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Sensitive test for sea mine identification based on polarization-aided image processing

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Abstract

Techniques are widely sought to detect and identify sea mines. This issue is characterized by complicated mine shapes and underwater light propagation dependencies. In a preliminary study we use a preprocessing step for denoising underwater images before applying the algorithm for mine detection. Once a mine is detected, the protocol for identifying it is activated. Among many correlation filters, we have focused our attention on the asymmetric segmented phase-only filter for quantifying the recognition rate because it allows us to significantly increase the number of reference images in the fabrication of this filter. Yet they are not entirely satisfactory in terms of recognition rate and the obtained images revealed to be of low quality. In this report, we propose a way to improve upon this preliminary study by using a single wavelength polarimetric camera in order to denoise the images. This permits us to enhance images and improve depth visibility. We present illustrative results using in situ polarization imaging of a target through a milk-water mixture and demonstrate that our challenging objective of increasing the detection rate and decreasing the false alarm rate has been achieved.

©2013 Optical Society of America

1. Introduction

The world’s oceans can be a potential danger for human activity due to naval mines [1, 2]. Minefields designed for psychological effect are usually placed on trade routes and are used to stop shipping reaching an enemy nation. They are often spread thinly, to create an impression of minefields existing across large areas. A single mine inserted strategically on a shipping route can stop maritime movements for days while the entire area is swept. Sea mines continue to be important in naval warfare because they can be used defensively or offensively and because of mines’ demonstrated success and capabilities [35].

Along with the variety of mines, there are many ways to search and neutralize them from the air, the surface of the sea and underwater. Sonar is the primary way potential mines are identified in the water when the Navy is hunting for explosives, but explosive ordnance disposal divers, marine mammals, video cameras on mine neutralization vehicles and laser systems can also be used [4, 5]. More than 1 billion dollars was earmarked for that purpose in the 2012 U.S. Navy’s budget [5]. In recent years, there has been much interest in designing autonomous underwater vehicles (AUVs) equipped with vision systems for remote control. A typical military mission for an AUV is to map an area to determine if there are any mines, or to monitor a protected area (such as a harbor) for new unidentified objects, e.g. AN/BLQ-11 (Boeing Company). However, light attenuation effects and visibility are two important issues for image quality acquired by these AUVs.

Mines detection followed by identification approaches have been developed over many years, e.g. by detecting changes between images of the same scene taken at different times [2, 6, 7]. From an application view, it requires large detection rates and very small false alarm rates. Here, as in some earlier work [2], we begin by considering a preprocessing step for denoising underwater images, an adapted scheme for detecting mines, a protocol for identifying them, and a specific decision making technique. In previous work, we have presented a composite filter called asymmetric segmented phase-only filter (ASPOF) which is an efficient means for quantifying the recognition rate [8]. The concept of the ASPOF was developed for increasing significantly the number of reference images in the fabrication of this filter. Because this initial work revealed low-quality images we investigate another approach for which a scene is viewed through a single wavelength polarimetric camera. The hardest challenge in imaging through a turbid medium is to increase the visibility depth. Using in situ polarization imaging of objects simulating mines through a milk-water mixture permits to partially alleviate the issue raising significantly the detection rate and decreasing the false alarm rate.

The rest of the paper is organized in the following way: In Sec. 2, we briefly review some related prior work on ocean optics and underwater mines. This is followed by a presentation of the preprocessing and detection algorithms in Sec. 3, together with a discussion of how the results are obtained and checked. We also present some results for the ASPOF in Sec. 4 and apply it to mine images. The principle of polarimetric observations for detecting mines and laboratory experiment are then presented in Sec. 5. We give a brief summary of the results and discuss some possible directions for future research in Sec. 6.

2. Some experimental facts on ocean optics and underwater mine

Two important issues regarding the current study concern: (1) the passage of an electromagnetic beam through seawater, which is characterized by poor visibility conditions, and (2) the geometry of the target with certain surface-scattering properties in the underwater environment.

