A number of spectral indices frequently used in burned area mapping studies have been calculated, which are reported in Table 3. Most of them employ the classical normalized difference formulation of the Normalized Difference Vegetation Index (NDVI) [22], but using one or both of the SWIR bands, which are sensitive to moisture content and consequently facilitate the discrimination of the burned areas. The indices are calculated considering the ground reflectance values of the Level-2A products in the range [ 0 , 1 ] , from either the pre-fire image or the post-fire one or both (as described in the following subsections). In the following, we use the notation S I pre and S I post to describe any index S I calculated from the pre-fire or the post-fire image, respectively (e.g., NDVI pre ). Moreover, the empirical rule-based classification (described in the next subsection) also considers the difference between the pre-fire and post-fire values for some of the indices, which is an indication of disturbance resulting from the fire. The difference, which is denoted as d S I for any index S I (e.g., dNBR ), is calculated as pre-fire minus post-fire value, i.e., d S I = S I pre − S I post .

The supervised classification approach followed by the proposed methodology requires a training set that is labeled automatically. To do so, we defined two

empirical rules that employ thresholds on differences or ratios of the pre-fire and post-fire spectral indices, following a similar approach with previous studies [8] [15]. It is generally impossible to define empirical rules that will classify correctly all (or almost all) pixels, due to the great variety of ecosystem types (e.g., sparsely vegetated areas, dense forests, shrublands, agricultural or pasture areas, etc.), illumination conditions, topography, and other factors. Therefore, these rules are defined in a way such as only pixels that can be characterized unambiguously as burned or unburned are labeled, in order to avoid introducing misclassifications into the training set as much as possible.

To this end, the features used to define the rules and the respective threshold values were determined empirically through a trial-and-error procedure on many wildfire events in Greece, in a way that only unambiguous burned or unburned pixels were labeled, in order to avoid introducing errors within the training set. Eventually, a pixel is classified as burned if it satisfies the rule defined by Equations (1)-(2):

MNDWI pre < − 0.3                     A N D   [ ( B8A ratio > 0.3   O R   dMIRBI < − 1.5 )   A N D ​   dNDII > 0.02 ] (1)

where

B8A ratio = B8A pre B8A post − 1 . (2)

Accordingly, an object is classified as unburned if it satisfies the rule defined by Equation (3):

MNDWI pre > − 0.25   O R   [ dNBR < − 0.015   O R ​   dNBR2 < − 0.015 ] . (3)

In both cases, the pre-fire MNDWI index is considered for discriminating water surfaces and artificial areas (buildings, roads, etc.), whereas the vegetation or burned area identification is performed by the remaining part of the corresponding rule. To avoid misclassifications by differences in illumination between the pre-fire and post-fire image acquisitions—possibly in combination with topography—a morphological opening (erosion followed by dilation) operator [30] is applied to the resulting rule-based classified image, considering a square structuring element with a side of 3 pixels (i.e., the 8-neighborhood). The opening operator effectively removes isolated single-pixel classifications, which exhibit a higher probability of having been misclassified.

Depending on the area, a larger or smaller proportion of pixels may be classified by the above procedure. Densely vegetated forest areas or severely burned areas are more likely to be labeled. In any case, the labeled pixels are used to formulate the training set and the remaining ones are categorized by the supervised classifier, as explained in the following.

The dataset used for the supervised classification considers 21 features extracted from multiple sources (“classification features image” module in Figure 2). More specifically, it is formulated considering:

1) the eight bands of the post-fire Sentinel-2 image reported in Table 1,

2) the first seven spectral indices of Table 3 calculated from the post-fire image (NDVI_post, MSAVI2_post, CSI_post, MIRBI_post, NBR_post, NBR2_post, and NDII_post), and

3) all features considered in the empirical rules of Equations (1)-(3), i.e., B8A_ratio, dMIRBI, dNDII, dNBR, dNBR2, and MNDWI_pre).

Having defined the feature set and the training set from the previous step, an SVM classification model [17] is learned subsequently, in order to classify the remaining image pixels. We used a radial basis function (RBF) kernel for the SVM formulation. The penalty constant C and the RBF kernel’s parameter γ are optimized via a 5-fold cross-validation procedure on all possible combinations for the two parameters, considering an exponentially increasing grid of possible values for each parameter. The trained SVM model is subsequently applied to classify all pixels not labeled by the empirical rules, thus resulting in the initial pixel-based classification map.

Pixel-based classification are typically severely affected by the salt-and-pepper phenomenon. The latter characterizes the phenomenon whereby individual pixels or small isolated regions are misclassified, either as unburned within the fire perimeter or as burned outside—and in many cases far away for—the fire perimeter, with a human observer being able to identify them easily as errors through visual inspection. These isolated errors are the result of image artifacts (because of illumination angle, topography, specular reflections, etc.) in combination with the fact that the pixel-based classification does not exploit any spatial information and the phenomenon becomes more prominent with the increase of spatial resolution. To overcome this limitation, the initial pixel-based classification described in the previous subsection is refined via the MSSC-MSF approach [18], which can effectively exploit both spatial and spectral information.

