# A Proposal for Automatic Coastline Extraction from Landsat 8 OLI Images Combining Modified Optimum Index Factor (MOIF) and K-Means

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Dataset

## 3. Methods

#### 3.1. Landsat Data OLI Pre-Elaboration

_{λ}= TOA planetary reflectance;

_{SE}= Local sun elevation angle; the scene center sun elevation angle in degrees is provide in the metadata (SUN_ELEVATION).

#### 3.2. Optimum Index Factor

_{i}= standard deviation of band I;

_{j}= standard deviation of band j;

_{q}= standard deviation of band q;

_{ij}= correlation coefficient of band i and band j;

_{iq}= correlation coefficient of band i and band q;

_{jq}= correlation coefficient of band j and band q.

#### 3.3. Modified Optimum Index Factor

_{i}, Max

_{j}, Max

_{q}are the maximum value of the respectively i,j,q selected bands, Min

_{i}, Min

_{j}, Min

_{q}are the minimum value of those bands. The amount of information present in each combination of bands is determined by the width of the range of values of each band: the wider the ranges, the higher the CF value.

#### 3.4. Image Classification Using K-Means

- Define k cluster and select k centroids from dataset randomly as initial clustering center;
- Calculate the Euclidean distance between k initial centroids and the data points of dataset and assign each data point to cluster with minimum distance;
- Calculate the average of data points that belongs to each cluster and reposition the new centroids;
- Repeat the second and third step until the centroids are not changing, which means the convergence point is reached, in order to obtain unchangeable cluster.

#### 3.5. Accuracy Tests

_{k}), dividing it with the length of effective coastline (L

_{k}) on which it develops. In this way, the values express more detailed information on the residuals and furthermore it is possible to provide the statistical parameters. The formula is:

_{k}is the area of the k-th element, L

_{k}is the length of the coastline of the k-th stretch. In consequence, DRI supplies n values, one for each polygon generated between the reference coastline and the extracted coastline.

## 4. Results and Discussion

#### 4.1. OIF and MOIF Results

#### 4.2. K-Means Application

#### 4.3. DRI Evaluation

- The group including all Landsat OLI multispectral bands (B1, B2, B3, B4, B5, B6, B7, B9);
- The first three classified band composition given by MOIF (B2, B5, B6; B2, B5, B7; B5, B6, B7);
- Three classified respectively 12th, 21st and 26th given by the MOIF (B3 B5 B6; B2 B3 B5; B3 B4 B5);
- The two middle classified band composition given by MOIF (B2, B3 B6; B1 B3 B6);
- One classified 43rd given by the MOIF (B3 B4 B6)
- The last three classified given by MOIF (B2, B3, B9; B3, B4, B9; B1, B2, B9);
- The first two classified band composition given by OIF (B2, B5, B9; B4, B5, B9).

#### 4.4. Classification Accuracy Evaluation

#### 4.5. Comparison with Other Study Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Study area: on the left, the location of the study area in the Tyrrhenian Sea in equirectangular projection and WGS 84 geographic coordinates (EPSG:4326); on the right, the visualization in RGB true color composition of Landsat 8 OLI images in UTM/WGS 84 plane coordinates expressed in meters (EPSG: 32632).

**Figure 3.**False color visualization (on the

**left**) and result of KM clustering (on the

**right**) applied to bands 2-5-6.

**Figure 4.**False color visualization (on the

**left**) and result of KM clustering (on the

**right**) applied to bands 1-3-6.

**Figure 5.**False color visualization (on the

**left**) and result of KM clustering (on the

**right**) applied to bands 1-2-9.

**Figure 7.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B2, B5, B6 band composition in frame 1.

**Figure 8.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B3, B4, B5 band composition in frame 1.

**Figure 9.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B3, B4, B6 band composition in frame 1.

**Figure 10.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B2, B3, B9 band composition in frame 1.

**Figure 11.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B2, B5, B6 band composition in frame 2.

**Figure 12.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B3, B4, B5 band composition in frame 2.

**Figure 13.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B3, B4, B6 band composition in frame 2.

**Figure 14.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B2, B3, B9 band composition in frame 2.

**Figure 15.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B2, B5, B6 band composition in frame 3.

**Figure 16.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B3, B4, B5 band composition in frame 3.

**Figure 17.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B3, B4, B6 band composition in frame 3.

**Figure 18.**Comparison between the reference coastline (in black) and the automatically vectorized coastline (in red) resulting from B2, B3, B9 band composition in frame 3.