2.1. Interaction of light in seawater

Water is responsible for the attenuation of light due to absorption. Three factors primarily affect underwater visibility: light penetration, biological species and particulate matter (e.g. suspended sand and silt). According to the size of these particles they scatter forward or backward light, resulting in reduced visibility [913]. Attenuation can be described using the Beer-Lambert law

I(z)=I(0)exp(αz)exp (dz)    
where I(0) is the intensity of the light at the origin, I(z) is the intensity at a distance z from the origin, α is the absorption coefficient, and d is the diffusion coefficient. Equation (1) implies that the underwater images should be taken at short range.

Some further observations that seem significant: first, scattering by particles and by the water itself affects image quality, i.e. maximum imaging distances range from centimetres in dirty water to more than 100 m in very clear water [14]. Second, non-uniform lightning conditions result in different intensity levels between images of the same area. Figure 1 illustrates the well-known fact that the underwater medium can significantly degrade the quality of the image. That is, small-angle forward scattering of light and non-uniform lightning conditions can cause images to blur and result in intensity differences between the images of the same area.

 figure: Fig. 1

Fig. 1 Illustration of the scattering and absorption of light in underwater imaging.

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Very recently, Kattawar described the approximations needed to solve the radiative transfer of sunlight through the deep oceans in order to understand the role of polarization as a possible tool for remotely sensing underwater objects [15]. Kattawar noticed that to date, there have been several theoretical studies [15], but very little direct experimental observations of underwater scenes in natural illumination.

2.2. Typical underwater mines

Figure 2 shows two standard mines with spherical (Fig. 1(a)) and cylindrical (Fig. 1(b)) geometries, and the Manta mine (Fig. 1(c)) [2]. The latter is a multi-influence shallow water sea mine, designed to be effective against landing crafts and small-mid tonnage vessels. The mine can be laid by surface vessels, helicopters and aircraft. The unique shape, the low target strength and magnetic signature make this kind of mine very difficult to detect. The mine logic is based upon a state of the art analysis of the target acoustic and magnetic influences. Finally, there is strong dependence of recognition performance on mine shape, e.g. a discriminating test for a cylindrical mine is to view it from different angles.

 figure: Fig. 2

Fig. 2 Examples of mines investigated in this work: (a) spherical mine, (b) cylindrical mine, and (c) Manta mine. These mines are immersed in seawater at a depth of 19 m. The camera is placed at 1.1m from the mines. Illumination comes from sunlight.

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The important thing to realize is that we are dealing with a complex, inhomogeneous medium in an ever-changing environment e.g. the optical properties of underwater mines eventually vary with time since mines are covered with alga, shells, sand, and sea grass. Additionally, rust which is produced for metal mines in the long run can affect their identification.

3. A first approach to mine detection

In this section, we will present the general principle for our preliminary observations for sea mine detection and identification.

3.1. Image preprocessing

The basic underlying principle of our proposed scheme is illustrated in Fig. 3 [2, 7]. Technically, it consists in undersampling images to decrease both processing time and noise thanks to the interpolation method used for pixel assignment. Indeed, pixels are replaced with a value computed from a bilinear interpolation of neighbor pixels. This method does not affect the edge contrast which is further enhanced as in [16] to improve the image acutance. As was described in [16], edges can be preserved by using a median filter and two special functions applied to the target image, i.e. the target image is first multiplied by its low-pass version, and then by the image for which the low-pass version has been subtracted.

 figure: Fig. 3

Fig. 3 Image preprocessing protocol. The first step consists in character suppression (block 2) that includes edges. Then undersampling and filtering allow us to reduce the size and noise (blocks 3 and 4). Edge enhancement improves the edge detection. The first row images show the results of each step. The second row images correspond to phase images on where the improvement on edge detection can be seen.

