# Automatic Semi-Global Artificial Shoreline Subpixel Localization Algorithm for Landsat Imagery

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Areas & Datasets

#### 2.1. Study Areas

#### 2.2. Data Pre-Processing

**.**The registration error will bring uncertainty to the accuracy assessment and is discussed in Section 5.1.

## 3. Materials and Methods

#### 3.1. Basic Principles of Subpixel Shoreline Localization

_{i},y

_{i}) is set, so the sum of intensity in the ith window is:

_{i},y

_{i}) is the current shoreline point’s pixel coordinate, G the pixel’s intensity, n the number of pixels in the shoreline segment, and m

_{1}, m

_{2}are the pixels’ number above or under the shoreline csegment in the local window, respectively. According to Assumption 2, the integral of the intensity in the ith window is:

_{i}

^{*}) can be described as:

_{i}) is defined as:

^{T}can be solved with intensity integral error minimization, and then the shoreline subpixel localization is determined.

#### 3.2. Challenges for Subpixel Shoreline Localization in Remote Sensing Images

#### 3.3. Shoreline Global Analysis

#### 3.3.1. Determination of Initial Shoreline Position

#### 3.3.2. Determination Initial Shoreline Position

#### 3.3.3. MCP Extraction

_{I}is the integral scale, g(σ

_{I}) the Gaussian convolution kernel with integral scale σ

_{I}, and L

_{a}the derivative computed in the a direction. The multi-scale Harris cornerness measure combines the trace and the determinant of the scale-adapted second moment matrix:

#### 3.4. Shoreline Semi-Global Analysis

#### 3.4.1. Designing Local Window

_{i}in Equation (10) is close to zero, so as to satisfy Assumption 2.

_{x}, G

_{y}). Then, the larger gradient is preserved as the points’ maximum gradient direction.

_{x}or G

_{y}) have a larger proportion in the segment, then that direction will be used as the main direction for the segment.

_{y}, the (m

_{1}+m

_{2}+1) ×1 local window is designed, and the cubic polynomial function of a segment is:

_{x,}the 1×(m

_{1}+m

_{2}+1) window is designed and the cubic polynomial function of segment is:

_{1}, m

_{2}to find the minimum gradient pixels (pixels in the blue box in Figure 4b). Once we find the minimum gradient pixels, their water index intensities are used to estimate the intensity A, B and their coordinates are used to set the window size [36].

_{i}and B

_{i}are the farthest pixels from the shoreline. To ensure the correlation between pixels in the local window, we limit ${m}_{1}\le 4,{m}_{2}\le 4$.

_{i}

^{*}and B

_{i}

^{*}:

_{i},y

_{i}) and (x

_{i+1},y

_{i+1}) are the adjacent shoreline points’ coordinates.

#### 3.4.2. Segmentation-Merge-Fitting Method

#### 3.5. Verification Method

_{Δ}is the sum of the area enclosed by the SGSSL shoreline and the reference shoreline, and L

_{real}is the length of the reference shoreline. In Figure 6, the black dotted line represents the reference shoreline and the solid line represents the shoreline determined by SGSSL.

## 4. Results

#### 4.1. Visual Comparison

#### 4.2. Quantitative Assessments

#### 4.3. Shoreline Detail Preservation Ability

## 5. Discussion

#### 5.1. Registration Error Influence on Quantitative Assessment

#### 5.2. Water Index

_{1},1566.50 – 1651.22 nm) band is used in the calculation of the MNDWI, and the most accurate and robust sub-pixel shoreline positioning results are often obtained using the SWIR

_{1}band [40]. Therefore, this paper prefers to use the MNDWI to enhance the differences between land and water, but, considering complicated offshore environments and data sources, in other coastal areas utilizing other water indices is acceptable.