Given an input image and a pixel-based classification, MSSC-MSF starts by segmenting the image by means of three different image segmentation algorithms (see Figure 2). For this purpose, we used the watershed segmentation [31], the Fuzzy C-Means (FCM) clustering [32], and the mean shift segmentation [33] algorithms. In all cases, the segmentation was performed considering only the four 10 m bands of Sentinel-2 (B02, B03, B04, and B08 in Table 1). This choice was made in order to a) reduce the overall computation requirements, b) exploit the finest spatial resolution provided by Sentinel-2, and c) increase the methodology’s generalization capabilities by using a simpler feature set for the segmentation process than that used for the pixel-based classification.

Watershed is a morphological approach to image segmentation that combines region growing and edge detection. The method is typically applied to a gradient of the original image and segments it into small adjacent but non-overlapping regions, where each region is associated with one minimum (i.e., homogeneous region) of the gradient image. Similarly to the original approach [18], we used the robust color morphological gradient (RCMG) [34] for this purpose. Conversely, FCM is a clustering algorithm, but we can derive a segmentation of the image by identifying and uniquely labeling the connected components (CCs) on the resulting clustering map. Final, mean shift is an efficient feature-space analysis approach that has been successfully used in the past for remotely sensed image segmentation [35] [36], as it balances between the spectral and the spatial information provided by the multispectral image.

For each segmentation, an equivalent classification map is produced fusing the segmentation result with the pixel-based classification obtained by SVM. More specifically, a majority voting is performed within each segment of the image, i.e., all pixels belonging to the segment are assigned to the class exhibiting the highest frequency in the classification map within this segment. Ultimately, the three independent classification maps are fused to select a set of markers. A pixel is labeled as marker if all three independent classification maps agree (i.e., belong the same class, in our case, either burned or unburned). Marked pixels retain their class, whereas all other are considered as unclassified. Effectively, this Multiple Spectral-Spatial Classification (MSSC) approach eliminates the salt-and-pepper phenomenon of the base pixel-based classification by exploiting the spatial information, which is provided by the segment-wise processing of the image. If all three independent classifications agree, it is assumed that the pixel has been correctly classified (markers), whereas the remaining pixels are considered ambiguous.

Finally, those ambiguous pixels are labeled by growing a Minimum Spanning Forest (MSF) rooted from the markers. Each image pixel is considered as a vertex of an undirected graph, connected with its eight immediate neighbors through edges. A weight is assigned in each edge, which is proportional to the dissimilarity between the two pixels. As a measure of dissimilarity, we used the spectral angle mapper (SAM) measure, which is defined by Equation (4):

SAM ( v i , v j ) = ∑ b = 1 B v i b ⋅ v j b ∑ b = 1 B v i b 2 ⋅ ∑ b = 1 B v j b 2 (4)

where B is the cardinality of the feature space (i.e., number of bands in the image) and v i = { v i 1 , … , v i B } and v j = { v j 1 , … , v j B } are the feature vectors of two neighboring pixels. The absolute SAM value is maximized for dissimilar feature vectors and minimized for equal ones. As shown in Figure 2, the SAM measure is calculated considering the full classification feature space, comprising the 21 features described in the previous subsection. In the case that two neighboring pixels are both markers, a zero weight is assigned if they belong to the same class and an infinite weight otherwise.

An additional vertex for each class (here two, burned or unburned) is inserted into the graph and connected with all markers belonging to the respective class. A root vertex is also inserted, connected with those extra vertices. With this configuration, running a minimum spanning tree algorithm (e.g., Prim's algorithm [37]) and then removing the extra vertices induces an MSF over the graph. Assigning all pixels grown from each marker to its class, ultimately results in labeling all unclassified pixels in the image. Effectively, each marker grows its tree by labeling neighboring unlabeled pixels, in a way that the total dissimilarity among pixels is minimized. A detailed description of the MSF procedure can be found in [18] and [38].

Vectorizing the final classification map and keeping only the areas labeled as burned, we derive the final burned area perimeter, which can be subsequently viewed or analyzed in a GIS environment.

Before reporting the numerical results, we provide here an example of the proposed algorithm’s application in Figure 3, in order to visually explain the various steps of the algorithm. We use the case of the Kallitechnoupoli wildfire (see Table 2), with Figure 3(a) showing a false-color composite of the post-fire Sentinel-2 image and the reference burned area perimeter superimposed with a black line. This was a devasting wildfire that started on July 23, 2018 in Attica, Greece and claimed the lives of more than 100 people. It presents several difficulties as a burned area mapping task, because the fire expanded to populated areas with significant vegetation cover (mostly pine trees in-between houses and within house yards), with some of the residential properties completely destroyed and others partially burned. As such, several regions in the scene are difficult to be correctly classified by a fully automated algorithm.

