First Order Statistics Classification of Sidescan Sonar Images from the Arctic Sea Ice

irst Order Statistics Classification of Sidescan Sonar Images from the Arctic Sea Ice S. Rueda, Dr. J. Bell, Dr. C. Capus Ocean Systems Lab. School of Engineering and Physical Sciences Heriot Watt University Riccarton EH14 4AS, Edinburgh, Scotland, UK Email: sr19@hw.ac.uk, J.Bell@hw.ac.uk, C.Capus@hw.ac.uk Abstract Polar regions, especially sensitive to small changes in temperature, play a key role in global climate change. Scientists are interested in evaluating the decline in local ice production. We will attempt to classify automatically irst Year (Y) ice, Multi Year (MY) ice and Deformed ice using Sidescan sonar images of the Arctic ice-shelf. We use 4-bit data (16 grey levels) ground truth images provided by an expert as a starting point of the study. These images have been obtained using a Sidescan sonar pointing upward. Our methods use first order statistics extracted from local areas of the image. The local histogram is fitted to three pdfs (Rayleigh, Log-normal and Gaussian distributions) whose parameters are extracted. A Chi-square test is used to evaluate the quality of the fit. The parameters are then used to classify the regions. The results obtained show that Y and MY ice follow Rayleigh or Log-normal distributions whereas Deformed ice is more like a Gaussian distribution. We have created a new method to classify ice types selecting the best fitting for each region. A classification of three classes (Y, MY and Deformed ice) is achieved with first order statistics. In future work we will investigate the potential of second order statistics to improve the classification. I. INTRODUCTION Changes in the Arctic region are closely related to global climate change. To study the interaction between the Arctic and climate, some expeditions have been undertaken and data has been extracted from the Pole. Our aim is to know the extent and the thickness of the sea ice, because we want to evaluate the decline in local ice production which can be an indication of climate change. As a result, we need to find out how much new ice has been formed, and how much is old. Other features of the ice cover, like Deformed ice regions, will give us more information about how climate change is affecting the Arctic. Sidescan sonar has been used to provide images from underneath the polar cap in the Arctic. The sidescan sonar has been put on a submarine which has travelled underneath the polar ice region creating images of the ice cover. With these images we want to identify environmental impacts on polar ice. As we have several thousand kilometres of image data, we will attempt to do an automated and consistent classification of ice types. We work with low quality images coded with 4- bit data (16 grey levels). We use as a base ground truth images manually classified by an expert on ice types. According to Sear and Wadhams [3] and Wadhams [4], each ice type presents its own characteristic features as well as some statistical properties. We can distinguish: - Multi Year ice (MY): rough surface. It presents hummocks and depressions. - irst Year ice (Y): smooth texture, generally featureless, though often criss-crossed with a pattern of narrow cracks. - Pressure ridges (R): linear sets of broken ice blocks. - Lead: represents open water or a zone recently refrozen. - Randomly Deformed ice (D): matrix with no identifiable structure. As stated by Sear and Wadhams in [3], MY ice, Deformed ice and Ridges are more likely to be juxtaposed, as well Y ice with leads. In the first stage, we redefine Deformed ice as rugged areas, usually with a white overall appearance. They rarely occur as simple bounded shapes. These often represent the infill areas between the more coherent Y and MY ice floes and include the linear ridge features. We will attempt to classify three classes: Y, MY and Deformed ice. We want to find out the statistical properties of each ice type texture to achieve a classification. A texture can be described by a random process. If the first order probability density function is invariant with spatial position, then the random process can be considered first order stationary. That means, that all the pixels in the image have the same probability of having a particular grey level. The first order probability density function of an image is its histogram. The first part of this study consist of explaining the methods that we use to achieve a classification of ice types. Then, in a second part we state the results obtained and finally we give a conclusion. The methods presented here, use histograms and probability density functions (pdf) to evaluate pixels distributions in the regions of interest (ROI). Then, we work with the pdf (because it is independent of the size of the ROI), subject to some minimum size constraint, to create a model of the regions selected. Therefore, we apply curve fitting techniques to the 1

