Encyclopedia of Ocean Engineering

Living Edition
| Editors: Weicheng Cui, Shixiao Fu, Zhiqiang Hu

Application of Image Processing in Ice–Structure Interaction

  • Qin ZhangEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-981-10-6963-5_131-1


The understanding of Arctic physical processes and sustainable exploration, exploitation, and management of Arctic resources require more detailed, precise, and continuous measurements of sea ice parameters. Because various types of ice are in the ice-covered regions and the sizes of the ice floes can range from about 1 meter to kilometers, the temporally and spatially continuous field observations of sea ice are necessary for marine activities. One of the best ways of observing the ice conditions in the oceans is by using aerial or nautical imagery. The use of cameras as sensors on mobile sensor platforms (e.g., unmanned vehicles) will aid the development of sea ice observation. It has the potential of continuous measurements with high precision, which is particularly important for providing detailed localized information of sea ice to ensure safe operations of structures in ice-covered regions (Haugen et al. 2011).

The collected ice images or videos must be analyzed by dedicated computer algorithms to extract useful ice information to dynamic ice estimators and for decision support in Arctic offshore engineering. Therefore, this article introduces image processing algorithms for providing the ice parameters that are important factors in the analysis of ice–structure interaction in an ice field. These useful ice parameters include ice concentration, ice types, ice floe size, and floe size distribution, and they are defined as follows.

Ice Concentration

Ice concentration (IC) is the ratio of ice on unit area of sea surface; it has been identified as one of the most influencing parameters on the magnitude of experienced forces during model tests (van der Werff et al. 2012; Comfort et al. 1999). To obtain ice concentration from a visual ice image, only the visible ice can be considered, including brash ice, and submerged ice if visible in the image. With the image area, the height of image taken above the ice sheet, and the segmentation which is the identification of the ice from water, the actual area of sea ice and sea surface can be derived. However, the actual domain area is not necessary for calculating ice concentration. In simplified terms, ice concentration from a digital visual image is defined as the area of sea surface covered by visible ice observable in the 2D visual image taken vertically from above, as a fraction of the whole sea surface domain area. Hence, it is the ratio of the number of pixels of visible ice to the total number of pixels within the image domain. Note that the domain area is an effective area within the image, excluding land or other nonrelevant areas. The ice concentration is then given by (Zhang et al. 2012a)
$$ {\displaystyle \begin{array}{l} IC=f\left(\mathrm{image},, \mathrm{area},,,\mathrm{height}\ \mathrm{above}\ \mathrm{ice}\;\mathrm{sheet},,\mathrm{segmentation}\right)\\ {}\quad =\frac{\mathrm{Area}\ \mathrm{of}\ \mathrm{all}\ \mathrm{visible}\ \mathrm{ice}}{\mathrm{Actual}\ \mathrm{domain}\ \mathrm{area}}\\ {}\quad =\frac{\mathrm{No}.\mathrm{of}\ \mathrm{pixels}\ \mathrm{of}\ \mathrm{visible}\ \mathrm{ice}\ \mathrm{in}\ \mathrm{image}\ \mathrm{domain}}{\mathrm{Total}\ \mathrm{no}.\mathrm{of}\ \mathrm{pixels}\ \mathrm{in}\ \mathrm{image}\ \mathrm{domain}}\end{array}}. $$

Ice Types

Sea ice is any form of ice found at sea which has originated from the freezing of sea water. Different types of sea ice have different physical properties. Since one generally assumes that brash ice has a dampening effect in models for calculating ice pressure and ice forces, it may be more convenient to estimate the distribution between three classes, that is, the ratio of ice floes, the ratio of brash ice, and the ratio of water. As defined (Løset et al. 2006):
  • Floe is any relatively flat piece of sea ice 20 m or more across. It is subdivided according to horizontal extent. A giant flow is over 10 km across; a vast floe is 2–10 km across; a big floe is 500–2000 m across; a medium floe is 100–500 m across; and a small floe is 20–100 m across.

  • Ice cake is any relatively flat piece of sea ice less than 20 m across.

  • Brash ice is accumulations of floating ice made up of fragments not more than 2 m across and the wreckage of other forms of ice. It is common between colliding floes or in regions where pressure ridges have collapsed.

