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

Abstract

The coastal environment is a natural and economic resource of extraordinary value, but it is constantly modifying and susceptible to climate change, human activities and natural hazards. Remote sensing techniques have proved to be excellent for coastal area monitoring, but the main issue is to detect the borderline between water bodies (ocean, sea, lake or river) and land. This research aims to define a rapid and accurate methodological approach, based on the k-means algorithm, to classify the remotely sensed images in an unsupervised way to distinguish water body pixels and detect coastline. Landsat 8 Operational Land Imager (OLI) multispectral satellite images were considered. The proposal requires applying the k-means algorithm only to the most appropriate multispectral bands, rather than using the entire dataset. In fact, by using only suitable bands to detect the differences between water and no-water (vegetation and bare soil), more accurate results were obtained. For this scope, a new index based on the optimum index factor (OIF) was applied to identify the three best-performing bands for the purpose. The direct comparison between the automatically extracted coastline and the manually digitized one was used to evaluate the product accuracy. The results were very satisfactory and the combination involving bands B2 (blue), B5 (near infrared), and B6 (short-wave infrared-1) provided the best performance.

1. Introduction

Defined as the boundary where land meets water [1], coastline can be identified from satellite images by using spectral information (signature) of the two neighboring elements [2,3]. However, in situ surveying provides the most precise results but is only practicable for small regions due to costs; indeed, it may be impossible if a study area is remote, treacherous or inaccessible [4]. Remote sensing allows us to overcome the difficulties due to the inaccessibility of the area to be surveyed and the use of satellite images rather than those captured by aerial vehicles or drones helps to contain costs. Consequently, in recent years, there has been an increase in the use of remotely sensed data supplied by optical sensor and synthetic aperture radar (SAR) on-board satellites to extract and map the coastline automatically or semi-automatically [5,6,7].

The detection and extraction of coastline data from satellite images are of great importance in several applications such as cartography and the environmental management of the entire coastal zone [8,9]. Coastline information is the basis for measuring and calibrating terrestrial and water resources and is the foundation for the excavation and management of coastal zone resources [10]. Particularly, information about coastline position, orientation and geometric shape is crucial for autonomous navigation, geographical exploration, coastal erosion monitoring and modeling, and coastal resource inventory and management [11].

Several techniques are described in the literature to detect coastline from satellite imagery and at least four different approaches can be distinguished: visual interpretation, classification techniques, water index and machine learning.

Visual image interpretation involves the human’s ability to examine and evaluate the content of images. Trained human interpreters combine spectral information viewed from the image with contextual information concerning the nature of the study environment to identify, delineate and classify specific features such as land cover, land use and, if the resolution permits, specific objects [12]. In consequence, the knowledge given by the expert on the different thematic object classes present in the image supports interpretation of coastal areas [13] and consequently provides information for coastline visual detection and manual vectorization [14,15].

As is known, pixel-based classification techniques include supervised and unsupervised approaches: the former provides better results than the latter but are time consuming and require a greater expenditure of resources due to the identification of training sites [16]. Nevertheless, supervised classification techniques are largely used for coastline extraction, especially when accurate results are required, such as for high and very high-resolution images [17]. Rather than on the satellite images, unsupervised techniques are more frequently applied to the products of their processing based on other algorithms [15,18].

While pixel-based classification uses only the spectral information of each pixel, object-based classification relies on information from a collection of similar pixels forming objects. In other words, this approach groups pixels taking into account also the context in which they are located, i.e., the size, shape and texture of the object, they can form by aggregating. The advantages of object-based classification over the traditional pixel-based approach are well known [19,20,21] and different applications are available for coastline extraction from satellite images, such as those in [22,23,24].

The water index approach aims to classify individual pixels in a given image into two classes: water and no-water. It has advantages of universality, user-friendliness and low computation cost in coastline data extraction [25]. The first issue is the identification of the multispectral bands necessary for generating the index [26]; this choice depends on the peculiarity of the two classes being compared (e.g., sea water/rock; lake water/gravel), so a careful analysis of the related spectral signatures is necessary [27]. The most largely used is the Normalized Difference Water Index (NDWI) introduced by McFeeters (1996) [28]: taking advantage of two bands such as the NIR (near-infrared) and green spectral bands, the NDWI can enhance the water bodies in a satellite image [29]. To obtain a higher accuracy from these indexes, a threshold appropriate for separating water and background classes should be identified [30]. Different solutions are possible for this issue, such as threshold automated research [31], manual adjustment, supervised classification or unsupervised classification [32].