pdf obtained in order to produce a minimum parameter model. We use Rayleigh, Log-normal and Gaussian distributions to fit our data. Then, we apply these parameters to classify ice types. The algorithms are tested on ground truth images to see the correspondence with the manually classified data. We present the results in one segmented image displaying the three ice types that we are interested on. II. METHODS A. The histogram and probability density function The histogram gives information about the frequency of occurence of grey levels in an image or region of interest. We have plotted the histograms for each ice type to see if there is a significant difference between them. To make the results independent of the number of pixels, we divide the histograms by the total number of pixels. We then obtain the probability density function of the regions of interest. If we take several regions of each ice type, the pdfs obtained are shown in ig.1. Probability density.45.4.35.3.25.2.15.1.5 ig. 1. PD COMPARISON Deformed ice Deformed ice Y ice Y ice Y ice MY ice MY ice 5 1 15 2 25 Gray level PD comparison of ice types We see that we can easily distinguish Y, MY and Deformed ice using the pdf. To produce a minimum parameter model of texture, standard curve fitting techniques can be applied to obtain an approximate fit to the curve of the image pdf. Then only the parameters required to describe the curves need to be stored to create a model to fit the texture. Y ice and MY ice seems to follow a Rayleigh or Log-normal distribution. Deformed is more like a Gaussian distribution. B. Distribution itting The sidescan sonar images that we are processing are the result of an acoustic field scattered from a random ice surface. According to Bell [1], the acoustic field is complex and follows Gaussian distributions when the number of elementary waves scattered tends to infinity. In addition, the amplitude of the field will have a Rayleigh distribution if its real and imaginary parts are uncorrelated and independent. This is the case for sidescan sonar images which are expected to have Rayleigh statistics except in the region of the image where the beam sent by the sonar was normal to the surface. The rougher the surface is, the less Rayleigh distribution it has. This is why the pdfs of Y and MY ice seem to follow Rayleigh distributions and Deformed ice looks more like a Gaussian distribution. This is due to the fact that deformed regions are very rough. 1) The Rayleigh distribution: the Rayleigh pdf is defined (1) in [2] by: where represents the grey level magnitude and is the scale parameter which is equal to the mean-square value of the individual amplitudes :. We have introduced an offset parameter in the formula to allow translations of the Rayleigh pdf in the axis. Therefore, we transform a one parameter distribution into a two-parameter distribution. This means that we can fit better our pdfs because they do not start always at. If we call the offset, the formula becomes:!#" $ %'& )(" -+*), /.)123 54 56 (2) We will try to apply fitting techniques to our data to describe the curves only with the parameters associated to the distributions. We use a least square error technique to find the best estimation of the data. This method consists of calculating the squared error, which is the sum of the squared differences between each sample and the expected value as predicted by the function. The least square error has the general expression: 789<?>A@ ;:! CBED (3) where! are the values of the original data andd are the values of the curve obtained by fitting the data. The results obtained with a Rayleigh fitting are shown in ig. 2. Probability Density unction.45.4.35.3.25.2.15.1.5 RAYLEIGH ITTING 5 1 15 2 25 3 Grey level ig. 2. The Rayleigh distribution fitting Apparently we can fit a Rayleigh in Y and MY ice regions, but for Deformed ice, the fitting does not look good. 2

M Y Y Z Z We cannot distinguish MY and Deformed ice just with the plots. We need to analyze the parameters of these distributions fitted to see if they can help to distinguish MY and Deformed ice. To separate the distributions we have used the parameter which is related HG - to the Rayleigh scale as:. The parameters and offset obtained are shown in Table I. TABLE I RAYLEIGH PARAMETERS b offset 2.1216 32 Y 23.1228 3 45.732 38 MY 5.5719 37 63.9795 26 D 55.1637 26 The rougher the region of ice selected, the higher the parameter is. The parameters are different for each ice type selected. We will see in the part of the Results how good is the classification using this method. 2) The Log-normal distribution: it is a two-parameter distribution described by its mean I and its standard deviation J. The formula used to fit the data is: DK! $ LI J J N PO.3QRS.2TVU)2 (4) XW If we apply curve fitting techniques to our data using Lognormal distributions, we get ig. 3. Probability Density unction.45.4.35.3.25.2.15.1.5 LOG NORMAL ITTING 5 1 15 2 25 3 Grey level ig. 3. The Log-normal distribution fitting As before, the plots of MY and Deformed ice are located in the same ranks of values. We need to have a look at the parameters to see if they are sufficient to distinguish between ice types. They are shown in Table II. As with Rayleigh distributions, the parameters are higher in MY and Deformed ice than in Y ice. This is also due to the roughness of the surface. A classification of three ice types can be achieved considering both parameters. TABLE II LOG-NORMAL PARAMETERS 53.785 1.282 Y 56.374 1.28 89.299 