  • Slush is snow which is saturated and mixed with water on land or ice surfaces or as a viscous floating mass in water after heavy snowfall.

For simplicity, the size of sea ice piece is the only criterion to distinguish ice floe and brash ice in this research. That is, any relatively flat piece of sea ice 2 m or more across is considered as “ice floe,” while any relatively flat piece of sea ice less than 2 m across is considered as “brash ice (piece).” And the rest of ice pixels, e.g., single ice pixels or the ice pieces that are too small to be treated as brash ice, are considered as “slush.”

Ice Floe Size and Floe Size Distribution

The estimation of ice floe size and floe size distribution among the “ice floes” gives an important set of parameters from ice images. In image processing, the ice floe size can be determined by the number of pixels in the identified floe. If the focal length f and camera height are available, the actual size in SI unit of the ice floes and floe size distribution can also be calculated (Lu and Li 2010) by converting the image pixel size to its SI unit size.

Image Processing Methods

A digital image is a numeric representation of a two-dimensional picture, and it is composed of pixels which are the smallest individual elements in the image. A pixel holds quantized values that represent the color or gray level of the image at a particular point.

Ice Pixel Detection

Ice concentration, as defined, is a binary decision of each pixel to determine whether it belongs to the class “ice” or to the class “water.” From Eq. 1, it is clear that the detection of the ice pixels from water pixels is crucial to obtaining the ice concentration from an ice image.

Otsu Thresholding

The pixels in the same region have similar intensity. Based on that sea ice is whiter than open water, ice pixels have higher intensity values than those belonging to water in a uniform illumination ice image. Thus, the thresholding, which is based on the pixel’s gray-level to turn a grayscale image into a binary image (whose pixels have only two possible intensity values, e.g., “0” and “1”), is a natural way to segment ice regions from water regions.

Assuming that an object is brighter than the background, the object and background pixels have intensity levels grouped into two dominant modes. A threshold value T is chosen to separate an image into an “object region” and a “background region.” Individual pixels are marked as “object” pixels if their value is greater than the threshold value and as “background” pixels otherwise, that is:
$$ g\left(x,y\right)=\left\{\begin{array}{ll}1& \mathrm{if}\;f\left(x,y\right)>T\\ {}0& \mathrm{if}\;f\left(x,y\right)\le T\end{array}\right. $$
where g(x, y) and f (x, y) are the pixel values located in the xth column and yth row of the binary and grayscale image, respectively. Then, the grayscale image is turned into a binary image. The key of thresholding method is how to select the threshold value.
The Otsu thresholding method (Otsu 1975) is one of the most common automatic threshold segmentation algorithms. It requires that the histogram (the distribution of gray value) is bimodal and the illumination is uniform. In this method, the histogram of the image is divided into two classes (i.e., the pixels are classified as either foreground or background), and the goal is to find the threshold value that minimizes the within-class variance, given by (Otsu 1975)
$$ {\sigma}_w^2(T)={\omega}_1(T){\sigma}_1^2(T)+{\omega}_2(T){\sigma}_2^2(T) $$
where ω1 and ω2 are the probabilities of the two classes separated by a threshold T and σ1 and σ2 are the variances of these two classes. The threshold with the maximum between-class variance also has the minimum within-class variance. The between-class variance is given by (Otsu 1975)
$$ {\displaystyle \begin{array}{l}{\sigma}_b^2(T)={\omega}_1(T){\left({\mu}_1(T)-\mu (T)\right)}^2+{\omega}_2(T){\left({\mu}_2(T)-\mu (T)\right)}^2\\ {}\quad \quad \cong {\omega}_1(T){\omega}_2(T){\left({\mu}_1(T)-{\mu}_2(T)\right)}^2\end{array}} $$
where μ1 and μ2 are the means of these two classes and μ(T) = ω1(T)μ1(T) + ω2(T)μ2(T). This expression can also be used to find the best threshold and to update the threshold value iteratively.