The advent of machine learning-based techniques presents an emerging trend in remote sensing applications and is also capable of supporting coastline data extraction from satellite images [33]. Machine learning is an important research field of artificial intelligence [34,35] that allows design and implementation of systems that learn from data and deduce patterns [36]. Several algorithms of machine learning are available in the literature for remote sensing applications and have been applied for coastline data extraction, such as k-nearest neighbor [37,38], support vector machine [39,40,41] and random forest [40,42,43].

Some of the abovementioned techniques are based on manual detection of the coastline or of the training sites, while others allow automatic image processing: the latter are more useful because automating the process reduces human errors and improves the standardization and efficiency of the studies [44].

This article aims to demonstrate that unsupervised approach, based on the k-means algorithm, allow us to obtain an accurate and automatic coastline detection, but only if it is applied to an appropriate selection of multispectral bands. The selected bands must be able to represent in an optimal way the differences among the pixels and, as consequence, to distinguish the water bodies from the context.

It is well known that multispectral images provide less useful information for classification the more correlated they are [45]. For this reason, for example, uncorrelated bands such as infrared and red are the basis of the vegetation indices and facilitate the identification of the biomass with respect to the bare soil and water bodies. However, correlation level alone is not enough for a good classification; in fact, a large amount of information is also required in each image to better distinguish the differences among the land cover classes included in the investigated areas. In other terms, the acquisition bands that are uncorrelated and presenting different reflectance values for the detected objects are to be preferred. Optimum index factor (OIF) [46] identifies the level of correlation among three selected bands and the amount of information they include: the higher the index value, the greater the decorrelation between the selected images as well as the total amount of information they include. To identify bands that not only are uncorrelated but also have a wide range of reflectance values, we propose in this article a new index named modified optimum index factor (MOIF). Our study demonstrates that the novel index combines, in better way than the OIF, the level of correlation between the images constituting each group, with the possibility of also establishing the amount of information that the same group contains. The experiments were carried out using Landsat 8 OLI multispectral images concerning the Tyrrhenian coast of the Calabria region (Italy), and the proposed method was developed in the GIS environment using the free and open-source Quantum GIS (QGIS) software (version 3.22) [47].

This paper is organized as follows. In Section 2, the main characteristics of the Landsat 8 OLI imagery used and the area are described. Section 3 presents the novel methodological approach based on the application of the k-means algorithm: the MOIF is introduced, explaining its capability to identify the correlation level of all possible three-band combinations and, at the same time, to highlight the amount of information included in each of those band combinations. Section 4 presents and discusses the results, comparing the levels of accuracy of the extracted coastlines. Section 5 concludes the paper with the generalization of the results.

2. Study Area and Dataset

The experiments were carried out on Landsat 8 OLI images, acquired on 21 June 2019 and concerning a part of Calabria region (Italy) as shown in Figure 1.

The Landsat 8 satellite is part of the long-running Landsat program, a joint effort of the U.S. Geological Survey (USGS) and the National Aeronautics and Space Administration (NASA) to monitor Earth from space [48].

The Landsat 8 satellite was launched on 11 February 2013 from Vandenberg Air Force Base, California; its orbit is polar sun-synchronous at 705 km (438 miles) altitude. Travelling at approximately 4.7 miles per second, the satellite moves from north to south while it is over the sunlit portion of the Earth and travels south to north over the dark side of the Earth [49]. One orbit takes about 99 min, so the satellite makes approximately 15 orbits in a 24 h period and covers the total globe in 16 days. The swath is 185 km and data are segmented in 185 × 180 km scenes. The Landsat 8 satellite payload consists of two science instruments—the Operational Land Imager (OLI) and the Thermal Infrared Sensor (TIRS), that combine historical features with technological innovations. The OLI is a push-broom sensor including a four-mirror telescope, which provides seasonal coverage of the global landmass at a spatial resolution of 30 m (visible, NIR, SWIR) and 15 m (panchromatic). Two new spectral bands have been added to the traditional Landsat acquisition bands: a deep-blue band for coastal water and aerosol studies (band 1), and a band for cirrus cloud detection (band 9) [50]. The TIRS takes data in two long wavelength thermal infrared bands at a spatial resolution of 100 m. Data are collected simultaneously in the same area by OLI and TIR sensors.

