# Object-Based Detection of Linear Kinematic Features in Sea Ice

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Data

^{°}and a −45

^{°}standard parallel [15], and is defined on an Eulerian grid [16]. The dataset used here (Figure 1) covers the entire year 2006. As already mentioned above, our algorithm detects LKFs based on the spatial variations of total deformation. This parameter is not available as a RGPS product, but can be easily computed from divergence and shear [17]. Possible issues arising due to the presence of outliers and quantization noise in the RGPS data are not considered here, since our development of an object-based detector for interrelated linear features does not include preprocessing steps for increasing the quality of the used data set. A possible preprocessing step could for example be based on the calculation of ice deformation as proposed in [18].

#### 2.2. Image Enhancement, Segmentation and Edge Detection

#### 2.3. Object Detection

^{°}compared to its previous segment. Otherwise, the line ends if the sum over the neighborhood falls below 2. This process is repeated until all possible lines contained in B have been detected. The result of this processing step is a set of objects, with each object containing a list of line vertices.

#### 2.4. Semantic Postprocessing

**B**and

**C**probably belong to one single object and could thus be connected, whereas

**A**and

**B**appear to be separate features which run in parallel. Even though

**D**is closest to

**B**, it would be considered to be a separate object due to the large orientation difference relative to

**B**.

- Calculate the angle ${\vartheta}_{i}$ for each object i from a line connecting the polyline endpoints and normalize to orientation: ${\theta}_{i}={\vartheta}_{i}\u27f6[{0}^{\xb0},{180}^{\xb0}]$. Hence, the entire polyline (rather than single polyline segments) is used to obtain the general object orientation.
- For each object i, select the set L of objects j which have a similar orientation $L:=\left\{|{\theta}_{j}\u2013{\theta}_{i}|<{35}^{\xb0}\right\}$. The limit of 35
^{°}was chosen based on investigations of the data, a more detailed description is given in the Appendix A. The value introduced here allows to tolerate a small degree of curvature in the detected objects. In the example above, L would include lines**A**and**C**, if**B**was used as the reference object. - Transform each object $i,j\in L$, to a local coordinate system $(\widehat{x},\widehat{y})$ with the $\widehat{x}$-axis parallel to i and the origin at the start point of i, $({x}_{i0},{y}_{i0})$.$$\left[\begin{array}{c}\widehat{x}\\ \widehat{y}\end{array}\right]=\left[\begin{array}{cc}cos{\vartheta}_{i}& sin{\vartheta}_{i}\\ \u2013sin{\vartheta}_{i}& cos{\vartheta}_{i}\end{array}\right]\phantom{\rule{0.166667em}{0ex}}\left[\begin{array}{c}x\u2013{x}_{i0}\\ y\u2013{y}_{i0}\end{array}\right]$$In the practical implementation, the positions of matching candidates j with respect to the reference object i are not known. For each object i, a maximum of two objects ${j}_{1}$ and ${j}_{2}$ can be found which can be attached to the start- or the end segment of i.
- Now we apply anisotropic scaling to compress objects i and j along the $\widehat{x}$ – axis. In this way, we implement different search tolerances in $\widehat{x}$ and in $\widehat{y}$ direction to avoid connections between close parallel lines. The scaled coordinates are now:$$\left[\begin{array}{c}\xi \\ \eta \end{array}\right]=\left[\begin{array}{c}\widehat{x}\\ \widehat{y}\end{array}\right]\phantom{\rule{0.166667em}{0ex}}\left[\begin{array}{c}\frac{1}{3}\\ 1\end{array}\right]$$In the example shown in Figure 5, this would rule out line
**A**and leave line**C**to be (correctly) connected to**B**. - Calculate the endpoint distance ${r}_{i,j}=\sqrt{{\xi}^{2}+{\eta}^{2}}$. If $min\left({r}_{i,j}\right)$ is below a user-defined threshold, objects i and j are concatenated.

## 3. Results and Validation

#### 3.1. Validation with Reference Data

#### 3.2. Plausibility Testing

^{°}orientation angle. In summary, the detected features fulfill the criterion of linearity stated in Section 2.3, and their length distribution and orientation are in line with the reference data.

## 4. Discussion

- analysis of individual features: as the geographical coordinates of each vertex of each detected object are known, LKFs can be analyzed on an individual basis. Values from the original deformation images or other parameters can be easily mapped back onto the observed features (Example: divergence and shear maps for the entire spatial domain, Figure 14).
- LKF intersection angles: fracture mechanics of the ice cause “typical” fracture patterns, and the intersection angles depend on properties of the material, similar to stress faulting in rocks. Here, we also consider cases in which one LKF ends in the vicinity of another LKF instead of intersecting it by applying a simple distance criterion. Each pair of LKFs (consiting of several segments with slightly varying orientations) is approximated by a pair of lines fixed to the respective start- and endpoints, and the intersection angle between those lines is calculated. The result for the entire scene from Figure 6a is shown in Figure 15. The relationship between fracture angles and strain magnitude is rather complex and depends on the type of strain (e.g., shear or divergence) and on material properties [1]. With given strain rates (such as in Figure 14) and LKF intersection angles derived from the detected objects, the data basis is available to analyze the material/fracturing properties of the sea ice in more detail. However, this type of analysis would exceed the scope of this study.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Appendix A

^{°}, and this value has been subsequently used as an upper threshold for the intersection angle.

