ON THE ANALYSIS OF OIL SPREADING IN BROKEN ICE

Transcription

1 Ice in the Environment: Proceedings of the 16th IAHR International Symposium on Ice Dunedin, New Zealand, 2nd 6th December 2002 International Association of Hydraulic Engineering and Research ON THE ANALYSIS OF OIL SPREADING IN BROKEN ICE Janne K.Ø. Gjøsteen 1 and Sveinung Løset 1 ABSTRACT Laboratory experiments have been conducted to investigate the process of oil spreading in cold waters in a broken ice cover. In each of the experiments, oil was poured on the water surface between ice floes in the center of the test area. The spreading process as well as the floe motion was recorded by four overhead video cameras. Each of them covered about a quarter of the experiment area. In this paper we describe closely how we prepared the pictures from the videos, and used them for automatic tracking of the floe trajectories, as well as finding the spatial and temporal distribution of the spilled oil. INTRODUCTION The experiments were carried out in a basin of dimension 30 6 m. However, the area where the experiments took place was reduced to a m section, separated from the rest of the basin by mobile booms. The ice floes were convex polygons, most of them with six corners and a diameter of about 0.5 to 1 m. Each of the floes were marked with two white paper markers, see Figure 5. An experiment started as oil was poured through a pipe with its outlet in the center of the test area. Shortly after the injection was completed, the ice cover was brought into motion by pulling one of the floes along the sides of the test area in a clockwise, circular motion. This floe was manoeuvered manually by two persons using two ropes attached to the floe. The experiment ended when the test area was covered with oil, or in some cases when no change of importance took place. It turned out that the cameras distorted the pictures significantly, which called for a transformation of the recorded images. By means of a grid with known dimensions we were able to find this transformation and apply it to all the pictures. After correcting each of the four camera images, they were stitched together to compose one larger image showing the complete test area. By using such completed pictures, we were able to track the position of the markers, which in turn gave the motion of the floes. Size and geometry of the oil 1 Deptartment of Structural Engineering, NTNU, N-7491 Trondheim, Norway

2 spill could be determined at any time using the same pictures. In this paper we will describe how we were able to track the trajectories of the floes and the geometry of the oil spill. DATA ACQUISITION Four cameras (black and white) were mounted on a frame above the basin, and were looking straight downwards. Each of them covered about one quarter on the test area, slightly overlapping each other. These four cameras were the primary source of information. The four cameras were connected to a multiplexer that made it possible to record one frame or picture from each camera consecutively. Afterwards, the tape was run through the multiplexer again to extract pictures for each of the four cameras and transfer them to separate tapes. The cameras were analog, and the tapes were digitized by a video card, Matrox (2002). Afterwards series of pictures were dumped at the same point in time for each of the four videos. For this purpose we used an image manipulation program, Adobe (2002). The time laps between the pictures had to be sufficiently small to allow us to determine the trajectories of the floes. CORRECTING THE IMAGES As mentioned, the overhead cameras distort the pictures, and this called for a transformation of the recorded images. We were able to do this by using a grid with known dimensions. The grid was placed on the water surface and recorded with the cameras. The outer dimensions for the wooden frame grid were m, and the inner squares were cm. The small size of the grid forced us to record the grid in two positions to cover each quarter of the test area, see Figure 1. We used a Matlab script to manually mark Figure 1: Example of how the grid was used. Note that we have drawn extra lines in the image to enhance them. points in the image, and save the pixel values for those points. A point was marked every place where the lines in the grid crossed each other. When all were picked, we knew the image coordinates or pixel values of the corners in each of the rectangles. As we knew the dimensions of the grid, we also knew the true position for each of the points. The rectangles in Figures 1 are in reality squares. All the squares have the same dimen-