For this application, a clip of Landsat 8 OLI imagery was used. We utilized 8 bands, all presenting 30 m pixel dimension, i.e., coastal, blue, green, red, NIR, SWIR1, SWIR2 and cirrus (as reported in

Table 1. Characteristics of Landsat 8 OLI multispectral bands used in this study.

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

). The clipped scene extended 100,000 × 60,000 m (UTM/WGS84 plane coordinates–33T zone: E1 = 550,000 m, N1 = 4,350,000 m, E2 = 610,000 m, N2 = 4,250,000 m). Those data were downloaded from USGS official website.

Extending from San Lucido (Cosenza) to Gioia Tauro (Reggio Calabria), in the Tyrrhenian Sea, the study area is indented and varied; it has long beaches interspersed with high coasts and port areas. In fact, it is characterized by coastal plains, such as Lamezia Terme to the north and Gioia Tauro to the south [51], while in the center it has a high promontory, in the Capo Vaticano area. Particularly in the past 40 years, many sea storms have flooded the waterfront in the Gioia Tauro area, causing damage to houses, bathing establishments and maritime works [52]. As a consequence, coastline monitoring is crucial, also in consideration of climate change events, and the automatic extraction of data from satellite images is of fundamental importance to reduce effort and work time.

We want to point out that with the proposed method we detected only the instantaneous coastline, which is defined as the position of land/sea intersection at one instant in time, specifically the instant of remotely sensed image acquisition [53]. In fact, we could not obtain absolutely accurate coastline data from a remote sensing image: what we obtained is only an approximation [54]. For a correct monitoring, we must consider the dynamic nature of the coastline, which produces a continuous shift over a day due to tidal fluctuations, being especially large for steeply sloped beaches located at macro-tidal areas [55]. In consequence, the date and time of acquisition of the satellite image are necessary, together with the knowledge of the tide level and the availability of a DTM of the study area: in this way, the horizontal position of the automatically extracted polyline can be corrected to obtain the real coastline. Since the purpose of our article was to illustrate a method for the automatic extraction of the coastline and not to show the results of an effective monitoring of coastal erosion phenomena, the aforementioned elaborations were not considered. In other words, the object of attention remains the instantaneous coastline and not the real one.

3. Methods

The workflow in Figure 2 shows the activies involved in the proposed method and the order they should go in. All steps can be developed in the GIS environment and the whole process may be automated using software tools that establish when one step has been completed successfully and the next step can begin.

Starting from the initial dataset (that includes all bands of Landsat 8 OLI), there is a pre-processing procedure for converting pixel values to reflectance. Subsequently, the MOIF values are calculated to establish the three bands to be subjected to the k-means for automatic classification. Finally, the coastline is extracted, and the accuracy of the results is evaluated. All these activities are described in detail in the following subsections.

3.1. Landsat Data OLI Pre-Elaboration

We used the formulas published by the USGS for converting the quantized and calibrated scaled digital numbers (DN) representing multispectral image data acquired by Landsat 8 OLI to top of atmosphere (ToA) reflectance [56].

Landsat data were converted from DNs to reflectance using the following formula:

$$\rho {\lambda }^{\prime }=M_{\rho } Q_{cal}+A_{\rho }$$

(1)

where:

ρλ′ = TOA planetary reflectance, without correction for solar angle (note that ρλ’ does not contain a correction for sun angle);

Mρ = Band-specific multiplicative rescaling factor from the metadata (REFLECTANCE MULT BAND x, where x is the band number);

Qcal = Quantized and calibrated standard product pixel values (DNs);

Aρ = Band-specific additive rescaling factor from the metadata (REFLECTANCE ADD BAND x, where x is the band number).