#### 5.3. Intensity Integral Error Analysis

_{i},y

_{i}), and the red line is the real shoreline that crosses the pixel (x

_{i},y

_{i}). The subpixel level coordinates of the point in the real shoreline are (x

_{0},y

_{0}), (x

_{0}∈[x

_{i}−1/2, x

_{i}+1/2], y

_{0}∈[y

_{i}−1/2, y

_{i}+1/2]). Once the local window size is determined by finding the minimum gradient pixels along the window direction, the window sizes m

_{1,}m

_{2}and the homogeneous intensity A

_{i}, B

_{i}are all obtained. At shoreline point (x

_{0},y

_{0}), the intensity profile is drawn along the window direction, presuming the direction lies in the y axes in Figure 11.

_{1},S

_{2},S

_{3}are areas enclosed by the intensity profile and the y axis (window direction),

_{i}can be described as:

_{i}is related to three factors: the window size (m

_{1}+m

_{2}+1), the homogeneous intensity difference (B-A), and the intensity slope at the shoreline point (x

_{0},y

_{0}). Regarding the three factors, the intensity slope is determined by image information. The other two factors are determined by appropriate homogeneous intensity estimation A, B and the window’s size (m

_{1}+m

_{2}+1), which can ensure that the e

_{i}approaches zero.

_{i}approaches zero, the relative error δ is calculated within the local window in Landsat OLI8 MNDWI images.

_{i}

^{*}is the integral of intensity in the ith window and calculated according to Equation (6). The reference shoreline coordinates are used to calculate S

^{*}

_{Ai}and S

^{*}

_{Bi}. SUM

_{i}is the sum of intensity in the ith window and calculated according to Equation (3).

#### 5.4. Segmentation-Merge-Fitting Process

#### 5.5. Robustness to Complex Offshore Environment and Salt-And-Pepper Noises

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Ideal binary image. A shoreline segment separates the image into two homogeneous regions with intensities A and B. The ith shoreline point locates in the yellow box, and m

_{1}, m

_{2}are the pixels’ number above or under the shoreline segment in the local window; ${{\text{}\mathrm{S}}_{{\mathrm{A}}_{\mathrm{i}}}}^{*}$ and ${{\mathrm{S}}_{{\mathrm{B}}_{\mathrm{i}}}}^{*}$ are areas covered by A or B in the local window.

**Figure 4.**Actual remote sensing image. (

**a**) Various shoreline morphology analysis; (

**b**) homogeneous conditions in the water index image.

**Figure 6.**Line matching schematic [15].

**Figure 7.**Visual comparison in experimental areas 1–5. Original images (R, band5; G, band4;B, band3) appear in the first column [(