3 sions, regardless of where in the picture they are. A transformation that satisfies these requirements will give us a picture almost free from distortions, except for small errors introduced in the correction procedure. We decided that the squares should be 50 by 50 pixels in the final, corrected image. In the original image, the rectangles were at most about 30 pixels wide. This means that the resolution of the final image is larger than for the original image, so no information should be lost in the process. This specific choice resulted in a final image of about pixels, while the original image had dimensions of pixels. (x 4, y 4 ) (x 3, y 3 ) (u 1, v 1 + N) (u 1 + N, v 1 + N) (x, y) (u, v) (x 1, y 1 ) (x 2, y 2 ) (u 1, v 1 ) (u 1 + N, v 1 ) (a) Original image. (b) Corrected image. Figure 2: Definitions of pixel values for the original and corrected image. For every pair of (u, v) (u 1, u 1 + N) (v 1, v 1 + N) we select a corresponding pixel coordinate (x, y) in the original image. The pixel (x, y) from the original image will be placed at position (u, v) in the corrected image. See Figure 2 for notation. Note that x and ys with subscript are pixel values marked in the original image, u 1 and v 1 are coordinates known from the grid, and N is in our case 50. Define u = u u 1 and v = v v 1 N N, (1) which both are numbers in the range (0, 1). They describe the relative position in the square of corrected image that we are working on right now. The mapping we used between the images is described by the equations: x = (1 v) (u x 2 + (1 u) x 1 ) + v (u x 3 + (1 u) x 4 ), (2) y = (1 u) (v y 2 + (1 v) y 1 ) + u (v y 3 + (1 v) y 4 ). (3) If we assume that the figure in our original image consists of straight lines, this will map the original lines on to the corrected lines. We do have curved lines, but the curvature is very small, so the error is negligible. STITCHING THE FOUR IMAGES TO ONE The stitching was done in three steps. The images were stitched together two by two, and finally those two were stitched together to one. In each step we used an image which had

4 some geometric feature that we could recognized in both images that were to be stitched. Images displaying the grid could be used, but also images with ice floes. When the pixel values of a specific feature had been picked in both images, we were able to combine them along a vertical or horizontal line that intersected this point. Figure 3: Example of camera views. It is quite straight forward, and is illustrated in the figures below. The four original images are shown in Figure 3. They are corrected, stitched two by two, and finally the resulting large image is shown in Figure 4. FLOE GEOMETRY The geometry of the floes was found by a Matlab script. The first image in a series was displayed, and the operator picked the coordinates of the floe corners. When the floe geometry is known, the center of mass can be computed by numeric integration. It is necessary to record the geometry of the floe in a convenient manner, and we chose to describe the floe as illustrated in Figure 5. Let the center of mass be denoted (x c, y c ). Each floe is defined to have as many arms a as it has corners, where each arm stretches from the center of mass to its respective corner. The angle between the system of reference and a 0 is denoted θ and the angle between a 0 and a n is α n. Let N be the number of corners in a floe and n (0, N 1). It is now sufficient to record N, a 0,..., a N 1 and α 0... α N 1 to describe the exact geometry of the floe, and for every time step (x c, y c, θ) will describe the exact location of the floe.

5 y Figure 4: Example of final, large image. a 2 a 1 α 2 α 1 α 3 α4 α 5 a 0 θ a 3 a 4 a 5 x Figure 5: Left: Definitions for description of a floe. Right: Each ice floe is marked with two white markers. MARKER DETECTION Each of the floes were marked with two white pieces of paper, each a quarter of an A4 sheet. See Figure 5. If we are able to track the position of these markers, we can also tell the trajectory of the floes. Both rotation and translation of the floes can be calculated. The main problems encountered when analysing the pictures for markers were the following: Reflections of the lights above the basin showed the same colour as the markers. The markers did not appear to be pure white in the recordings. In some sections of the test area they seemed to be darker than others. To keep track of the time, it was necessary to have it printed in the corner of the pictures. The text was white with black borders, and caused problems when a marker passed these areas of the image. The oil was released using a pipe, and its presence disturbed the view. Some of the images were garbled, containing black sections or lines, with the rest

6 of the image sometimes shifted up or down. It was probably caused by signal error between the cameras and the multiplexer. A semi-automatic routine for detecting the markers was developed. For the first image of a series, an approximated position was selected manually for each marker. The following steps were then repeated for each picture: 1. For each marker, the intensity of the picture in its close neighbourhood was calculated. Based on this a limit was set for which intensity should be regarded to be white (markers). This was to overcome the problems we encountered because the markers appeared to have slightly different colours depending on their location in the test section. 2. For each marker, a new position was estimated by extrapolating its past motion. Around this position a search was made for white pixels. Due to the estimation, the search area can be fairly small, which again reduces errors introduced by reflections in the water. 3. The positions of the detected white pixels were averaged to obtain the center of the marker. 4. If a marker can t be found, one of the following options must be chosen manually by inspecting the image: A position for the marker is suggested, and the complete procedure is repeated to detect the marker. A position for the marker is given. Skip the marker in this image, and search for it in the next one. The position will then be estimated based on this and old information. The program implementing this algorithm was written in C for efficiency reasons, using a toolkit to handle the graphics, Gtk (2002). MOVEMENT OF THE FLOES When the markers had been found and tracked, the next step was to determine the movement of the floes based on this information. For a floe, let the centers of the two markers be given by the coordinates x 1, y 1 and x 2, y 2. In addition, the floe s center of mass is given by x c, y c. A mark denotes the corresponding coordinates in the previous picture, see Figure 6 for illustration. The known parameters in one step are all the coordinates from the previous picture, as well as the coordinates of the markers in the present picture. To define the new position of the floe, we need to find the angle ϕ it has turned in addition to the distance the floe has travelled. As a start, we calculate two parameters, the angle β between the vectors a and b shown at right in Figure 6 and the ratio q between their lengths. Both parameters are constant and can be found by solving the equation [ ] [ ] [ ] x2 x 1 cos(β) sin(β) xc x = q 1 y 2 y 1 sin(β) cos(β) y c y 1 for the first image in a series. This image is anyway used to find the floe geometry and for that reason we know the coordinates of the mass center. We are then left with only two unknowns, and the system can be solved. (4)