Then, TOA reflectance with a correction for the sun angle is calculated using the formula:

$$R_{\lambda }=\frac{\rho {\lambda }^{\prime }}{\sin {\theta }_{SE}}$$

(2)

where:

R_λ = TOA planetary reflectance;

θ_SE = Local sun elevation angle; the scene center sun elevation angle in degrees is provide in the metadata (SUN_ELEVATION).

Both formulas are applied using Raster Calculator, the QGIS tool that allows performance of multiple tasks of map algebra [57], i.e., mathematical calculations based on operators and functions, selection queries, or development in map algebra syntax [58].

3.2. Optimum Index Factor

The optimum index factor (OIF) was developed by Chavez et al. (1982) [46] as a method for determining the three-band combination that maximizes the variability in a particular multispectral scene [59]. The determination of the optimal combination of spectral intervals providing the maximum information with the minimum number of bands is of fundamental importance in remote sensing applications [60]. The OIF aims to maximize information content and avoid duplication. For this reason, it is based on the amount of total variance and correlation within and between all possible three-band combinations in the dataset [61]. OIF is calculated using the following formula:

$$OIF=\frac{St{d}_i+St{d}_j+St{d}_q}{\left|Cor{r}_{i,j}\right|+\left|Cor{r}_{i,q}\right|+\left|Cor{r}_{j,q}\right|}$$

(3)

where:

Std_i = standard deviation of band I;

Std_j = standard deviation of band j;

Std_q = standard deviation of band q;

Corr_ij = correlation coefficient of band i and band j;

Corr_iq = correlation coefficient of band i and band q;

Corr_jq = correlation coefficient of band j and band q.

The larger the OIF value, the better the band combination.

Since the beginning OIF has been largely applied to Landsat datasets that include six multispectral bands with spatial resolution equal to 30 m (Landsat 5 and Landsat 7) or eight multispectral bands with the same spatial resolution (Landsat 8 and Landsat 9), so the selection of the most useful combination is crucial. Considering that they are also free of charge, we decide to use Landsat 8 OLI images for this study.

In our experiments, OIF was applied to each three-band combination, so 56 values were obtained, considering the 8 bands of Table 1.

3.3. Modified Optimum Index Factor

However, the OIF method has its limitations and there is no guarantee that the selected band subset is the optimal combination [62]. In fact, this index uses the correlation coefficient to identify the possibility of duplication of information and entrusts the variance with the task of identifying the amount of information. Bands with lots of “information” (high standard deviation) and a little “duplication” (low correlation between bands) will produce high OIF values [63]. However, the standard deviation may not be sufficient to underline the usefulness of an image in differentiating land cover classes. More useful for the purpose of identifying the amount of information present in an image would be the integration of the variance with the extension of the range of reflectance values present in the image itself. Even if they measure both the spread or variability of a dataset, variance and range are not coincident. In fact, two images with the same (low) variance value can present different widths of the reflectance range: the widest range carries out more information as it helps to better distinguish different types of land cover.

For example, Landsat 8 imagery includes the cirrus band, which provides information on the presence of clouds in the observed scene, effectively expressing a strong non-correlation with the other bands but characterized by a small amount of information on the investigated area. In other words, combinations including cirrus usually present a low level of correlation but also offer a low amount of information that does not contribute to accurately distinguish different land covers. Nevertheless, the low value of correlation with the other bands contributes to the high value of OIF while band compositions including images with limited range of values (like B9) are not optimal.

In this work, we proposed to overcome this drawback by introducing the corrective factor (CF) supplied by the following formula:

$$C{F}_{ijq}=Mean\left(Ma{x}_i-Mi{n}_i;Ma{x}_j-Mi{n}_j;Ma{x}_q-Mi{n}_q\right)$$

(4)

where i,j,q are the considered bands, Max_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.

The product between CF and OIF determines the MOIF:

$$MOIF=C{F}_{ijq}\ast OI{F}_{ijq}$$

(5)

In other terms, MOIF incorporates in a single value the degree of non-correlation and the amount of information in better way than OIF as it introduces a multiplication factor which is the average of the extensions of the reflectance ranges of the three bands considered. The higher the MOIF value, the stronger the contrast between water and non-water.

