A Depolarization Ratio Anomaly Detector to Identify Icebergs in Sea Ice Using Dual-Polarization SAR Images

Icebergs represent hazards to maritime traffic and offshore operations. Satellite synthetic aperture radar (SAR) is very valuable for the observation of polar regions, and extensive work was already carried out on detection and tracking of large icebergs. However, the identification of small icebergs is still challenging especially when these are embedded in sea ice. In this paper, a new detector is proposed based on incoherent dual-polarization SAR images. The algorithm considers the limited extension of small icebergs, which are supposed to have a stronger cross-polarization and higher cross- over copolarization ratio compared to the surrounding sea or sea ice background. The new detector is tested with two satellite systems. First, RADARSAT-2 quad-polarimetric images are analyzed to evaluate the effects of high-resolution data. Subsequently, a more exhaustive analysis is carried out using dual-polarization ground-detected Sentinel-1a extra wide swath images acquired over the time span of two months. The test areas are in the east coast of Greenland, where several icebergs have been observed. A quantitative analysis and a comparison with a detector using only the cross-polarization channel are carried out, exploiting grounded icebergs as test targets. The proposed methodology improves the contrast between icebergs and sea ice clutter by up to 75 times. This returns an improved probability of detection.

bergs passing through the spatial gaps between the sounders, it is useful to identify icebergs 51 for validating the detection algorithms developed for SAR images. 52 The paper is organized as follows. Section I provides a brief introduction on iceberg 53 detection and polarimetric radar. Section II introduces the new detector that is tested with 54 RADARSAT-2 and Sentinel-1 data in Section III and IV respectively. An ordinary approach to iceberg detection considers the exploitation of algorithms previ-57 ously developed for ship detection. More specifically, several of these methodologies aim 58 at discriminating between targets and background clutter performing a statistical test on the 59 image brightness. The problem of selecting the threshold can be solved using the Neyman-60 Pearson lemma on the probability of detection (P d ) or false alarms (P f ) [14]. The most 61 common methodology is called constant false alarm rate (CFAR) and set a threshold that is 62 supposed to keep P f constant [15], [16], [17], [18], [19], [20], [21], [22], [23]. CFAR algo-63 rithms are generally (but not necessarily) applied to single intensity images. When only a single image is available, one important advantage of using a CFAR methodology, compared detections. 89 By using different polarizations, we want to add more physical information that can in-90 crease the contrast between targets and clutter.
where H stands for linear horizontal and V for linear vertical (therefore the HV image is ob-  Unfortunately, currently radar satellites (including RADARSAT-2, ALOS-2, TanDEM-X and Sentinel-1) can only provide very large swaths with dual-polarization data [33]. This is a 110 limitation for applications as iceberg detection, since the use of large swaths is fundamental.

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For this reason, we propose a detector combining the HH-and HV-polarized intensity data.

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On the other hand, it is expected that the use of quad-polarimetric data can improve the de-113 tection performance. In the future, the availability of polarimetric images with large swaths 114 may provide significant improvements in iceberg detection for operational purposes. In this section, a new algorithm is proposed for the detection of small icebergs embed-118 ded in sea ice. The design is based on the idea of producing a methodology that could be 119 eventually used operationally. At the moment, there are two clear constraints for operational 120 algorithms:

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(1) Data availability: we need to exploit acquisition modes able to cover large areas (e.g.

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(2) Processing burden: an operational detector should be fast and not excessively reliant on 125 high processing burden. For this reason, we tried to develop an algorithm that is efficient 126 and fast.

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The algorithm is based on the observation that icebergs or thick/deformed sea ice ex-128 hibit a different polarimetric behavior compared to thinner sea ice. Specifically, the cross 129 polarization channel and the ratio between cross-and co-polarizations (here referred as de-130 polarization ratio) increase. There are several physical explanations for such observations loss compared to sea ice. This allows for a much larger penetration of electromagnetic waves 133 in the iceberg (depending on the wavelength), which may lead to volume scattering or scat-134 tering from randomly oriented parts inside the ice body (e.g. ice lenses or pipes). Another 135 explanation is the presence of multiple reflections (specifically even-bounces) with random 136 orientations. Such multiple reflections can occur as double-bounce with the clutter surface 137 or the presence of cracks and structures in the ice body (e.g. pinnacles). In order to have 138 an increase of the cross-channel, the corner of the double-bounce has to have an orientation 139 (as seen by horizontally or vertically polarized waves) different from horizontal or vertical.