**Figure A1.**Cost function for intersection angle tolerance values ranging from 5

^{°}to 60

^{°}, in steps of 2

^{°}. The dotted line marks the 35

^{°}threshold.

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**Figure 1.**RGPS (Radarsat Geophysical Processor System) example data set (4 January 2006), calculated total deformation.

**Figure 2.**Image enhancement: (

**a**) Logarithm-scaled total deformation ${I}_{l}$; (

**b**) Result of histogram equalization; (

**c**) DoG (Difference of Gaussian) filtered image. red: ${I}_{f}>0$, blue: ${I}_{f}<0$.

**Figure 4.**Example neighborhoods/detection steps. The magenta lines symbolize detected polyline objects. (

**a**) Line start; (

**b**) Direction change; (

**c**) Intersection.

**Figure 5.**Example for demonstrating the problem of connecting adjacent LKFs. Dotted lines indicate single segments of the real LKF, the solid lines represent the major orientation of the LKF. In the search ellipse, the end point of line

**B**can potentially be connected to line

**C**or

**D**. The decision is based on differences between the major orientations.

**Figure 6.**Detected objects, different minimum length ${l}_{min}$ and number of detected objects n. (

**a**) ${l}_{min}$ = 4 px, n = 208; (

**b**) ${l}_{min}$ = 6 px, n = 160; (

**c**) ${l}_{min}$ = 8 px, n = 124.

**Figure 7.**Intrinsic accuracy of the validation data. (

**a**) Reference features in ${\mathbf{R}}_{\mathbf{0}}$. The yellow box marks the location of Figure 7b; (

**b**) Reference line example. Hatched area: mean value ± standard deviation of the seven individually determined results from the ${\mathbf{R}}_{\mathbf{0}}$ data set (dashed white lines).

**Figure 8.**Uncertainties in LKF localization. (

**a**) Endpoint deviation = average of the lengths of the two magenta lines connecting the endpoints of lines

**A**and

**B**; (

**b**) Contributions to the localization error (magenta lines). Since

**A**and

**B**are sampled at different $(\widehat{x},\widehat{y})$-positions, line

**B**is interpolated at the $\widehat{x}$-positions of line

**A**. The interpolated line is denoted

**B**${}_{\mathrm{resampled}}$ in the figure.

**Figure 9.**Distribution of mean endpoint distances. (

**a**) ${\mathbf{R}}_{\mathbf{0}}$: N = 129, $\sigma $ = 1.75 px; (

**b**) ${\mathbf{R}}_{\mathbf{0}}^{+}$: N = 136, $\sigma $ = 1.25 px; (

**c**) ${\mathbf{R}}_{\mathbf{10}}$: N = 1411, $\sigma $ = 2.75 px.

**Figure 10.**LKF length error distribution (in percent of the total line length). (

**a**) ${\mathbf{R}}_{\mathbf{0}}$: N = 129; (

**b**) ${\mathbf{R}}_{\mathbf{0}}^{+}$: N = 136; (

**c**) ${\mathbf{R}}_{\mathbf{10}}$: N = 1411.

**Figure 11.**Distribution of localization errors. (

**a**) ${\mathbf{R}}_{\mathbf{0}}$: N=129, $\sigma $ = 0.75 px; (

**b**) ${\mathbf{R}}_{\mathbf{0}}^{+}$: N = 136, $\sigma $ = 0.75 px; (

**c**) ${\mathbf{R}}_{\mathbf{10}}$: N = 1411, $\sigma $ = 0.75 px.

**Figure 12.**Endpoint distance vs. integrated line length as an indicator of feature linearity. (

**a**) Detected objects; (

**b**) Reference data (${\mathbf{R}}_{\mathbf{10}}$).

**Figure 13.**Feature length and orientation. Lines having angles of 0

^{°}are oriented along the parallels, lines with 90

^{°}angles are oriented in meridional direction. (

**a**) Feature length distribution; (

**b**) Distribution of feature orientation angles.

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Linow, S.; Dierking, W. Object-Based Detection of Linear Kinematic Features in Sea Ice. *Remote Sens.* **2017**, *9*, 493.
https://doi.org/10.3390/rs9050493

**AMA Style**

Linow S, Dierking W. Object-Based Detection of Linear Kinematic Features in Sea Ice. *Remote Sensing*. 2017; 9(5):493.
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**Chicago/Turabian Style**

Linow, Stefanie, and Wolfgang Dierking. 2017. "Object-Based Detection of Linear Kinematic Features in Sea Ice" *Remote Sensing* 9, no. 5: 493.
https://doi.org/10.3390/rs9050493