1.385 MY 94.917 1.41 17.125 1.354 D 88.855 1.519 3) The Gaussian distribution: it is a bell shaped model defined by two parameters: the mean I and the standard deviation J. This kind of distribution follows the formula: DK! $ LI J J N M #O.)VU)2 (5) XW If we use this distribution to fit our data we get the curves in ig. 4. Probability density function.45.4.35.3.25.2.15.1.5 GAUSS ITTING 5 1 15 2 25 Grey level ig. 4. The Gaussian distribution fitting Only Deformed ice is well fitted by Gaussian distributions. The parameters I and J obtained for all the fittings presented are shown in Table III. TABLE III GAUSSIAN PARAMETERS 56.248 16.632 Y 61.354 19.88 94.177 3.483 MY 99.34 32.94 17.787 3.185 D 137.277 41.246 As before, the rougher the surface is, the higher the mean is. But we know from inspection of ig. 4. that this distribution does not fit Y and MY ice well, only Deformed ice. We will see in section III that a good classification cannot be achieved using Gaussian distributions. 3

^ 4) Comparison between fitting techniques: we have used a Chi-square ([ ) test to determine the consistency of the fitting. It compares the pdf data with the fitted distribution for each method applied. The formula used is: [ <\ $] B_^ (6) ] where are the values of the pdf of our data, which represents the probability of pixels within the region selected having a grey level ` ^, and is the value of the fitted distribution at grey level`. Applying this method for the same representative regions, we can see how good are our fittings. We have selected some characteristic regions for the three ice types considered, the [ values obtained for all the distributions used are shown in Table IV. TABLE IV CHI SQUARE PARAMETERS Rayleigh Log-normal Gaussian.2699.2472 18.2692 Y 785.618.32138 acbdadfehgjikl.19579.5481 acba)mjkjmhgjik)n.1128.7456.2636 MY.15733.7747.246.817.2952.7944.23566 1.8559.3844 D.22987.25737.6626.17258.2911.1412 If we analyze these results, we can notice that for Y ice, a good fitting is found with Rayleigh and Log-normal in most of the cases. The best fitting is found using a Log-normal distribution because it has the lowest values for the regions of interest selected in this case. The Gaussian distribution does not fit Y ice well, because the[ value is very big. or MY ice, all three distributions seems to fit the data well. Overall, the best fitting is again obtained when we use the Log-normal distribution to fit the data. But the Rayleigh distribution provides the best fit for one case only. The Gaussian distributions fit MY ice well but they are worse than the other two distributions because the [ value is always higher. or Deformed ice, Gaussian distribution seems to fit the data better because the values represented are lower than the others. or the other two distributions, the Rayleigh distribution seems more consistent than the Log-normal distribution. Y, MY and Deformed. 1) Classification using the fitted Rayleigh, Log-normal and Gaussian parameters: firstly, we define some training patterns representative of each class (Y, MY and Deformed ice) taken from various images. Then, we fit the distributions to them and get the associated parameters. Secondly, we form a vector of targets which provides correspondence between the parameters of the training patterns and the classes they belong to. Thirdly, we cut the image selected into regions of interest (ROIs), with or without overlapping, of a user-defined size and apply the fitting techniques to obtain the distribution parameters of the regions. After analyzing the statistical properties of regions with different sizes, we can state that the minimum size of the regions that we can use without losing the statistical properties is 25 x 25 pixels. inally, a linear discriminant classifier is used to compare the parameters obtained for each region with those of the training patterns to assign a class to each of the image regions. When we get the class of each region we form a new image putting each class in one colour. We have defined Y ice in black, MY ice in white and Deformed ice in grey. 2) Classification using the best fitted parameters: we have seen that Y and MY ice were well fitted with Log-normal and Rayleigh distributions because they presented the lowest [ values for these ice types. Nevertheless, Deformed ice was best fitted by Gaussian distributions. Consequently, it would be interesting to use the [ value to perform our classification, and get the best results than we can. Each region will be classified by the method which best fits its pdf. Therefore, we have stated a new method (cf. ig. 5) which selects for each ROI considered in the image, the best fitted distribution comparing the [ values for the Rayleigh, Lognormal and Gaussian distributions. In other words, as before, we divide the image into regions and we classify each of them independently. We calculate the Rayleigh, Log-normal and Gaussian parameters and the[ value for each ROI. We assign the method that we need to use for each region considering the lowest [ value. With this method we achieve the best classification for each region considered. These results agree with our observations from the plots, which are that Y and MY ice are best fitted by a Log-normal or a Rayleigh distribution but Deformed ice is best fitted by a Gaussian distribution. C. Classification with irst Order Statistics Using the parameters obtained with the methods presented above, we can achieve a segmentation of the three ice types: ig. 5. Schematic of classification process 4