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Interestingly, this explanation does not require the dielectric constant to be very low (i.e. dry 141 conditions) and could be applied to wet conditions as well. This is because in wet conditions 142 the wave penetration is very limited and the icebergs appear as a set of oriented surfaces.

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The fact that the two previous explanations cover two different wetness conditions, in 144 theory, provides the detector with a wider applicability. As a final remark, it is interesting to 145 notice that the same observation can include two physical processes that are very different 146 from the polarimetric point of view. Random volume scattering is an incoherent process 147 with a low degree of polarization, while oriented even-bounce is highly coherent. This is a 148 clear indicator that the exploitation of polarimetric data is advantageous not just to detect the 149 icebergs, but also to retrieve geophysical parameters and/or information about the scattering 150 and reflection processes taking place.

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Two boxcar filters are applied over the HV and HH intensity images, exploiting two dif-152 ferent window sizes: a smaller test window w test and a larger training window w train . Details 153 on the dimensions are provided in next section. The detector, which we call DPolRAD, can 154 be written as: where test and train are the spatial averages using the test and training windows respec-156 tively and T Λ is a threshold.

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To gain some physical understanding of the proposed formula, some mathematical manip-158 ulations can be carried out. If the averages are expressed explicitly the following equation 159 can be derived (the mathematical manipulations are reported in the Appendix): ρ stands for cross-over-co polarization ratio, in the following defined as depolarization ratio.

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The subscript is used to identify if the ρ is estimated in the ring area or the training area. The 162 ring area is composed by the pixels of the training area that do no belong to the test area (e.g.

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a ring of pixels around the test area). As mentioned previously, this observable is sensitive 164 to the presence of volume scattering or orientated structures. Rρ is the ratio between the ρ 165 inside the test area over the one in the ring around the test area (i.e. Rρ = ρtest ρ ring ). RHV is 166 the ratio of the HV intensity in the test area over the ring area (i.e. RHV = |HV | 2 test |HV | 2 ring ). c is 167 a factor such that N train = cN test where N train and N test are the number of pixels inside the 168 training and test windows. ρ ring and ρ train are the depolarization ratios in the ring and the 169 entire training windows respectively.

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Analyzing some special condition is possible to gain insights into the nature of the detec-171 tor:

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(1) It is easy to proof that Λ is equal to zero if the depolarization ratio and the HV intensity 173 do not change between the ring and the test area. This is because ρ ring = ρ train and Rρ = RHV = 1. As a consequence, homogeneous areas will provide a Λ that is equal 175 to zero.

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(2) If and only if the depolarization ratio and the HV intensity are higher in the test area than 177 in the ring, then Λ becomes very large. An easy way to test this is by considering the 178 limit of Rρ and RHV going to infinity: Clearly, Rρ and RHV will never reach infinity in real data due to the noise level (i.e. the 180 values in the ring areas cannot be exactly zero).

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(3) Finally, if the volume or multiple reflections decrease drastically from the ring to the test To summarize, if an iceberg of the right size enters the test window, the value of Λ in-185 creases triggering a detection. However, if the iceberg or sea ice is significantly larger than 186 the test window it will contaminate the training window not providing a sufficient anomaly 187 to trigger the detector. The size of the test area depends on the size of the iceberg to detect.

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On the other hand, the size of the training area depends on the requirement we have in de In the following, we denote this expression as "HV-DePolRAD". If a pixel of the HV in- In order to test the detector, real RADARSAT-2 and Sentinel-1 data are exploited. In this 231 first section, results with quad-polarimetric Fine RADARSAT-2 acquisitions are presented.

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The latter are provided with a rather small swath width of around 25 km, therefore their use 233 for operational purposes is restricted to strategic areas. The test presented here demonstrates 234 the capabilities of the detector using image products with high spatial resolution. Moreover

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it is easier to identify icebergs visually and hence provide a mean of evaluating the detection In order to increase the probability to observe icebergs, the data were acquired in the basin  Table I presents the main characteristics of data exploited.

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Only a zoom of the second acquisition is shown here to provide a closer look at the detection 247 masks near the melange margin.      Table II summarizes some characteristics of all the EW Sentinel-1 images exploited [37].