**a**,

**e**,

**i**,

**m**,

**q**)]; final shoreline morphological control point set (SMCPS) and segmented shorelines are in the second column [(

**b**,

**f**,

**j**,

**n**,

**r**)]; semi-global subpixel shoreline localization (SGSSL) results in the third column [(

**c**,

**g**,

**k**,

**o**,

**s**)]; and magnified images of the third column in the fourth column [(

**d**,

**h**,

**l**,

**p**,

**t**)].

**Figure 8.**Mean absolute error (MAE) with registration errors compensated illustration (

**a**) vertical shoreline, (

**b**) registration error compensated results for the vertical shoreline, (

**c**) horizontal shoreline and (

**d**) registration error compensated results for the horizontal shoreline.

**Figure 9.**MAE with registration errors compensated illustration (

**a**) 3D surface results (

**b**) 2D computation results.

**Figure 12.**Local window samples and their relative error distribution. (

**a**) Samples of local windows in the experimental areas; (

**b**) distribution of relative error.

**Figure 13.**SMF process. (

**a**) Initial shoreline and primary MCPs; (

**b**) one problematic shoreline segment in yellow box; (

**c**) the magnified version of green box in (

**b**); (

**d**) supplementary MCPs in the problematic shoreline segment; (

**e**) the merged MCPs in the problematic shoreline segment; (

**f**) the final shoreline morphological control point set; (

**g**) the fitted subpixel shoreline segments; (

**h**) the magnified version of green box in (

**g**).

**Figure 14.**Semi-global subpixel results in complex offshore environment. (

**a**) three categories of suspended sediments in the original image (R, band5; G, band4; B, band3); (

**b**) three categories of suspended sediments in the MNDWI image.

**Figure 15.**PAE and SGSSL results in salt-and-pepper noises. Percentage of area occupied by various levels of noise: (

**a**) 0%; (

**b**) 1%; (

**c**) 2%; (

**d**) 3%; (

**e**) 4%; and (

**f**) 5%.

**Figure 16.**Positioning errors comparison of PAE and SGSSL in different noise percentages. (

**a**) MAE difference between PAE and SGSSL in different noise percentages; (

**b**) Max positioning errors comparison between PAE and SGSSL in different noise percentage.

Experimental Areas 1/2 | Experimental Area 3 | Experimental Areas 4/5 | ||
---|---|---|---|---|

Location | Caofeidian Port | Caofeidian Port | Xiamen coastal area | |

Shoreline type | artificial | artificial | artificial | |

Geometric morphology | simple straight | combination of quasi-straight and curved shape | high curvature/combination of quasi-straight and curved shape | |

Experimental image | Data | Landsat-8 OLI images (Path 122, Row 033) | Landsat-8 OLI images (Path 122, Row 033) | Landsat-8 OLI images (Path 119, Row 043) |

Date | 04/25/2015 | 04/25/2015 | 10/13/2015 | |

Resolution | 15 m fusion image | 15 m fusion image | 15 m fusion image | |

Reference image | Data | GF-2 image | GF-2 image | GF-2 image |

Date | 05/31/2015 | 05/31/2015 | 02/06/2015 | |

Resolution | 1 m fusion image | 1 m fusion image | 1 m fusion image |

Experimental Area | MAE (m) | SD (m) | RMSE (m) | LM (m) |
---|---|---|---|---|

1 | 2.94 | 1.93 | 3.51 | 2.87 |

2 | 3.34 | 2.16 | 3.97 | 3.30 |

3 | 3.67 | 3.06 | 4.77 | 3.72 |

4 | 2.72 | 2.61 | 3.77 | 2.77 |

5 | 2.48 | 1.72 | 3.02 | 2.51 |

Experimental Area | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Subpixel Shoreline Length (m) | 3206.22 | 3000.19 | 2739.38 | 6324.41 | 3572.84 |

Reference Shoreline Length (m) | 3205.25 | 2994.95 | 2675.57 | 6236.77 | 3571.32 |

Length Difference Ratio | 0.03% | 0.17% | 2.33% | 1.39% | 0.04% |

Error Indicator | Primary Shoreline | Final Shoreline Segments Result | |||
---|---|---|---|---|---|

Total | Seg 1 | Seg 2 | Seg 3 | ||

MAE (m) | 10.53 | 2.58 | 3.22 | 2.12 | 2.66 |

SD (m) | 12.11 | 1.84 | 2.20 | 1.26 | 1.97 |

low Concentration | High Concentration | ||
---|---|---|---|

Large Area | Small Area | ||

MAE (m) | 0.96 | 2.28 | 3.55 |

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## Share and Cite

**MDPI and ACS Style**

Song, Y.; Liu, F.; Ling, F.; Yue, L.
Automatic Semi-Global Artificial Shoreline Subpixel Localization Algorithm for Landsat Imagery. *Remote Sens.* **2019**, *11*, 1779.
https://doi.org/10.3390/rs11151779

**AMA Style**

Song Y, Liu F, Ling F, Yue L.
Automatic Semi-Global Artificial Shoreline Subpixel Localization Algorithm for Landsat Imagery. *Remote Sensing*. 2019; 11(15):1779.
https://doi.org/10.3390/rs11151779

**Chicago/Turabian Style**

Song, Yan, Fan Liu, Feng Ling, and Linwei Yue.
2019. "Automatic Semi-Global Artificial Shoreline Subpixel Localization Algorithm for Landsat Imagery" *Remote Sensing* 11, no. 15: 1779.
https://doi.org/10.3390/rs11151779