K-means Clustering

Clustering is a statistical data analysis method that divides a data set into many groups (Basak et al. 1988), and it has been widely used in image segmentation, especially classifying the objects into many groups. This method is based on the mathematical distance measure between individual observations and groups of observations to find hidden structures in unlabeled data and assign the unlabeled data into groups, so that the data in one group are more similar to each other than to those in other groups.

Among various clustering algorithms, k-means is one of the simplest but most popular clustering algorithms. The goal of k-means clustering is to minimize the within-cluster sum of distance to partition a set of data into k clusters (MacQueen 1967). The step-by-step algorithm for this method in image segmentation is described below:

Step 1: For image processing, a set of gray levels is given:
$$ f\left({x}_1,{y}_1\right),f\left({x}_2,{y}_2\right),\cdots, f\left({x}_n,{y}_n\right). $$
Step 2: Partition this set into k clusters:
$$ {f}_i\left({x}_1,{y}_1\right),{f}_i\left({x}_2,{y}_2\right),\cdots, {f}_i\left({x}_{n_i},{y}_{n_i}\right)\quad \quad i=1,2,\cdots, k. $$
Step 3: Calculate the local means of each cluster:
$$ {c}_i=\frac{1}{n_i}\sum \limits_{m=1}^{n_i}{f}_i\left({x}_m,{y}_m\right)\quad \quad i=1,2,\cdots, k. $$
Step 4: Gray level f(xj, yj) (j = 1, 2, …, n) belongs to set p (p = 1, 2, …, k) if it has the shortest distance to set p than any other sets:
$$ \mid f\left({x}_j,{y}_j\right)-{c}_p\mid \le \mid f\left({x}_j,{y}_j\right)-{c}_i\mid \quad \quad i=1,2,\cdots, k. $$

Iterate Steps 3 and 4 until the local means are unchanged.

Ice Floe Boundary Detection

In image processing, the detection of ice floe boundaries can be used to distinguish individual ice floes. With the individual ice floe identification result, ice floe characteristics, such as location, area, perimeter, and shape measurements of each ice floe, together with the floe size distribution can thereby be estimated. Thus, ice floe boundary detection is a vital for extracting information of ice floes from ice images.

In an actual ice-covered environment, especially in marginal ice zone (MIZ), ice floes typically touch each other, and the edges between touching floes may be difficult to identify in digital images. This issue significantly affects the analysis of individual ice floe properties and floe size distribution. Among various floe boundary detection methods, for example, derivative boundary detection (Zhang et al. 2012a, b), morphology-based method (Zhang et al. 2012a, b; Banfield 1991; Banfield and Raftery 1992), watershed-based algorithms (Blunt et al. 2012; Zhang et al. 2013), etc., the GVF (gradient vector flow) snake-based approach (Zhang et al. 2015; Zhang and Skjetne 2015) is the most advanced method nowadays.

The GVF snake algorithm (Xu and Prince 1998) is an extension of the traditional snake (also known as active contours) algorithm (Kass et al. 1988) (the details of the traditional and GVF snake algorithms can be found in “Appendix A”). It has a good capability in the detection of weak boundaries. However, proper initial contours (an initial contour is a starting set of snake points for the evolution) are required by the GVF snake algorithm in ice floe boundary detection, especially when detecting the boundaries of massive ice floes. For each ice floe, it was showed that the initial contour close to the actual floe boundary, located inside the floe and centered as close to the ice floe center, is most effective (Zhang and Skjetne 2015). To accomplish the requirements of the initial contour without manual interaction, an automatic contour initialization algorithm based on the distance transform (the details of the distance transform can be found in “Appendix B”) and its regional maxima (a regional maximum is a connected component of pixels with a value greater than any of its neighbors) is concluded as follows (Zhang and Skjetne 2014, 2015):
  • Step 1: Convert the ice image into binary image after separating the ice from the water, in which case the pixels with value “1” indicate ice and pixels with value “0” indicate water; see Fig. 1a.

  • Step 2: Perform the distance transform to the binary image, and find the regional maxima shown as the green numerals in Fig. 1b.

  • Step 3: Merge the regional maxima into a big one if they have a short distance to each other, and then find the “seeds” that are centers of the regional maxima (including the merged ones), shown as red “+” in Figs. 1b and 2b.