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Figure 3 shows the most prominent features in the image and its phase (when the spectrum amplitude is set to unity) due to this preprocessing protocol. We point out that this preprocessing step allows us to significantly enhance the visibility of the mine edges.

3.2. Mine detection

The mine detection method, as described in [2], consists of edge detection in the phase image. We slice the image into bands as shown in Fig. 4. For each band we look for 2 edges corresponding to the two sides of the object.

 figure: Fig. 4

Fig. 4 Illustration of the detection method. Red and blue lines delimit the studied bands.

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This method necessitates that the images have a good contrast. To illustrate the impact of our procedure, we present results here for several situations. In order to more conveniently demonstrate the reliability and robustness of our algorithm several parameters are introduced (with reference to Fig. 5) [17]: the true detection rate Pd, the false alarm rate Pfa, the false non detection rate Pndf, and the true nondetection rate Pndv. We analyze 6 video sequences corresponding to 7800 images. A summary of the results for the three types of mine is presented in Table 1.

 figure: Fig. 5

Fig. 5 Zoom of a specific image in a video sequence showing how to define the detection rate Pd and the false alarm rate Pfa. The frame in blue corresponds to a true detection area.

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Tables Icon

Table 1. Results of the detection algorithm. Each row corresponds to a specific type of mine.

Review of Table 1 shows the performance for different types of mines. While Pd is larger than 60% and Pndv is greater than 88%, we observe that Pfa remains small. Some videos are called empty ones because no mine was detected but may contain various objects such as the piece of rope shown in Fig. 6. One might be tempted to attribute the false alarm rate to these objects. Having illustrated the nature of the problem, we now describe how we can increase the performances of our system by using the ASPOF

 figure: Fig. 6

Fig. 6 Image from a video with no detected mine, but containing a piece of rope which contributes to the false alarm rate.

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4. ASPOF and mine detection

The basic principle of correlation is to compare a target image with a reference one [6, 7, 18, 19]. Among the many correlation filters which have received attention, we focus in this paper on composite phase only filters (POF) defined such that the amplitude of the reference image spectrum is unity [20]. Indeed, Ref [8, 21]. argued that the ASPOF, which consists in merging several reference images after application of a specific spectral optimization method, allows us to decrease significantly the number of correlation operations to be achieved.

To make a decision, the correlation peak should be characterized precisely (shape, height, etc). These metrics will determine the degree of similarity between the target and reference images. Several discrimination factors are used in the literature, e.g. the adapted peak-to-correlation energy (PCEA) [22]). The PCEA is given by the ratio of the energy in the correlation peak to the overall energy of the correlation plane

PCEA=x=x0tx=x0+ty=y0ty=y0+t|2C(x,y)|2x=1x=Ny=1y=M|C(x,y)|2+3x=x0tx=x0+ty=y0ty=y0+t|C(x,y)|2
where (x0,y0) denote the position of the correlation peak, C(x,y) denotes the value of the correlation plane at point (x,y), t is set to the number of neighboring pixels used, and (N,M) denote the size (in pixels) of the correlation plane. A distinct advantage of the PCEA is that it permits evaluation of the relative importance of the correlation peak with reference to the noise of the correlation plane. This Eq. (2) represents a normalisation of the peak-to-correlation energy (PCE) criterion. Since there are two filters which combine in one, it is possible to obtain 2 correlation peaks. We multiply the correlation peak by a factor 2 to favor one of the two peaks (when the power 2 is applied we have a factor 4 in the numerator). To compare with the all correlation plane we have to modify the denominator to have 4 times this zone.