Bands | Wavelength (Micrometers) | Resolution (Meters) |
---|---|---|

1–Coastal aerosol | 0.43–0.45 | 30 |

2–Blue | 0.45–0.51 | 30 |

3–Green | 0.53–0.59 | 30 |

4–Red | 0.64–0.67 | 30 |

5–Near Infrared (NIR) | 0.85–0.88 | 30 |

6–Short-wave infrared (SWIR 1) | 1.57–1.65 | 30 |

7–Short-wave infrared (SWIR 2) | 2.11–2.29 | 30 |

9–Cirrus | 1.36–1.38 | 30 |

Ranking | Composition | OIF | Ranking | Composition | OIF |
---|---|---|---|---|---|

1 | B2 B5 B9 | 0.185793 | 29 | B1 B7 B9 | 0.084795 |

2 | B4 B5 B9 | 0.179868 | 30 | B2 B3 B6 | 0.083436 |

3 | B2 B5 B6 | 0.161869 | 32 | B6 B7 B9 | 0.081616 |

4 | B2 B5 B7 | 0.161682 | 33 | B4 B6 B9 | 0.079554 |

5 | B2 B6 B9 | 0.160785 | 31 | B1 B2 B5 | 0.083167 |

6 | B5 B6 B9 | 0.152709 | 34 | B3 B6 B9 | 0.068931 |

7 | B5 B7 B9 | 0.149738 | 35 | B1 B2 B6 | 0.068889 |

8 | B1 B4 B5 | 0.145300 | 36 | B1 B3 B7 | 0.067815 |

9 | B3 B5 B9 | 0.143396 | 37 | B1 B4 B7 | 0.066368 |

10 | B2 B4 B5 | 0.137307 | 38 | B1 B4 B9 | 0.065971 |

11 | B1 B3 B5 | 0.137066 | 39 | B1 B3 B9 | 0.064266 |

12 | B1 B5 B9 | 0.134586 | 40 | B4 B6 B7 | 0.059485 |

13 | B2 B7 B9 | 0.129449 | 41 | B1 B2 B7 | 0.058933 |

14 | B2 B3 B5 | 0.128051 | 42 | B2 B4 B7 | 0.058430 |

15 | B1 B5 B7 | 0.127501 | 43 | B2 B3 B7 | 0.058208 |

16 | B4 B5 B6 | 0.126693 | 44 | B3 B6 B7 | 0.055408 |

17 | B2 B6 B7 | 0.119407 | 45 | B4 B7 B9 | 0.050217 |

18 | B1 B5 B6 | 0.119198 | 46 | B3 B4 B6 | 0.049167 |

19 | B5 B6 B7 | 0.112271 | 47 | B1 B3 B4 | 0.049148 |

20 | B4 B5 B7 | 0.111690 | 48 | B2 B4 B9 | 0.047537 |

21 | B3 B5 B6 | 0.111136 | 49 | B3 B7 B9 | 0.044217 |

22 | B3 B4 B5 | 0.100531 | 50 | B2 B3 B9 | 0.043139 |

23 | B3 B5 B7 | 0.100150 | 51 | B1 B2 B3 | 0.033455 |

24 | B1 B6 B9 | 0.095998 | 52 | B3 B4 B7 | 0.032920 |

25 | B1 B4 B6 | 0.085985 | 53 | B1 B2 B4 | 0.032286 |

26 | B1 B6 B7 | 0.085925 | 54 | B2 B3 B4 | 0.030907 |

27 | B2 B4 B6 | 0.085484 | 55 | B3 B4 B9 | 0.028967 |

28 | B1 B3 B6 | 0.085092 | 56 | B1 B2 B9 | 0.022450 |

Bands | Min | Max | Difference |
---|---|---|---|

B1 | 0.097669 | 0.483244 | 0.385575376 |

B2 | 0.075677 | 0.521998 | 0.446321465 |

B3 | 0.055101 | 0.576271 | 0.521169759 |

B4 | 0.034242 | 0.642815 | 0.608572632 |

B5 | 0.025000 | 0.818819 | 0.793818826 |

B6 | 0.012838 | 1.319435 | 1.306597019 |

B7 | 0.008784 | 1.314435 | 1.305651118 |

B9 | 0.000000 | 0.069334 | 0.069333822 |

Ranking | Composition | MOIF | Ranking | Composition | MOIF |
---|---|---|---|---|---|