Similarly to OIF, MOIF produced 56 values in our study, one for each three-band combination.

Note that band selection is an effective pre-processing way to reduce the number of available images and use only those that are useful for a particular perspective [64]. Most of the existing methods select bands according to a single criterion, such as the extraction of specific features, e.g., roads, water body, forests, etc. Usually, it is necessary to set up different band combination schemes according to the spectral characteristics for different observation objects. In fact, if on the one hand the spectral signature allows recognition of an object or a type of land cover [65], on the other hand there are definite wavelength values that better enhance the specificity of the spectral response of this object or land cover, such as (630–690 nm), and (770–895 nm) for vegetation [66]. Consequently, there are some bands that are better than others in enhancing the difference of such objects or land covers [65]. The water indices, such as NDWI, automated water extraction index (AWEI) [67], modified normalized difference water index (MNDWI) [68], based on the selection of two or more bands that better highlight the behavior of water bodies with respect to the context, are also part of this perspective. However, the bands that allow water to be highlighted in a scene, including bare soil and vegetation, are usually uncorrelated and with a wide range of different values, as is the case for NIR and/or SWIR bands compared to the visible. We believe that looking for uncorrelated bands with a high information content can lead to precise selection of those same bands that are involved in the water indices or help define new indices.

3.4. Image Classification Using K-Means

Clustering is a process that divides a set of objects into groups (clusters) according to the predefined criteria such that objects in the same cluster are more similar to each other than other objects in different groups [69]. K-means clustering is a popular technique in analysis and pattern recognition [70]. It is an unsupervised classification algorithm, in particular belonging to family of partitional clustering that decomposes a dataset into a set of disjoint groups [71].

The k-means algorithm was proposed by J. MacQueen [72] and the main purpose is to describe a process for partitioning an N-dimensional population in k sets on the basis of a sample. In other words, the goal is to produce groups of variables with a high degree of similarity within each group and a low degree of similarity between groups [73]. In the k-means algorithm, the choice of number of k classes or clusters for classification which is established a priori is important. For every cluster, the position of centroids in the dataset is defined, which represents the center of the cluster. K-means is an iterative algorithm that performs the procedure of iteration until the centroids’ position is stabilized. The k-means algorithm consists in the following steps:

• 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.

K-means is applied to the whole dataset as well as to all three-band compositions. The binary maps produced by applying the k-means were submitted to automatic vectorization, finally producing 57 different coastlines, one for the whole dataset, the others resulting from three-band compositions.

3.5. Accuracy Tests

Accuracy tests were carried out on a selected subset of the resulting coastlines. In the literature, quantitative assessments are usually conducted by comparing the detected coastlines with the reference one, which is manually delineated coastline [17,74]. In this study, we compared each selected coastline with the reference one, achieved by photointerpretation and manual vectorization on the RGB true color composition. Particularly, we considered the coastline resulting from the unsupervised classification of all bands as well as those derived from 14 of the 56 three-band compositions. This selection aimed to analyze the accuracy of the results related to the variability of MOIF, so subsets presenting high, middle and low values of the proposed new index were chosen. In addition, we also selected two band combinations presenting the higher values of OIF (i.e., the first and the second classified) to better compare the different results provided by the two indices considered.

Due to the imperfect overlap between each automatic extracted coastline and the reference coastline, polygons were generated by the layer overlay. In the literature, there is a methodology that allows deriving the level of accuracy of the shift between these two lines, called the distributed ratio index (DRI) [34]. This derives from the ratio index (RI) which is given by the ratio between the sum of the areas of the polygons (A) and the length of the coastline chosen as a reference (L):

$$RI=\frac{A}{L}$$

(6)

The difference between these two indices is that the DRI also provides parameters such as the standard deviation, and the minimum and maximum values of the shift, in order to supply the degree of accuracy. In fact, this index considers the area of each polygon generated (A_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:

$$DRI=\frac{A_k}{L_k}$$

(7)

where A_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.