4.1. Mine identification

After these preliminaries, we now turn our attention to the detail of the detection algorithm applied to images for which an object has been identified (with reference to Table 1). We use a multiscale edge detector in order to improve the correlation algorithm and the ASPOF. When the mine is correctly identified by correlation, the detection rate is noted Pdc. When the mine is incorrectly identified, the error rate is noted Ptype, e.g. a cylindrical mine can be identified as a spherical one depending on the viewing angle of observation. When correct identification occurs, the PCEA is always larger than a given threshold. The value of this threshold is set arbitrarily based on experimental data (more than 7800 underwater images / from Topvision project). Now, the PCEA can be smaller than the threshold. In that case, the detection is considered as a false alarm (noted Pfa) such that

PdPdcifPCEA>thresholdandifthemineiscorrectlyidentifiedPdPtypeifPCEA>thresholdandifthemineisincorrectlyidentified,PdPfa

More than 10000 correlation filters were fabricated which contain the three types of object viewed from different angles and at different length scales. Only filters with length scale corresponding to the mine-to-camera distance were selected. This allows significant reduction of the number of operations to be realized.

Figure 7 shows respectively Pdc, Ptype, Pfac, Pndfc, and Pndvc at a variety of different Manta mine-to-camera distances. In this figure, the x-axis denotes the distance measured between the mine (target) and the camera (sensor). The y-axis denotes the obtained probability. We point out that: In all distance intervals, the probabilities should be equal to 1 for the case where an object is present and to 1 for the case where there is no object (i.e. in Fig. 7, Pdc + Ptype + Pndfc = 1 and Pfac + Pndvc = 1). The Fig. 7 illustrates that for distances in the range from 1.5 to 2 m, good identification performance is achieved; e.g when the distance between the target and the sensor is equal to 2 m, we have a detection probability equal to 0.77 and a false alarm is very close to 0.

 figure: Fig. 7

Fig. 7 Identification of the Manta mine as a function of the mine-to-camera distance.

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In a similar way, Fig. 8 shows Pd (blue), Pdc (green) using the ASPOF, and Pdc (red) using the POF. The conclusion is similar to the previous one. For distances larger than 1.50 m, the ASPOF performs better than the POF.

 figure: Fig. 8

Fig. 8 Comparison of the identification performances for the POF and ASPOF as a function of the Manta mine-to-camera distance.

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4.2. Discussion

There are a number of important points to make in summarizing these findings. First, the numbers in Table 2 demonstrate that a good identification has been achieved for the Manta mines. The comparison between the 2 considered filters, the ASPOF and the classical Composite-POF, confirmed this observation. Even, the image quality and the distance change the edge detector results, this can be explained by: the ASPOF is a combination of 2 POF filters. So, some information from the first POF filter can help identification by the second POF filter and vice versa. However, it is inefficient for the cylindrical ones and very poor for the spherical ones. This behavior can be understood by considering firstly that the edges of the Manta mine are correctly detected with our preprocessing protocol, which is beneficial for identification. Unfortunately, this is not the case for the spherical mine. For cylindrical mines, linear sides are correctly detected with the detection algorithm. But in the filter, the cylinder boundaries of the mine are more significant than its linear sides. Thus correlation does not provide a single peak. In addition, the cylindrical object is only partially contained in the images. Should this be the case, correlation with a full cylinder leads to poor identification results. Another interesting feature of these results is that the fabrication of the ASPOF can lead to noisy correlation planes and/or two correlation peaks. But Eq. (2) considers only the most intense peak. Consequently, another peak will has for effect to decrease the PCEA. Additionally, one can image to introduce additional treatments to improve the image quality, but the cost to pay will be an increase of the processing time. Here, we wish a processing time of the identification algorithm which is typically the frame rate (25 images per s). This and other complications are of foundational importance to the field of sea mines detection and identification, yet due to length scale considerations, real mines can be challenging to identify.

Tables Icon

Table 2. Comparison of the identification performances for the different mines.

5. Polarization

Fortunately, we can do better. One line of thought beginning with Sabbah [23] and Chang and associates [24], seeks to use light polarization to alleviate the aforementioned limitations.