  • Step 4: Initialize the circular-shaped contours located at the seeds with the radii selected according to the pixel value at the seeds in the distance map; see the blue circles in Figs. 1b and 2b.

Fig. 1

Contour initialization algorithm

Fig. 2

Touching ice floe separation based on GVF snake

After initializing the contours, the GVF snake algorithm is run on each contour to detect the floe boundary. By superimposing all the detected boundaries over the binarized ice image, it allows to separate touching ice floes and thereby be able to identify individual floes, as shown in Fig. 2.

Floe Shape Enhancement

Some segmented floes may contain holes or smaller ice floes inside after boundary detection, and the shape of the segmented ice floe is rough. To smoothen the shape of the ice floe, morphological cleaning is used after ice floe boundary detection.

Morphological cleaning is a combination of first morphological closing and then morphological opening (Soh et al. 1998) on an image. Assume A is a binary image and B is a chosen structuring element (a structuring element is a shape that is used to probe an input image and draw conclusions on how the structuring element fits or misses the shapes in the input image. It can be represented as a matrix of 1 s, indicating the points that belong to the structuring element, and 0 s indicating otherwise); the morphological closing of A by B, denoted AB, is a dilation followed by an erosion (the details of dilation and erosion operations can be found in “Appendix C”):
$$ A\bullet B=\left(A\oplus B\right)\ominus B $$
where ⨁ and ⊖ denote dilation and erosion, respectively. The morphological closing is the complement of the union of all translations of B that do not overlap A. It tends to smooth the contours of objects, generally joins narrow breaks, fills long thin gulfs, and fills holes smaller than the structuring element as seen in Fig. 3b.
Fig. 3

Morphological cleaning by using a 2 × 2 square structuring element

The morphological opening of A by B, denoted AB, is an erosion followed by a dilation:
$$ A\circ B=\left(A\ominus B\right)\oplus B. $$

The morphological opening is the union of all the translations of B that fit entirely within A. It can remove complete regions of an object that cannot contain the structuring element, smooths object contours, breaks thin connections, and removes thin protrusions as shown in Fig. 3c.

To ensure that smaller ice floes contained in larger floes are removed, the morphological cleaning should be performed on smaller floes first. Thus, the shape enhancement includes following two steps (Zhang and Skjetne 2014):
  • Step 1: Arrange all the segmented ice floes from small to large.

  • Step 2: Perform the morphological cleaning to the arranged ice floes in sequence.

The shape enhancement result is shown in Fig. 4c.
Fig. 4

Ice shape enhancement

Applications in Arctic Offshore Engineering

Model Ice Image Processing Applications

Before performing an analysis at full scale, the dynamic positioning (DP) experiments in model ice at the Hamburg Ship Model Basin (HSVA) in May 2011 allow for the testing of relevant image processing algorithms. This section shows the applications of the image processing techniques for determining important ice parameters from model ice data in the model-scale ice–structure analysis.

In these DP experients, a managed ice condition was obtained by cutting the level ice layer into predefined ice floe shapes, and the behavior of two different model ships (an Arctic drillship and a polar research vessel) in a broken-ice field was studied. Four different types of ice fields were tested, varying in ice concentration and ice floe size distribution, as shown in Table 1. The model ice image data provided from the experiments includes two complete overview pictures from run nos. 5100 and 5200 and the videos of each of the four model test runs (see Table 1). The overall tank images were retrieved by stitching 28 top view pictures taken before execution of the model tests, showing a complete overview of the ice floe distribution in the ice tank, as seen in Fig. 5. The videos captured the local conditions around the fixed model vessel with a constant heading of 180° during each run by a top view video camera moving along with the carriage and model, as seen in Fig. 6. The four model ice videos are more than 24 min long with a frame rate of 25 fps. Since a video is composed from a sequence of frames, by gathering the result for each analyzed frame, the model ice parameters over time are retrieved. Before applying the algorithms to these videos, one frame per second is found sufficient, and each frame was fed to the program for further processing (Zhang et al. 2012b).
Table 1

Managed ice conditions in the test runs, target values (full scale)

Run no.