7 (x 2, y 2 ) ϕ (x 1, y 1 ) (x c, y c ) (x 2, y 2 ) (x c, y c) (x 1, x 2 ) (x 2, y 2 ) b (x 1, y 1 ) β a (x c, y c ) Figure 6: Definition of points and angles. We are interested in the angle ϕ that a floe rotates. That is the same angle as the line through the markers rotates, and it is described in the same manner as above by the equation [ ] [ ] [ x2 x 1 cos(ϕ) sin(ϕ) x = 2 ] x 1 y 2 y 1 sin(ϕ) cos(ϕ) y 2. (5) y 1 Ideally, the length between the markers is constant, but in reality, it will vary slightly due to errors introduced when the markers are detected. For this reason, we must normalize the vectors by their length, which means that they both will have unit length before we solve for ϕ. OIL DETECTION The distribution of oil was found more or less manually. A snapshot was analysed by an image manipulation program, Gimp (2002) to determine the area covered by oil. By counting the number of pixels, and using the relationship between pixels and area, we were able to determine the real size of the oil slick. UNCERTAINTIES There are a number of uncertainties that need to be mentioned. In the process of correcting and building the images, they are introduced at the following points: 1. Marking the grid points. 2. The choice of where to stitch the four images together. An estimate of the maximal spatial error introduced is 3 cm, corresponding to an uncertainty of about 10 in angular computations, but it is probably smaller in most sections of the image. The areas that show the largest errors are the edges of the four original images, which means the sides of the composite image, as well as a horizontal and vertical section in the middle of the image. We believe that the uncertainties could be reduced to a large degree if the images were of better quality. We should have in mind that cameras of a relatively low quality were used to record the analog film, the film was then digitized, and pictures dumped from the digitized film. In this process, quality suffers. Another general problem is that we can hardly separate between thin and thick oil by visual inspection. The choice of detecting the oil manually increases the accuracy, as oil drops on floes or other dark areas of choice can be ignored.

8 When it comes to detection of markers, a number of difficulties were encountered. This will affect the calculated location and angle of the floe, and introduces an uncertainty of the same magnitude as the spatial uncertainty. CONCLUSIONS From the process we learned the following that others should be aware of if they intend to do something similar: You should use high quality video cameras, preferably digital, if you plan to use video as your primary source of data. It could very well be better with one camera in an oblique position. Then you only have to adjust the picture according to the grid and can avoid the stitching process. If the complete pictures are to be composed from several overhead cameras, be sure that they do not distort the picture. The griding process can then be avoided, and the images can be stitched together without further corrections. In general it is amazing how much information you can extract even from low quality data, if time allows. ACKNOWLEDGMENT The authors would like to thank the Hamburg Ship Model Basin (HSVA), especially the ice tank crew headed by Karl-Ulrich Evers, and Per Olav Moslet for additional assistance during the tests. The research activities carried out at the Large Scale Facility ARCTE- CLAB were granted by the Human Potential and Mobility Programme from the European Union through contract HPRI-CT Financial support from Norsk Hydro and The Research Council of Norway is gratefully acknowledged. They would also like to thank Kristian Gjøsteen for assistance with some of the programming tasks. REFERENCES Adobe. Adobe Premiere 6.0, (2002). Gimp. GNU Image Manipulation Program, (2002). Gtk. The GIMP Toolkit, (2002). Matrox. Matrox Marvel G400-TV, (2002).