated the physical mechanism and signal properties of acoustic scattering from different underwater targets. The scattering waves can represent the characteristics of underwater target. Li et al. (2010) studied the feature extraction and fusion based on the characteristics of underwater target. In order to deal with the limitations of underwater target feature extraction, Sun and Li (2013) proposed a method based on empirical mode of decomposition and Wigner-Ville distribution (WVD) to extract the highlight features of a small underwater target, which is proved to be effective in underwater target recognition.

Mathematical morphology originally took shape in 1960s, for about 60 years, its application has expended to image, video, mechanics and many other fields. The theory of morphology can be applied to many aspects of image processing, for instance, target recognition, image reconstruction, etc. As a new image processing method, it has been used in image analysis and processing fields. For underwater acoustic area, Liu and Sang (2003) proposed an underwater acoustic image processing method based on mathematical morphology.

In this paper, reconstruction cross-component removal (RCCR) (Soledad et al., 2011) based on morphological reconstruction is applied to process target echo. Short-time Fourier transform and Wigner-Ville distribution are combined and used in a new way to analyze highlight structure of underwater target echo.

2 Features of target echo

In order to obtain the features of target echo, analysis in time domain and frequency domain are necessary. Since underwater target echo is a type of non-stationary signal, it needs to be described in both time and frequency domains, i.e., using joint function to show the features of underwater target echo. In this paper, short time Fourier transform (STFT) and Wigner-Ville distribution (WVD) are applied.

2.1 Target model in this paper

According to the theory of highlight model (Tang, 1994), the transfer function for single highlight is

where Am(r, ω) is the amplitude factor; τmis time delay, which is determined by the distance between the equivalent scattering center and the reference point, together with a function of azimuth angle θ; φmis the phase jump that is produced when the echo forms. In this case, the transfer function of the target which has N highlights can be described as：

In this paper, the target model is a cylinder with semi-spherical head, as shown in Fig. 1. According to acoustic scattering features of the target, this target model can be divided into a spherical crown and a cylinder. To get this target echo highlight model, highlight parameters of the two components, spherical crown and cylinder with limited length, need to be studied. Highlight parameters of sphere and cylinder are shown in Tables 1 and 2, respectively.

In order to analyze the geometrical highlight structure of target echo, echo types concerned in this paper include mirror-reflection wave and edge wave (elastic wave was not concerned in this paper).

During the experiment, incident sound wave reached the target model horizontally. Therefore, the wave front paralleled to the rotational axis of the target model’s azimuth angle. It should be noted that when θ equaled to certain values, highlights might be in the shadow zone. In this case, not all the highlights could appear at the same time. Highlights from mirror reflection appeared at abeam, end and spherical crown, and highlights at abeam and end only appeared when the sound wave reached the target model vertically. In other words, when θ=0° andθ=360°, mirror reflection highlights appeared at end; when 90 °＜ θ ＜ 270°, highlights appeared at spherical crown. Since the rotating range of the target model was 0°-360°, the relation of highlight position and the incident angle is illustrated in Table 3.

When the relationship between locations of highlights and the angle of incident sound wave is known, the transform function can be calculated. The time delay (from the reference center) is a necessary parameter of each highlight. In accordance to the water tank experiment, the rotational center (i.e. the center of the cylinder part) of the target was selected to be the reference center O. Assuming that far field condition was met, the sound wave arrived at the surface of the target could be considered as plane wave. Therefore, time delay of each highlight could be obtained, as listed in Table 4.

Fig. 1 The target model

Table 1 Highlight parameters of sphere

Table 2 Highlight parameters of cylinder

Table 3 Relation of highlight position and incident angle

Table 4 Time delay of highlights

2.2 Cross component of WVD

In this paper, linear frequency-modulated (LFM) signal was selected to be the emitting signal in experiment.

Then its WVD is

For a complex harmonic signal with amplitude 1, i.e. z( t) = ejω1t+ ejω2t, its WVD is

In which the auto-component is,

And the cross-component is,

If the signal has multiple components, cross-components will be introduced by dot product calculation. No matter how far the components are from each other in time-frequency plane, WVD cross components always exist, and have serious effect.