It has been shown that backscattering preserves the light polarisation state in a linear polarization configuration, whatever the distance [15, 2528] (Fig. 9). In a circular polarization configuration, backscattering polarization varies with distance. Thus helicity varies [2527]. It is more difficult to develop a system which is optimized with respect to several parameters such as mine-to-camera distance, material, etc.

 figure: Fig. 9

Fig. 9 Concept diagram of the polarization filtering in a linear polarization scheme.

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Since the nature of the object to be identified is unknown to us, its degree of depolarization remains difficult to estimate. Thus, we cannot select an optimal polarisation state. As the backscattering light keeps its polarisation state in a linear polarization system, we can limit this problem. Linear polarization will be used in what follows.

5.1. Optical setup for the proposed technique

In this work we are interested in a underwater polarimetric imaging setup such as depicted in Fig. 10. It consists of a commercially available digital underwater camera (Sealife DC1400 Pro Video Set) [29]. Its main specifications are as follows: image sensor of 14 mega pixel high resolution CCD, 26 mm wide angle lens, internal memory of 20 MB, underwater field of view of 51°, and depth rated to 60 m. The scene of interest is illuminated by 3 white LED. Full control of the incident polarization state is achieved by fixing a linear polarizer in front of the light source. A second polarizer in front of the camera allows us to analyze the reflected light.

 figure: Fig. 10

Fig. 10 (a) Light source and camera used in our in situ experiments; (b) Experimental arrangement for the polarization optical imaging in the backscattering geometry.

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The large volume tank (Fig. 11) is filled with natural water (6000 L) and semi-skimmed milk. The experiments are designed to mimic in situ conditions, allowing optical measurements on unperturbed suspended particles with a set of instruments that can be normally employed at sea. Milk is composed of spherical particles of different size (casein molecules ~0.04-0.3 µm and fat globules ~1-20 µm). For a long-time, scattering experiments have suggested that milk can mimic the scattering properties of sea water [3032]. Semi-skimmed milk contains more fat globules resulting in a Mie scattering regime. The estimated scattering coefficient μs for semi-skimmed milk is 1.40c cm−1 where c is the concentration of milk in water [30]. The attenuation length (or optical thickness) τ0 is defined as the product of the scattering coefficient μs by the physical depth d, so that τ0 = μsd. For the wavelength considered here, the absorption coefficient of milk can be safely ignored with respect to the scattering coefficient. Extinction coefficient data ranging between 0.1 and 4 m−1 were reported earlier for seawater. Milk concentration was adjusted to obtain extinction coefficient in this range. When 1 L of skimmed milk is dispersed in 6000 L of water, the scattering coefficient is µS = 0.007 cm−1.

 figure: Fig. 11

Fig. 11 A picture of the large volume tank.

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Our discussion of the proposed technique can be illustrated concretely with the help of effective examples. Following the detailed discussion of Table 2, it was found that the spherical mines are the least identified. In the in situ polarization imaging of a target through a milk-water mixture we used two identical metallic near-spherical objects (diameter = 5.7 cm). One is rusted (Fig. 12(a)) and the other is painted (Fig. 12(b)). A pebble has been also glued to the painted object to test the robustness of our identification algorithm. The horizontal distance between the object and the camera is then varied to investigate the dependence of the visibility depth on the image from 0.70 m to 1.80 m.

 figure: Fig. 12

Fig. 12 Two examples of target used: (a) rusted sphere, and (b) painted sphere.

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In Figs. 13 and 14, we present the object visibility changing due milk addition. The object is clearly discernible in Fig. 13 corresponding to pure water. The same object becomes more difficult to distinguish when milk is added to water (Fig. 14).

 figure: Fig. 13

Fig. 13 Target in pure water.

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 figure: Fig. 14

Fig. 14 Target in turbid water consisting of 1 L of skimmed milk dispersed in the tank containing 6000 L of water.