1 | B2 B5 B6 | 0.137412 | 29 | B1 B3 B6 | 0.062779 |

2 | B2 B5 B7 | 0.137202 | 30 | B3 B6 B7 | 0.057872 |

3 | B5 B6 B7 | 0.127468 | 31 | B1 B6 B9 | 0.056367 |

4 | B2 B6 B7 | 0.121738 | 32 | B1 B5 B9 | 0.056020 |

5 | B4 B5 B6 | 0.114403 | 33 | B4 B6 B9 | 0.052625 |

6 | B5 B6 B9 | 0.110446 | 34 | B1 B4 B7 | 0.050877 |

7 | B5 B7 B9 | 0.108250 | 35 | B1 B3 B7 | 0.050011 |

8 | B1 B5 B7 | 0.105615 | 36 | B1 B7 B9 | 0.049761 |

9 | B4 B5 B7 | 0.100820 | 37 | B1 B2 B6 | 0.049106 |

10 | B2 B6 B9 | 0.099729 | 38 | B2 B4 B7 | 0.045975 |

11 | B1 B5 B6 | 0.098775 | 39 | B1 B2 B5 | 0.045068 |

12 | B3 B5 B6 | 0.097117 | 40 | B2 B3 B7 | 0.044105 |

13 | B4 B5 B9 | 0.088238 | 41 | B3 B6 B9 | 0.043589 |

14 | B3 B5 B7 | 0.087485 | 42 | B1 B2 B7 | 0.041990 |

15 | B1 B4 B5 | 0.086597 | 43 | B3 B4 B6 | 0.039929 |

16 | B1 B6 B7 | 0.085862 | 44 | B4 B7 B9 | 0.033202 |

17 | B2 B4 B5 | 0.084613 | 45 | B3 B7 B9 | 0.027947 |

18 | B2 B5 B9 | 0.081097 | 46 | B3 B4 B7 | 0.026724 |

19 | B2 B7 B9 | 0.078588 | 47 | B1 B3 B4 | 0.024824 |

20 | B1 B3 B5 | 0.077696 | 48 | B1 B4 B9 | 0.023386 |

21 | B2 B3 B5 | 0.075179 | 49 | B1 B3 B9 | 0.020909 |

22 | B6 B7 B9 | 0.072953 | 50 | B2 B4 B9 | 0.017814 |

23 | B2 B4 B6 | 0.067290 | 51 | B2 B3 B4 | 0.016237 |

24 | B3 B5 B9 | 0.066168 | 52 | B1 B2 B4 | 0.015503 |

25 | B1 B4 B6 | 0.065943 | 53 | B1 B2 B3 | 0.015088 |

26 | B3 B4 B5 | 0.064459 | 54 | B2 B3 B9 | 0.014909 |

27 | B4 B6 B7 | 0.063863 | 55 | B3 B4 B9 | 0.011577 |

28 | B2 B3 B6 | 0.063246 | 56 | B1 B2 B9 | 0.006744 |

Composition | MOIF Ranking | OIF Ranking | Min (m) | Max (m) | Mean (m) | Dev. ST. (m) | RMSE (m) |
---|---|---|---|---|---|---|---|

B1 B2 B3 B4 B5 B6 B7 B9 | - | - | 0.016 | 623.013 | 7.655 | 13.967 | 15.927 |

B2 B5 B6 | 1 | 3 | 0.000 | 35.940 | 7.417 | 5.286 | 9.108 |

B2 B5 B7 | 2 | 4 | 0.000 | 38.313 | 7.480 | 5.428 | 9.242 |

B5 B6 B7 | 3 | 19 | 0.000 | 43.118 | 7.638 | 5.205 | 9.243 |

B3 B5 B6 | 12 | 21 | 0.927 | 81.696 | 7.436 | 5.553 | 9.281 |

B2 B3 B5 | 21 | 14 | 0.000 | 82.084 | 7.466 | 5.727 | 9.410 |

B3 B4 B5 | 26 | 22 | 0.000 | 82.153 | 7.566 | 5.665 | 9.452 |

B2 B3 B6 | 28 | 30 | 0.016 | 83.120 | 8.120 | 5.190 | 9.637 |

B1 B3 B6 | 29 | 28 | 0.023 | 83.120 | 8.191 | 5.180 | 9.692 |

B3 B4 B6 | 43 | 46 | 0.000 | 623.013 | 7.508 | 12.448 | 14.537 |

B2 B3 B9 | 54 | 50 | 0.056 | 952.779 | 19.398 | 69.361 | 72.022 |

B3 B4 B9 | 55 | 55 | 0.211 | 10,288.667 | 22.029 | 318.800 | 319.560 |

B1 B2 B9 | 56 | 56 | 5.456 | 11,580.885 | 4280.705 | 3341.667 | 5430.578 |

B2 B5 B9 | 18 | 1 | 0.000 | 63.827 | 7.264 | 6.309 | 9.621 |

B4 B5 B9 | 13 | 2 | 0.000 | 53.103 | 7.611 | 5.814 | 9.577 |

Composition | MOIF Ranking | OIF Ranking | Accuracy | Water | No-Water |
---|---|---|---|---|---|