3 Morphological reconstructions

If the morphological information of auto-components can be gained by processing STFT, morphological theory can be used on WVD to remove cross-components and keep auto terms. In this paper, morphological reconstruction is applied to solve this issue.

3.1 Erosion and dilation

Erosion and dilation are two primary operations of morphological processing (Zhu, 2013). To understand the morphological method used in this paper, a brief introduction of these two operations is included.

With A being the image set and B a structuring element, the erosion of A by B, denoted asAΘ B, is

or

or

The equation indicates that the erosion of A by B is the set of the points in A that the point z passes through when B shifts in A, where z is a given point in B.

Fig. 2 is an example of erosion, A is a solid square with length d, structuring element B1is a square with length d /3, and B2is a rectangle with length d and widthd/3. Both B1and B2have an origin, respectively. From the result of erosion, AΘ B1is a square with length 2d/3, and AΘ B2is a straight line.

As for dilation, with A being the image set and B a structuring element, the dilation of A by B, denoted asA⊕B, is defined as,

or

or

The equation of dilation is based on reflecting B about its origin. The dilation of A by B then is the set of the area that B passes through when a base point in B shifts in A, such that B and A overlap by at least one element.

Similar to Fig. 2, Fig. 3 is an example of dilation. The results show that A⊕B1is a square with width 4d/3, and A⊕B2is a rectangle with length 2d and width 4d/3.

Fig. 2 Erosion of A by B1and B2

Fig. 3 Dilation of A by B1and B2

3.2 Morphological reconstruction method

This method involves two images and a structuring element. One image, the marker, contains the starting points for the transformation; the other image, the mask, constrains the transformation. The structuring element is used to define connectivity.

Central to morphological reconstruction are geodesic dilation and geodesic erosion. Using f to denote the marker image and g the mask image, the geodesic dilation of size 1 of the marker image with respect to the mask is denoted by. Geodesic dilation is to compare the marker image g and the dilation of the marker image δ(1)(f), and extract the smallest value of each point,

and geodesic erosion is,

where(1)ε denotes erosion. Geodesic erosion completes erosion operation of the marker image, then it is compared with the marker image and the biggest value of each point is derived.

The positions of auto terms of WVD and STFT are almost the same and the morphology of auto terms are similar. According to morphological reconstruction, STFT can be used as the marker image and WVD the mask image. Additionally, the image features from WVD and STFT are processed with dilation reconstruction method.

The process of RCCR method is illustrated as Fig. 4. The major idea of this method is to extract auto items of the signal from WVD and reconstruct it, and then remove cross components to reduce its influence on auto items.

In order to make the result of morphological reconstruction more accurate, pre-process is necessary after STFT. This pre-process is to conduct threshold segmentationand homotopic thinning on the STFT result. Therefore, morphological structure information of STFT could be obtained and marker image f is available. On the other hand, WVD of input signal is used as mask image g. In this way, STFT’s time-frequency resolution was improved and ensured that positions of auto items are the same in WVD and STFT.

Fig. 4 The schematic diagram of Reconstruction crosscomponent removal (RCCR)

4 Experiments

An experiment is conducted in an anechoic tank to collect the acoustic scattering waves from a target model. The size of the tank is 25 m long, 15 m wide and 10 m deep. The equipment of the experiment is shown in Fig. 5.

A monostatic sonar array is used to transmit and receive signal. The LFM pulse is used as transmitted signal. The data collection synchronizes with transmitting signal, so the time delay will be measured exactly. The target model is a cylinder with semi-spherical head, which is hung by ropes to a rotating stent. In the experiment, the target model rotates horizontally, which can achieve the acoustic scattering waves under different incident angles. Best efforts are made to ensure that the array and target model are in the same depth and the target rotate uniformly.

For all the data obtained in the experiment, the pulse width and frequency range are normalized. The position of the target and the direction of incident sound wave in any angle θ are shown as Fig. 6.