The training set derived from the empirical rules (see Section 3.2) comprises

only the unambiguous burned or unburned pixels (Figure 3(b)), which are either severely burned vegetated areas or unburned vegetated areas. Ambiguous areas such as sparsely vegetated areas, semi-burned areas, or areas in the wildland-urban interface are (correctly) not included in the training set. The initial pixel-based SVM classification (Figure 3(c); see Section 3.3) exhibits a fairly good performance, but with a high salt-and-pepper phenomenon outside the fire perimeter, as well as significant omission errors within the fire perimeter.

The three spectral-spatial classifications (see Section 3.4) result in generally different results. Watershed (Figure 3(d)) is more or less a superpixel segmentation algorithm (i.e., it usually generates very small segments) and, as such, it removes the salt-and-pepper misclassifications, but also exhibits relatively high commission error, misclassifying large areas to the north of and outside the fire perimeter as burned. On the other hand, FCM (Figure 3(e)) is a clustering algorithm and, as such, it is closer to the pixel-based SVM result. The mean shift classification (Figure 3(f)) is somewhere in-between the previous two, since it exploits both spatial and spectral information.

The markers (Figure 3(g)) are defined as all pixels that the three segmentation-based classification agree. Closely inspecting Figure 3(a), Figure 3(b), and Figure 3(g), we can observe that indeed the hard-to-discriminate regions are left unmarked. The MSF algorithm (Figure 3(h)) finally labels the unmarked regions, resulting in the most accurate classification result. Comparing the initial (Figure 3(c)) and the final (Figure 3(h)) classifications, it becomes apparent that the MSSC-MSF approach improves the thematic consistency of the mapping process significantly, which is also reflected in the numerical comparison presented in the following.

For quantifying accuracy, well-known measures derived from the confusion matrix were calculated, namely, sensitivity, specificity, accuracy, and Matthews correlation coefficient (MCC) [39]. Correct classifications in a confusion matrix are either true positives (TP) or true negatives (TN), i.e., pixels correctly classified as burned or unburned, respectively. The errors are described as false positives (FP; pixels classified as burned but their true label according to the reference was unburned) and false negatives (FN; pixels classified as unburned but their true label according to the reference was burned). Sensitivity is (inversely) related to omission errors (burned areas misclassified as unburned) and is defined by Equation (5):

Sensitivity = T P P , (5)

where P is the total number of pixels labeled as burned in the reference set. Specificity is related to commission errors (unburned areas misclassified as burned) and is defined by Equation (6):

Specificity = T N N , (6)

where N is the total number of pixels labeled as unburned in the reference set. Accuracy is the ratio of correctly classified areas to the area of the reference perimeter—being the most commonly used measure of classification performance—and is defined by Equation (7):

Accuracy = T P + T N P + N . (7)

Finally, MCC takes into consideration both omission and commission errors, being a correlation coefficient between the observed and predicted binary classifications and is generally regarded as a balanced measure that can be used even if the classes are of very different sizes [40]. It is defined by Equation (8):

M C C = T P ⋅ T N − F P ⋅ F N ( T P + F P ) ⋅ ( T P + F N ) ⋅ ( T N + F P ) ⋅ ( T N + F N ) . (8)

Table 4 reports the values of the accuracy measures for both the initial pixel-based SVM classification and the final ones for each test case. The proposed methodology exhibits higher accuracy values in most of the regions compared to the initial pixel-based classification, which is usually attributed to the higher sensitivity (fewer omission errors) with similar specificity values. For two cases (Zemeno and Kallitechnoupoli), the performance of the proposed method is much higher than the base classification, especially in terms of MCC values. In purely absolute terms, the proposed method exhibits classification accuracies greater or equal to 0.92 and MCC values greater or equal to 0.85. Such a performance is perfectly acceptable for operational applications on a national level, especially taking into consideration that it is a fully automated process.

Complementary to the numerical results reported above, we provide a visual comparison between the initial pixel-based SVM classification and the final one for all six wildfires of Table 2 in Figures 4-9. This comparison confirms the differences and additionally highlights the qualitative superiority of the proposed framework. One the one hand, the proposed methodology eliminates the salt-and-pepper phenomenon of the initial pixel-based classification outside the fire perimeter. Because the latter are usually isolated pixels misclassifications, the specificity measure (see Table 4) is not greatly affected negatively. Nevertheless, it is significant for the pixel-based classification in many cases, such as the Farakla (Figure 5), the Kallitechnoupoli (Figure 8), and—most prominently—the

Zemeno (Figure 7) wildfires. On the other hand, the pixel-based SVM classification seems to systematically underestimate the burned area within the fire perimeter, resulting in higher omission error.