IC [%]

Floe size 1 (45%) [m]

Floe size 2 (40%) [m]

Floe size 3 (15%) [m]





















Fig. 5

Overall tank image for run no. 5100. Target ice concentration of 86%

Fig. 6

One frame in the original video. Run no. 5400

Ice Concentration

Both Otsu thresholding and k-means clustering methods have been used to determine the ice concentration in model basin for run nos. 5100 and 5200. The analysis results are compared with the target ice concentration values, as presented in Table 2. Because the intensity values of all the model ice pixels are significantly higher than water pixels, both methods give similar result (Zhang et al. 2012b) and are both effective, as shown in Fig. 7.
Table 2

Ice concentrations derived from different methods


Target value (%)

Otsu (%)

K-means (%)

Run no. 5100




Run no. 5200




Fig. 7

Ice pixel detection for run no. 5100

When analyzing the ice concentrations in the vicinity of the model ship, the impediments around the tank in the videos are removed, and the vessel in the middle bottom of the tank is eliminated by a black rectangle, as seen in Fig. 8a. Then, the Otsu’s and the k-means methods are applied in the video processing to calculate the ice concentration as a function of time. Figure 9 shows the variation of the calculated ice concentration in time for all test runs based on the Otsu’s method, and the average ice concentrations after reaching the limiting values in all test runs are summarized in Table 3. Reduced ice concentration in the initial part of the test runs (before convergence) is related to the model ship positioning. It is an unwanted phenomenon, since it reduces the effective length of the ice tank. In all test runs, it was observed that the ice concentration in the near vicinity of the model was reaching a limiting value of approximately 80–89%, irrespective of the starting ice concentrations and floe sizes. This phenomenon can be explained by the tank’s wall effect. That is, the ice floes were compacted by the model ship toward the end of the basin, such that the ice concentration asymptotically approached a limiting value.
Fig. 8

Frames of run no. 5100 at 816 s and ice detection

Fig. 9

Time-varying IC of run nos. 5100–5400 based on Otsu thresholding

Table 3

Average IC after reaching saturation in all test runs

Run no.





Start time (s)





Average IC





Within the image analysis results, the time series of the ice concentration have been compared with the absolute total hull forces that were measured during the tests to investigate the relation between the ice concentration and the hull forces (see Fig. 10, for instance) (van der Werff et al. 2012). Further investigations are under consideration.
Fig. 10

Hull force and ice concentration time series for run no. 5100 (high IC, large floes)

Model Ice Floe Monitoring

In one of the model ice tests as seen in Fig. 11a, the ice floes were modeled square shapes with predefined side lengths, and the largest floe has an area less than a predefined value. To evolve the GVF snake algorithm effectively for identifying ice floe boundaries, an automatic initial contour initialization method was introduced in section “Ice Floe Boundary Detection.”. However, it is difficult for the contour initialization method to initialize the contours for each square-shaped ice floe as shown in Fig. 11b, so that the GVF snake algorithm is unable to find all floe boundaries and many floes still touch each other as shown in Fig. 11c. Thus, an additional round of contour initialization and segmentation is required.
Fig. 11

Crowded model ice floe segmentation

In this model ice test, although these model ice floes are not perfect squares, most of the floes could be approximated as rectangles with a length-to-width ratio less than the given threshold. Based on the characteristics of these rectangle-shaped model ice floes, the following three criteria can be used to determine whether it is necessary to initialize the contours and conduct a second segmentation (Zhang et al. 2015):
  • The ice floe area is less than a given threshold.

  • The ice floe has a convex shape (it could be done by determining if the ratio between the floe area and its minimum bounding polygon area is larger than the threshold).

  • The length-to-width ratio of the minimum bounding rectangle of the ice floe is less than the threshold.

Note that these criteria are designed for segmenting the rectangular-shaped crowded model ice floes only. For crowded model ice floes with other shapes, the criteria can be replaced by the corresponding shape criteria.

After a segmentation step, the algorithm will stop if all the segmented floes satisfy these criteria. Otherwise, the algorithm must find the floes that do not satisfy any of these criteria, find their seeds, initialize new contours, and perform the segmentation again (e.g., seen in Fig. 11d, e). After several segmentation steps, some segmented floes may still not satisfy the criteria. This is mainly because the boundaries of those floes are too weak to be detected. However, the total number of segmented floes will converge to a final solution. Therefore, the algorithm is made to stop if the total number of floes segmented after steps N and N + 1 are equal, in combination with an absolute stop criterion.