In addition, to verify the thematic accuracy of the unsupervised classification, obtained for each considered band composition, test sites are used. The manual vectorization of the coastline divides the scene into two macro areas, i.e., sea and land. Since the classification difficulty is mainly for the pixels near the coastline, we decided to consider a buffer of 300 m around the land–sea separation line. In this way, there were two extensive test sites, one of water and the other of no-water separated by the coastline.

In this way, it was possible to determine each time how many pixels were correctly and incorrectly classified. In particular, we proceeded with the construction of the confusion matrix: it is a powerful tool that determines and quantifies the correctness of the classification. The confusion matrix is nothing more than a table of values where each row represents the real values, while each column the predicted values. In the diagonal there are the elements classified correctly, i.e., belonging to the “true” class. From this matrix, it is possible to calculate three significant accuracy values, called user accuracy (UA), producer accuracy (PA) and overall accuracy (OA).

The UA is given by the number of accurately classified pixels divided by the pixels assumed as belonging to that class. PA is the ratio of correctly classified pixels to the total pixels belonging to that class. Finally, OA is given by the total of correctly classified pixels of each class divided by the total pixels [75].

4. Results and Discussion

4.1. OIF and MOIF Results

The resulting OIF values for the 56 band combinations are listed in

Table 2. Ranking using OIF.

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

in descending order (the higher the value, the better the ranking).

In the first positions of the ranking provided by the OIF index, there are the band compositions including B9, as was to be expected. In fact, as mentioned in the previous section, the cirrus band has characteristics that make it strongly decorrelated from the others. It generally has brighter pixels for presence of clouds and dark ones in other areas: the main feature is the visualization of clouds at high altitude, which could not be visible in other spectral bands. Although B9 has poor information on the land cover of the investigated scene, our experiments confirmed that in many cases, band compositions including cirrus presented high values for OIF. Due to this problem, a new ranking was drawn up given by the new index (MOIF).

The maximum, minimum and difference values of the bands that are necessary for calculating CF (Equation (4)) are reported below (

Table 3. Values for CF calculation.

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

).

The maximum and minimum values provide further confirmation of the poor information of B9, when compared to the other bands. The difference obtained between the maximum and the minimum of each band allowed us to calculate the MOIF index that substantially changed the ranking of the band combinations (

Table 4. Ranking of band compositions using MOIF.

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

).

The new ranking obtained overturns the previous one. We can see that the first classified compositions do not have the cirrus band: since the aim is to identify optimal subsets that ensure a lot of information to better distinguish the types of land cover, the classification is more reliable.

4.2. K-Means Application

In this section, three emblematic false color compositions and their k-means classification are shown. Particularly, the first (Figure 3), the middle (Figure 4) and the last classified (Figure 5) based on MOIF values are selected.

From a first visual analysis, as the MOIF decreases, the classification worsens, and therefore the separation between sea and land given by the coastline is less accurate. In particular, the k-means application to the composition of the bands 1-2-9 returned a great part of Calabria territory fragmented as many islands surrounded by the sea that penetrates for many kilometers inside the land. The result was clearly wrong and there was no need to calculate DRI for certifying the unreliability of the coastline extractable in this case. Nonetheless, in order to have a numerical type of analytical indicator that allowed ranking the compositions of bands in relation to the accuracy of the coastline that can be extracted from them, DRI was calculated in each of the possible cases.

4.3. DRI Evaluation

Table 5. Statistical values of DRI for the extracted coastlines.

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

shows the statistics of DRI obtained for 15 of the resulting coastlines. Particularly, we considered the coastline supplied by the k-means application to the following band compositions:

• 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).

For comparison with the pixel size, i.e., 30 m, as well as to establish the accuracy of the extracted coastline, the DRI results are given in meters.

The DRI values show a better performance as the MOIF index increases. The first classified composition, including blue, NIR and SWIR1 bands (B2 B5 B6), has the best RMSE value (9.108 m), while the maximum (35.940 m) is close to pixel dimension. The two band compositions following in the standings show slightly worse results (RMSE equal to 9.242 m and 9.243 m, respectively).