III. RESULTS We use the image ig. 6. because it has all three classes and we have a full ground truth classmap as shown in ig. 7. We have applied this methods to other images and the results of the segmentation found are also good. The image that we will attempt to classify has 179 x 2852 pixels and is shown in ig. 6. ig. 9. Classification using Rayleigh distributions (non overlapped regions of size 25x25 parametero) It seems that classifying only with the parameter gives a more accurate classification, and the result is closer to the classes defined in the ground truth image. ig. 6. Original image Y ice, MY ice and Deformed ice (D) The ground truth image that we use is shown in ig. 7. In order to follow class boundaries of the original image in a smoother way, we consider overlapped regions of size 25 x 25, shifting one pixel at a time. We get the result in ig. 1. ig. 7. Ground Truth Image Y ice, MY ice and Deformed ice (D) ig. 1. Classification using Rayleigh distributions (overlapping regions of size 25x25) A. Classification using Rayleigh parameters If we use the parameters and offset to achieve a classification, for non-overlapped regions with size 25 x 25, we get the result presented in ig. 8. The result is very good but the algorithm with overlapping is comparatively very slow because we need to perform 25 x 25 times as many calculations. We extract the boundary contours for each class and plot over the original image to see how good the classification is. The result is shown in ig. 11. ig. 8. Classification using Rayleigh distributions (non overlapped regions of size 25x25 parameters o and offset) If we use only to classify, the result appears in ig. 9. ig. 11. Contour result overlapped on the original image (MY ice: white contour Deformed ice: red contour Y ice: others) 5

B. Classification using Log-normal parameters As before, using non-overlapped regions of size 25 x 25, we get ig. 12. This offers the best accuracy/time trade-off, so we did not continue with overlapped regions. ig. 14. Classification using best fitted distributions (non overlapped regions of size 25x25) ig. 12. Classification using Log-normal distributions (non overlapped regions of size 25x25) C. Classification using Gaussian parameters We found that if classes were confused with a large region size, the results cannot be improved with reduced region sizes. With Gaussian parameters and dividing the image into nonoverlapped regions with size 5 x 5, we obtain ig. 13. IV. CONCLUSION We presented a classification of ice types using first order statistics and curve fitting techniques. The results obtained show that Y and MY ice are well fitted by Rayleigh or Log-normal distributions whereas Deformed ice tends to follow a Gaussian distribution. Applying a linear classifier with these three distribution types, we got good results if we used Rayleigh or Log-normal distributions but with Gaussian distributions confusion appears between MY and Deformed ice. or this reason we proposed another method to select the best classification for each region of the image using a [ parameter. This gave us the best results with curve fitting techniques. We found that the minimum size ROIs that we could use to conserve the statistical properties was 25x25 pixels. If the regions of the image are overlapped when we do the classification, the results more accurately follow the class boundaries of the original image. ig. 13. Classification using Gaussian distributions (non overlapped regions of size 5x5) As we can see there is a confusion between MY and Deformed ice. Therefore we do not need to classify this with smaller regions because the result will not be better. D. Classification using best fitted parameters Using the method presented above to select the distribution which best fits each region, without overlapping and for regions with size of 25 x 25, we achieve the classification shown in ig. 14. ACKNOWLEDGMENTS The sidescan sonar images used in this study were provided by The Scottish Association for Marine Science. In particular we wish to thank Martin Doble for providing the ground truth images that helped us in classification of the ice types. This work has been partially supported by the 5th ramework Program of research of the European Community through the AMASON (EVK3-CT-21-59) project and by the Conseil Régional de Bretagne through the Ulysse fellowship. REERENCES [1] J. BELL, A model for the Simulation of Sidescan Sonar, PhD Thesis, Heriot-Watt University, 1995 [2] G.R. ELSTON, Sonar Simulation a Visualisation Using an Acoustic Pseudospectral time-domain Model, PhD Thesis, Heriot-Watt University, 23 [3] C.B SEAR and P. WADHAMS, Statistical properties of Arctic sea ice morphology derived from sidescan sonar images, Progress in Oceanography, Vol. 29, No. 2, pp. 133-16, 1992 [4] P. WADHAMS, The underside of Arctic sea ice imaged by sidescan sonar, Nature Vol. 333, No. 6169, pp. 161-164, 1988 6