Finally, the ice shape enhancement algorithm is performed on the overall segmented model ice floe image to obtain the final model ice floe identification result. Figure 12 presents an example showing the crowded model ice floe identification result from Fig. 5 and the corresponding floe size distribution of an overall ice tank image (Zhang et al. 2015).
Fig. 12

Crowded model ice floe image identification and floe size distribution from Fig. 5

This model ice floe identification algorithm has been applied to an ice surveillance video to monitor the maximum floe size entering the protected vessel from a physical ice management operation, as seen in Fig. 13b. The maximum floe size for each frame is calculated as a function of time as seen in Fig. 14. Based on this result, a warning can be sent to the risk management system if the estimated risk based on the maximum floe size is too large.
Fig. 13

Model ice video processing

Fig. 14

Maximum floe size entering the protected vessel

Sea Ice Image Processing Applications

The Norwegian University of Science and Technology (NTNU) expedition Oden Arctic Technology Research Cruise 2015 (OATRC’15) was carried out in the Arctic region in September 2015. During the research cruise, one of the helicopter flight missions was to capture ice conditions in the marginal ice zone (MIZ). The images contain valuable ice information in the MIZ. In this section, several methods are sequentially presented with an example to demonstrate an automated procedure for ice floe and brash ice identification, their numerical representation, and forthcoming ice field generation.

Sea Ice Image Processing

Most of the ice, we called “light ice,” can be identified by Otsu thresholding method. However, the “dark ice,” whose pixel intensity values are close to water pixels, may be lost. To determine more ice pixels, the k-means clustering method is used to divide the image into three or more clusters, considering the cluster with the lowest average intensity value to be water and the other clusters to be ice. The “dark ice” is then obtained by comparing the difference between Otsu threshold detection result and k-means clustering detection result, as seen in Fig. 15d.
Fig. 15

Sea ice image processing result

Thereafter, the GVF snake-based floe boundary detection method is run on the image layers of “light ice” and “dark ice” to individually derive “light ice” segmentation and “dark ice” segmentation. Collecting all the segmented ice pieces from both “light ice” and “dark ice” layers, the shape enhancement is then performed to complete the identification. According to section “Ice Types,” the identified ice pieces are simply distinguished into ice floes and brash ice by defining a brash ice threshold parameter (e.g., number of pixels or area). Then the remaining of detected ice pixels, most of which are the detected boundary pixels between the touching floes, are considered to be “slush.” The sea ice image processing result is then four layers of ice floes (58.00%), brash ice (4.85%), slush (21.21%), and water (15.94%). The processed result of Fig. 15a can be found in Fig. 16, where a total of 2888 ice floes and 3452 brash ice pieces are identified from Fig. 15a.
Fig. 16

Sea ice image processing result of Fig. 15a

Sea Ice Numerical Modeling

Based on the image processing results, the identified ice floes and brash ice pieces are further simplified for the numerical simulation of the ice–structure interaction. In this modification, each sea ice floe is represented by a bounding polygon, and the brash ice pieces were reshaped by circular disks of equivalent area (Zhang 2015).

Figure 17 shows an example of sea ice modeling for Fig. 15a. A close-up view of a few ice floes and brash ice in the middle of Fig. 15a is given in Fig. 18, with the blue boundaries of the polygons/circles superimposed on top of the original segmented ice pixels. It is obvious to see that the polygonized floes will not be smaller than the actual identified floes and may overlap with other floes and brash ice pieces. Identifying the overlaps of floe-floe, floe-brash, and brash-brash is important when using the identified ice floes and brash ice as a starting condition for the initialization of an ice field in a numerical simulation for ice–structure interactions (Lubbad et al. 2015). To indicate these overlaps, an “overlap flag” is added to each polygonized floe to record the serial number of the floes and brash ice pieces with which the current floe overlaps and the “overlap flags” of brash-brash and brash-floe are also registered in this modeling (Zhang and Skjetne 2018).
Fig. 17