Fig. 5 Experiment equipment

Fig. 6 Target direction and incident sound wave

4.1 Energy distribution of target echo

It is assumed that the distance between the source and the target meets the far field condition. In the experiment, the monostatic array is static (i.e., the direction of incident sound wave did not change), and the target completes counterclockwise rotation with uniform velocity, meanwhile echo data is recorded.

The actual target echo energy distribution is drawn by using echo data obtained in experiment, as shown in Fig. 7. The change of each highlight echo with rotation angle can be observed. Comparing data in Tables 3 and 4, it is clear that the energy distribution of theoretical and experiment echoes have similar change tendency. In other words, theoretical positions where mirror-reflection wave and edge wave of the target echo’s geometric highlight structure should appear are proved by experiment.

However, this image cannot fully present the features oftarget echo. In actual experiment, multiple interfering lines might appear in echo energy distribution figure. For instance, the reflection echo lines of the rope and hook used to hang the target or other objects exist here. In this case, it is difficult to determine which track it was from the real target echo.

Fig. 7 Actual echo energy distribution

4.2 Cross components removal

Based on target echo energy distribution obtained in the experiment, the RCCR method is used to extract geometric highlights of target echo. The results are shown as below.

According to the waveform files got at angle1θ, time domain waveform and matched filtering of all the basic elements in the receiving array are calculated. Comparing the calculated results and actual working situation of basic elements in the experiment, data of an element channel is selected to be processed.

The scattering wave received by this channel is shown in Fig. 8. Fig. 8(a) shows the original data in the time domain without any processing and Fig. 8(b) shows the frequency spectrum after normalization. The data between sampling points [6 500, 8 500] in original oneof the target echo data is intercepted and used as the input data for RCCR later.

According to RCCR method, the first step is to conduct STFT on signal, and the result is shown as Fig. 9(a), then conduct pre-process on the outcome of STFT, the result is shown as Fig. 9(b). The result obtained after STFT and pre-process is the marker image in morphological reconstruction process. From Fig. 9(b), the marker image contents only one slant.

The following step is to calculate WVD of the data and the result is shown as Fig. 10(a), which is used as the mask image in RCCR. From Fig. 10(a), a line spectrum with relatively high brightness can be observed, beside which there are a few slants with less energy. The darker line spectrum results from reflection of the rope. By using the mask and marker image, RCCR process can be completed and the result is shown as Fig. 10(b). Compared with Fig. 10(a), the outline of processed result is narrower and only one bright line spectrum is kept, which proved that noise and reflection of rope echo are filtered. Also, the geometric highlights of target echo are strengthened.

Fig. 8 Signal received by the element

Fig. 9 The results of STFT and pre-process

Fig. 10 The results before and after processing

Additionally, the processing result shows clearly that there is a highlight with more energy, then it can be determined that the target model is abeam. Based on the original position of the target and selected files, calculation proves that conclusion is correct. In other words, at angle 1θ, RCCR is proved to be functioning.

Besides experiment at angle1θ, two more experiments at different angles are conducted. All three experiments prove that RCCR works well at different angles.

5 Conclusions

The acoustic scattering waves of an underwater target usually consist of multiple components. In some time-frequency distributions with high resolution, such as Wigner-Ville distribution, the cross-componentscan lead to difficulty in analysis. Combining morphological image processing and time-field analysis of signal, this paper applies RCCR method to underwater target echo analysis. This method is not only able to detect target echo, but also strengthen the real geometric highlights and restrain the cross components in WVD and other interferes. Introducing morphological image processing methods into the underwater acoustic field provides a possible direction in solving underwater target detection and recognition issues.

For future work, CW pulse may be selected as emitting signal. Since only LFM is discussed in this paper, whether RCCR method can be used for CW pulse or other types of signal is to be studied.

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10.1007/s11804-015-1293-y

1671-9433(2015)02-0208-07

Received date： 2014-07-18.

Accepted date： 2014-10-08.

Foundation item： Supported by the National Natural Science Foundation of China, under Grant No.51279033 and the Natural Science Foundation of Heilongjiang Province, China, under Grant No. F201346.

*Corresponding author Email： lixiukun@hrbeu.edu.cn

? Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2015