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More details on acquisition times are provided in a following table.
289 Figure 3 shows the location of three of the 31 acquisitions to provide an idea of the geo-290 graphical area of interest and coverage.   Boxcar filter: 3 × 3 pixels.

C. Contrast enhancement 307
The capability of the HV-DPolRAD to enhance the contrast between icebergs and sea ice 308 is described in the following. The test window considers 3 × 3 pixels, while the training 309 window is 63 × 63 pixels. The results for the 6 images are shown in Figure 6. The scaling 310 used for these images is exactly the same as exploited for the HV magnitudes. The images 311 appear darker, because the sea ice clutter is strongly reduced. In these images, when the large frames instead of ring windows is that the former allow to have more clutter samples 330 that are different from zero. In this preliminary approach, the pixels equal to zero or above 331 a high empirical threshold are excluded to calculate the mean clutter. In the future more 332 elaborated methods to set the threshold will be investigated. This includes the attempt to  In the second series of images (Figure 9), the HV-DPolRAD seems again able to detect selected because the sea ice clutter is brighter and therefore it represents a harder challenge 354 to the detectors. Interestingly, the HV-DPolRAD is able to detect points that are missing in 355 the CA-CFAR detection mask. This is thanks to the enhanced contrast between sea ice and 356 icebergs.

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In the future, more work will be dedicated at understanding the potentialities of proposed 358 algorithms for operational purposes. Among other analysis, points as time burden and opti-359 mal threshold or windows selection will be tackled.

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The values for iceberg brightnesses used in the analysis are the ones representing the 370 maximum inside the bright area visually identified as iceberg after the smoothing with the 371 test window. These are the pixels that will contribute more for achieving the detection.

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The clutter brightnesses are estimated in each acquisition separately, using very large areas 373 containing sea ice. In this areas, the pixels previously identified as icebergs are removed to

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It is apparent that the contrast is highly improved and the clutter is strongly reduced. To 389 visualize this result, Figure 10 plots the ratios between the HV-DPolRAD and HV mean con-390 trasts and sea ice clutter levels. In the plot these are called "factor of improvement" since they 391 tell how many times the contrast is increased and the clutter level is reduced. Specifically, the 392 red curve was obtained from meanC(HV DP olRAD) meanC(HV ) , while the blue curve was calculated using 393

Clutter(HV )
Clutter(HV DP olRAD) . In March (colder conditions) the improvement in contrast seems to be 394 generally higher than 60 times (with few cases higher than 100). In April, the improvement 395 in contrast is more variable and probably depends on melting conditions that makes icebergs 396 less visible. In average, the factor of improvement is 75. Regarding the reduction of sea ice 397 clutter, this seems to be always higher than 20 in both months and average at approximately 398 35.

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The probability of detection for the HV-DPolRAD is always equal to one (all icebergs  icebergs and sea ice. The latter could also be used by ice analysis to aid visual inspection.

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The detector was tested with RADARSAT-2 quad-polarimetric data and Sentinel-1 Extra

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Wide swath HH/HV images. We selected 31 Sentinel-1 images acquired in the East Coast  In the future, more work will be dedicated to evaluate the potentialities of the proposed al-427 gorithms for operational use. Among other analyses, time burden and comparison of method-428 ologies for optimal threshold and windows selection will be tackled.

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In this section the derivation of the formula used to gain a physical understanding of the 431 detector is provided. We start from the expression: If |HV | 2 tr |HH| 2 tr = ρ tr we can rewrite Λ as: The averaging can be represented as the sum of the pixels inside an averaging window, divided by the total number of pixels considered. This is |HV i | 2 test = 1 Ntest Ntest i=1 |HV i | 2 . Additionally, the training window is composed by the test window plus a ring of pixels around the test window. Applying these two manipulations to the previous formula we obtain: If we define N ring = cN test the equation can be written as: Going back with the representation with angular brackets and considering the definition of the depolarization ratio the following expression can be written: If we define the ratio between the HV intensity of the test area over the ring area as RHV = |HV | 2 test |HV | 2 ring the expression can be modified as: Additionally we can define the ratio between the polarization ratio in the test over the ring area as ρ test = ρ ring Rρ. The expression becomes: ring Rρ −1 + cρ −1 ring RHV −1 − ρ tr