The composition of the band classified 12th has a very excellent RMSE value (9.281 m) if compared to the first three, worsening the maximum value (81.696 m). The other two band compositions taken into consideration (21st and 26th) stabilize their RMSE value around the value 9.4 m as well as the maximum shift reached (about 82 m).

Instead, for the 28th and 29th classified compositions we can see RMSE values (respectively 9.637 m and 9.692 m) that still do not differ much from that of the first classified composition, but the maximum value so far remains more than double the pixel size (83.120 m).

Starting from the 43th composition, a deterioration is noted both in terms of RMSE (14.537 m) and maximum (623.013 m).

The 54th composition according to MOIF values shows that the high correlation between B2 and B3 as well as the low level of information included in B9 aggravates the accuracy of the extracted coastline. In fact, in this case, we have bad statistics for DRI (RMSE equal to 72.022 m and maximum equal to 952.779 m). The situation is becoming worse for the last classified band compositions (B3, B4, B9 and B1, B2, B9), showing a rapid increase of the shift between each extracted coastline and the reference one.

In addition, the last two combinations of bands (B2, B5, B9 and B4, B5, B9) slip from the top positions, given by the OIF, to the 18th position and 13th position, respectively, according to the MOIF index. The results show that the application of the new index is consistent with the variation in the results supplied by the accuracy evaluation.

To show on map the different accuracy level of results related to the MOIF values, we selected three zones respectively in the north (Frame 1), middle (Frame 2) and south part (Frame 3) of the study area (Figure 6).

Four scenarios were considered for each frame, the first associated with the best performing band composition (B2, B5, B6), the second associated with a composition classified at the 24th position (B3, B4, B5), the third associated with a composition classified at the 43th position (B3, B4, B6), and the fourth presenting one of the worst performances associated with a composition classified at the 54th position (B2, B3, B9), as resulting from the DRI application. The results of the above mentioned band compositions for the frame 1 are shown in the Figure 7(B2, B5, B6), Figure 8(B3, B4, B5), Figure 9(B3, B4, B6) and Figure 10(B2, B3, B9). In analogous way, Figure 11, Figure 12, Figure 13 and Figure 14 concern the frame 2 and Figure 15, Figure 16, Figure 17 and Figure 18 the frame 3, repeating the band compositions in the same order.

In each case, the automatically extracted coastline (in red) was compared to the reference coastline (in black).

Due to the raster to vector conversion, the lines are jagged, as they followed the shape of the pixel (smoothing was not applied in our experiments). In all cases, the coastline extracted from the band composition associated to the higher value of MOIF was very close to the reference coastline. Vice versa, maps showed very high deviations between the reference coastline and the coastline extracted from the band composition associated to a low value of MOIF.

The images above highlight the effectiveness of the index used, emphasizing how the decorrelation among the bands and the amount of information in each band influenced the accuracy of the automatic extracted coastline. In fact, as the value of the MOIF decreases, we see a gradually increasing distance between the reference coastline and the one automatically extracted from the considered band combination.

4.4. Classification Accuracy Evaluation

Table 6. Thematic accuracy values.

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

shows the thematic accuracy values for the 15 band compositions selected for our tests and classified with the k-means.

The OA accuracy values close to 1 indicate correct classification.

The results of the thematic accuracy are also very satisfactory and in fact confirm in other terms what the DRI had already anticipated. The first band combination, given by the MOIF, (B2, B5, B6), also remains the best in this case reaching the highest OA value, as well as proceeding from the highest to the lowest MOIF value, the OA decreases, synonymous with a worsening classification. In fact, in the last places we find the band compositions(B3, B4, B9 and B1, B2, B9) that have a low OA value (0.8).

4.5. Comparison with Other Study Results

Finally, we can evaluate the effectiveness of the proposed approach comparing the results with those obtained by other researchers, especially in terms of accuracies achievable using different methods.