Sea ice modeling for Fig. 15a

Fig. 18

A close-up view of floe ice, brash ice, and their corresponding simplifications in modeling

Ice Field Generation

The numerical representation of sea ice is utilized to generate its corresponding ice field to bridge the gap between a natural ice field and its numerical applications, e.g., simulations involving ice–structure interactions. A major challenge of utilizing the digitalized ice field is overlaps among ice floes and brash ice. These overlaps are the consequence of both the input image’s visual noise (e.g., the foggy bottom-left corner) and inaccuracies introduced by the adopted image processing technique (e.g., the procedure to polygonize the segmented ice floes). A non-smooth discrete element method (DEM) is adopted to resolve all the overlaps among different bodies and assign basic physics to each ice floe and brash ice (Zhang and Skjetne 2018; Zhang 2020).

Ice floes are treated as discrete bodies after importing the ice field’s numerical representation into the non-smooth DEM-based simulator, and floe pairs involving overlap are labeled with red color in Fig. 19a. Afterward, for each calculation iteration, the collision detection algorithm identifies existing contacts; and the collision responses are calculated and applied to eliminate the overlaps. Figure 19b shows one snapshot of the ice field domain, within which overlaps are gradually resolved. Notably, for saving computation resources, not all the ice floes are involved in the calculation of each iteration. For ice floes without overlap and that are far away from the overlapped ice floe clusters, they are in “sleeping mode” in the adopted algorithm (see Fig. 19b).
Fig. 19

Ice floe field generation

Figure 19a shows that ice floes in the ice field’s bottom-left corner have more overlaps. This is mainly because of the input image’s visual noises. Nevertheless, applying the above non-smooth DEM calculation procedures, all the overlaps are eventually resolved in Fig. 19c, and its corresponding final ice field is shown in Fig. 19d. After resolving the overlaps, the exact location of each ice floe in Figs. 19d and 17a is not the same, but with only minor differences. On the other hand, each ice floe’s shape and size and the overall ice field’s ice mass are conserved.

Similarly, brash ice can be imported into the same non-smooth DEM-based simulator and be treated as discrete bodies. From a non-smooth DEM calculation’s point of view, the simplification of each brash ice as a disk with equivalent area makes the collision detection and consequent collision response calculation much easier comparing to arbitrary polygons. Given the amount of brash ice and its relatively small mass, this simplification is reasonable and has been adopted in previous studies (Konno 2009; Konno et al. 2011, 2013).

For the current demonstration, the identified brash ice in Fig. 16b and its numerical representation in Fig. 17b are additionally imported to the ice field in Fig. 19a. This is illustrated in Fig. 20a, which shows relatively much more overlaps. An enlarged view within the field center is also presented. The circular disk-shaped bodies are the brash ice representations.
Fig. 20

Ice field generation with both floe ice and brash ice

It is computationally efficient to make the circular disk-shaped simplification for brash ices. For the current ice field composition, i.e., 58.00% ice floe and 4.85% brash ice, the calculation time to resolve all overlaps for the cases with and without brash ice poses no significant difference. In both cases, the bottleneck for calculation time is on the overlap resolution in the bottom-left corner’s large ice floes. However, it is expected that as the amount of brash ice increases, the calculation time would also increase, which eventually becomes the decisive bottleneck for the calculation. To certain point, it might be more efficient to model brash ice as a continuum, e.g., a viscous flow, which is governed by conservation laws as a material collection.


Various image processing techniques have been introduced in this entry to extract useful ice information from the collected ice image data to support the estimation of ice forces that are critical to marine operations in the Arctic. The introduced methods have been applied to both model and sea ice image data to give some results applicable for ice engineering. More results and better information of ice from visual images will be investigated by further development of these image processing techniques.



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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Marine TechnologyNorwegian University of Science and TechnologyTrondheimNorway

Section editors and affiliations

  • Zhenhui Liu
    • 1
  • Wenjun Lu
    • 2
  1. 1.SURFAker Solutions, NorwayTrondheimNorway
  2. 2.Norwegian University of Science and TechnologyTrondheimNorway