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In Fig. 15(a), we present the unpolarized image, whereas Fig. 15(b) and Fig. 15(c) show respectively the corresponding contrasts for the linearly parallel polarized (LPP) and linearly crossed polarized (LCP) images. Polarization is shown to a useful tool for significantly increasing the visibility of the object which is practically invisible in 15(a). The visibility enhancement is most effective when LCP is used. This is consistent with what others have observed [24].

 figure: Fig. 15

Fig. 15 (a) Unpolarization image of the near-spherical object, (b) same object imaged with LPP, and (c) imaged with LCP. The target localization is framed in red. The camera-to-object distance is fixed to 1.50 m.

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5.2. Algorithm

Images are then preprocessed using the scheme shown earlier in Fig. 3. We use a multiscale edge detector in order to improve the correlation algorithm and the ASPOF.

5.3. Results and discussion

In order to more conveniently demonstrate the efficiency of the system, a lot of images with (typically 11000) or without (typically 21000) polarizers were recorded for each configuration. A compilation of these different features is shown in Table 3.

Tables Icon

Table 3. Comparison of the identification performances for the three objects considered and different polarization conditions.

In Fig. 16, Fig. 17, and Fig. 18, the camera-to-object distance dependence of Pdc, Pfa, Pndfc, Pfa, and Pndvc is shown for the LCP and LPP states. Pndfc corresponding to not detected objects and Pndvc corresponds to true nondetections. In Figs. 16, 17 and 18, we point out that the Pdc + Pfa(images with object) + Pndfc = 1 and Pfa (images without object) + Pndvc = 1.

 figure: Fig. 16

Fig. 16 Identification results with raw images as a function of the object-to-camera distance. Red stars correspond to horizontal distances between the object and the camera for which no object is present. Red rectangles correspond to the identification area.

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 figure: Fig. 17

Fig. 17 As Fig. 16 for linear parallel polarization.

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 figure: Fig. 18

Fig. 18 As Fig. 16 for linear crossed polarization.

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There are many points for consideration. First of all and as shown in Figs. 16-18, decreasing the object-to-camera distance increases the recognition rate of the object because the visibility is increased. Secondly, Fig. 17 and Fig. 18 also report that the use of LCP allows us better identification performances than LPP. Several factors influence the recognition rate of the object. We note that the detection rate is larger than 90% with a corresponding false alarm rate less than 2% when the sole target is present in the scene. However, when a pebble is added to the target the detection rate decreases significantly while the false alarm rate increases. We also note that the false alarm rate is pretty large for the images where the object is not visible. This is due to the detection of the suspension cable. To appreciate this point, we performed additional tests by including a filter describing a square object in the ASPOF base. In this case less than 0.5% of total images are identified as containing a square object. This demonstrates the robustness of identification in strong contrast to the previous unpolarization images. Third, we would like to close by highlighting the role of the suspension cable. Evidently, it is possible to make use of a Hough transform to identify the cable in the image. In that case, the modified Pfa and Pcable are summarized in Table 4.

Tables Icon

Table 4. Comparison of the false alarm rate with or without cable detection.

6. Conclusions and future directions

To summarize, we have outlined an experimental scheme employing an ASPOF to extract the full characteristics on mine identification. The results reported here demonstrated the feasibility of our scheme using in situ polarization imaging of a target through a milk-water mixture. In our opinion, this clearly demonstrates the benefits of polarimetric observations for improving the visibility depth and increasing the detection rate and decreasing the false alarm rate.

Our work opens up several other interesting and important questions (in no specific order): It is possible to use this method to more complex types of mine? What are the possible improvements of our technique? As stated in the introduction, the exploration of our approach in more representative oceanic conditions, i.e. effects of turbulence [33] and phytoplankton, can be a formidable challenge. The coastal zone of Brest offers an opportunity to examine diverse water types with varying particulate and turbulence conditions. One way of dealing with complex object identification, within the framework outlined in this paper, is to consider multispectral polarimetric imagery [34]. We therefore hope that our study is of benefit to scientists interested in underwater imaging not only in sea mine warfare but also in applications such as marine biology and archaeology.