Liu et al. [25] in 2017 analyzed the performance of coastline extraction by integrating downscaling, pan-sharpening and water index approaches in increasing the accuracy of coastline extraction from Landsat 8 OLI images. They considered a portion of Ningbo coast (East China Sea) mainly containing bedrock coast, artificial coast and flat sandy coast and used ZiYuan-3 surveying satellite (ZY-3) MS image to extract the reference coastline. Applying the traditional water index method to extract coastline directly from original MS images (resolution: 30 m), they obtained a mean absolute difference (MAD) equal to 18.62 m between the resulting coastline and the reference one, with maximum positive difference (MPD) equal to 124.19 m and minimum negative difference (MND) equal to 223,89 m. Better results were achieved using pan-sharpened images (MAD = 13.54 m, MPD = 129.47, MND = 107.11 m) but those are not comparable with our study, which does not consider data fusion. However, the approach we propose based on MOIF and K-means ensures better accuracies and not only with the first classified band combination (B2, B5, B6), but also with others, such as B2, B5,B7; B5,B6, B7; B3, B5, B6; B2, B3, B5 and B3, B4, B5.

In 2017, El Kafrawy et al. [76] examined the performance of six different methods used to extract shorelines from Landsat 8 images. They compared the output with a shoreline detected by high-resolution image Pleiades B1 (0.50 m). The experiments showed that all coastlines extracted were within a pixel shift (30 m), but the thresholding band ratio method was the most accurate approach with an RMSE of 9.54 m, which is still less accurate than results we obtained with our approach.

Tuan et al. in 2018 [77] evaluated the accuracy of coastline extraction using three water indices (NDWI, MNDWI and AWEI) applied to Landsat 8 imagery and compared the results with a practical shoreline, obtained considering ground-truthing positions identified during a field survey. This study revealed that the AWEI was a more accurate approach than NDWI and MNDWI, with an RMSE of 12.4 m.

Alcaras et al. [78] in 2019 applied NDWI to Landsat 8 OLI images to detect the Tyrrhenian coastline of the Campania region (Italy) presenting, similarly with our study area, long beaches as well as high coasts and port zones [79]. Alcaras et al. used maximum likelihood classification (MLC), one of the most common classification methods in remote sensing based on Bayes’ theorem, to determine a threshold to separate seawater from land in an NDWI map. They obtained MAD=16.84 m between the resulting coastline and the reference one, achieved with visual interpretation and manual vectorization of RGB composition. In this case, the accuracy was also lower than that provided by the method we propose.

5. Conclusions

The experiments carried out on Landsat 8 OLI images concerning a part of the Calabria region highlight the effectiveness of the proposed approach for coastline data automatic extraction based on an unsupervised method, such as the k-means, and the use of a new index, the MOIF. This index gives as a single value the combination of the degree of correlation and the amount of information overall provided by the specific three bands considered. In other words, this index makes it possible to identify the three bands which simultaneously are highly uncorrelated and exhibit a wide range of values, so as to facilitate the distinction between water and no-water (i.e., soil and vegetation).

To establish the accuracy of the results, we used the DRI, which provided the deviation between the reference coastline and the automatically extracted one, as well as thematic accuracy indices (i.e., PA, UA and OA) extracted from confusion matrix. Both approaches corroborated the validity of the proposed method. In fact, the results were very encouraging: the best three-band composition given by the new index, i.e., B2, B5, B6, provided the best statistics of DRI, with RMSE value lower than the pixel dimensions and with a maximum value slightly exceeding this dimension. DRI confirmed that the effectiveness of MOIF seems to be better than that of OIF in selecting the optimal three-band composition for coastline extraction. Similarly, the thematic accuracy provided by the OA values confirmed the indications of the MOIF: the best resulting combination was B2, B5, B6.

The experiments carried out show that it is preferable to apply k-means on a three-band composition rather than on all available bands at the same time: DRI values and thematic accuracy indices confirm that increasing the data to be processed in the unsupervised classification can introduce confusion, as in this case, and worsen the results rather than produce an enhancement of the thematic accuracy.

Regarding the future developments of this work, further studies will be focused on the possibility of extending the proposed approach to other satellite images, especially those presenting higher resolution than Landsat 8 OLI, in order to evaluate the correctness of the suggested index, i.e., MOIF, for the identification of the three uncorrelated bands including a high level of information. Furthermore, we will mainly focus on the possibility to find the best method for automatic coastline data extraction comparing the proposed approach with others available in literature such as water index approaches (e.g., NDWI) and machine learning approaches.