B1 B2 B3 B4 B5 B6 B7 B9 | - | - | UA | 0.97832 | 0.96982 |

PA | 0.96757 | 0.97984 | |||

OA | 0.97389 | ||||

B2 B5 B6 | 1 | 3 | UA | 0.98095 | 0.98108 |

PA | 0.97986 | 0.98211 | |||

OA | 0.98102 | ||||

B2 B5 B7 | 2 | 4 | UA | 0.98131 | 0.97949 |

PA | 0.97812 | 0.98248 | |||

OA | 0.98037 | ||||

B5 B6 B7 | 3 | 19 | UA | 0.97938 | 0.96533 |

PA | 0.96253 | 0.98094 | |||

OA | 0.97202 | ||||

B3 B5 B6 | 12 | 21 | UA | 0.97983 | 0.96429 |

PA | 0.96135 | 0.98139 | |||

OA | 0.97168 | ||||

B2 B3 B5 | 21 | 14 | UA | 0.98213 | 0.95876 |

PA | 0.95500 | 0.98367 | |||

OA | 0.96977 | ||||

B3 B4 B5 | 26 | 22 | UA | 0.98019 | 0.96038 |

PA | 0.95692 | 0.98182 | |||

OA | 0.96975 | ||||

B2 B3 B6 | 28 | 30 | UA | 0.96621 | 0.96840 |

PA | 0.96639 | 0.96823 | |||

OA | 0.96734 | ||||

B1 B3 B6 | 29 | 28 | UA | 0.96634 | 0.96853 |

PA | 0.96654 | 0.96834 | |||

OA | 0.96747 | ||||

B3 B4 B6 | 43 | 46 | UA | 0.80091 | 0.98911 |

PA | 0.99100 | 0.76838 | |||

OA | 0.87626 | ||||

B2 B3 B9 | 54 | 50 | UA | 0.65335 | 0.99768 |

PA | 0.99876 | 0.50178 | |||

OA | 0.74261 | ||||

B3 B4 B9 | 55 | 55 | UA | 0.75470 | 0.82372 |

PA | 0.83013 | 0.74631 | |||

OA | 0.78693 | ||||

B1 B2 B9 | 56 | 56 | UA | 0.99286 | 0.52264 |

PA | 0.02875 | 0.99981 | |||

OA | 0.52924 | ||||

B2 B5 B9 | 18 | 1 | UA | 0.98316 | 0.95884 |

PA | 0.95504 | 0.98462 | |||

OA | 0.97029 | ||||

B4 B5 B9 | 13 | 2 | UA | 0.98154 | 0.96100 |

PA | 0.95756 | 0.98306 | |||

OA | 0.97071 |

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## Share and Cite

**MDPI and ACS Style**

Figliomeni, F.G.; Guastaferro, F.; Parente, C.; Vallario, A.
A Proposal for Automatic Coastline Extraction from Landsat 8 OLI Images Combining Modified Optimum Index Factor (MOIF) and K-Means. *Remote Sens.* **2023**, *15*, 3181.
https://doi.org/10.3390/rs15123181

**AMA Style**

Figliomeni FG, Guastaferro F, Parente C, Vallario A.
A Proposal for Automatic Coastline Extraction from Landsat 8 OLI Images Combining Modified Optimum Index Factor (MOIF) and K-Means. *Remote Sensing*. 2023; 15(12):3181.
https://doi.org/10.3390/rs15123181

**Chicago/Turabian Style**

Figliomeni, Francesco Giuseppe, Francesca Guastaferro, Claudio Parente, and Andrea Vallario.
2023. "A Proposal for Automatic Coastline Extraction from Landsat 8 OLI Images Combining Modified Optimum Index Factor (MOIF) and K-Means" *Remote Sensing* 15, no. 12: 3181.
https://doi.org/10.3390/rs15123181