Acknowledgments

The authors thank P. Delrot, J. Corbel, and M. Dubreuil for technical assistance. The raw mine images contained in this work have been provided by the Groupe d' Etudes Sous-Marines de l'Atlantique within the TOPVISION project coordinated by Thales Underwater Systems SAS. This work was supported in part by the Techno-Vision Programme launched jointly by Ministère de l’Enseignement Supérieur et de la Recherche and Ministère de la Défense, and also by Région Bretagne. Lab-STICC is Unité Mixte de Recherche CNRS 6285

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Figures (18)

Fig. 1
Fig. 1 Illustration of the scattering and absorption of light in underwater imaging.
Fig. 2
Fig. 2 Examples of mines investigated in this work: (a) spherical mine, (b) cylindrical mine, and (c) Manta mine. These mines are immersed in seawater at a depth of 19 m. The camera is placed at 1.1m from the mines. Illumination comes from sunlight.
Fig. 3
Fig. 3 Image preprocessing protocol. The first step consists in character suppression (block 2) that includes edges. Then undersampling and filtering allow us to reduce the size and noise (blocks 3 and 4). Edge enhancement improves the edge detection. The first row images show the results of each step. The second row images correspond to phase images on where the improvement on edge detection can be seen.
Fig. 4
Fig. 4 Illustration of the detection method. Red and blue lines delimit the studied bands.
Fig. 5
Fig. 5 Zoom of a specific image in a video sequence showing how to define the detection rate Pd and the false alarm rate Pfa. The frame in blue corresponds to a true detection area.
Fig. 6
Fig. 6 Image from a video with no detected mine, but containing a piece of rope which contributes to the false alarm rate.
Fig. 7
Fig. 7 Identification of the Manta mine as a function of the mine-to-camera distance.
Fig. 8
Fig. 8 Comparison of the identification performances for the POF and ASPOF as a function of the Manta mine-to-camera distance.
Fig. 9
Fig. 9 Concept diagram of the polarization filtering in a linear polarization scheme.
Fig. 10
Fig. 10 (a) Light source and camera used in our in situ experiments; (b) Experimental arrangement for the polarization optical imaging in the backscattering geometry.
Fig. 11
Fig. 11 A picture of the large volume tank.
Fig. 12
Fig. 12 Two examples of target used: (a) rusted sphere, and (b) painted sphere.
Fig. 13
Fig. 13 Target in pure water.
Fig. 14
Fig. 14 Target in turbid water consisting of 1 L of skimmed milk dispersed in the tank containing 6000 L of water.
Fig. 15
Fig. 15 (a) Unpolarization image of the near-spherical object, (b) same object imaged with LPP, and (c) imaged with LCP. The target localization is framed in red. The camera-to-object distance is fixed to 1.50 m.
Fig. 16
Fig. 16 Identification results with raw images as a function of the object-to-camera distance. Red stars correspond to horizontal distances between the object and the camera for which no object is present. Red rectangles correspond to the identification area.
Fig. 17
Fig. 17 As Fig. 16 for linear parallel polarization.
Fig. 18
Fig. 18 As Fig. 16 for linear crossed polarization.

Tables (4)

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Table 1 Results of the detection algorithm. Each row corresponds to a specific type of mine.

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Table 2 Comparison of the identification performances for the different mines.

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Table 3 Comparison of the identification performances for the three objects considered and different polarization conditions.

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Table 4 Comparison of the false alarm rate with or without cable detection.

Equations (3)

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I(z)=I(0)exp(αz)exp (dz)    
PCEA= x= x 0 t x= x 0 +t y= y 0 t y= y 0 +t | 2C(x,y) | 2 x=1 x=N y=1 y=M | C(x,y) | 2 +3 x= x 0 t x= x 0 +t y= y 0 t y= y 0 +t | C(x,y) | 2
P d P dc if PCEA>threshold and if the mine is correctly identified P d P type if PCEA >threshold and if the mine is incorrectly identified, P d P fa
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