A Novel Remote Sensing Index for Extracting Impervious Surface Distribution from Landsat 8 OLI Imagery

: The area of urban impervious surfaces is one of the most important indicators for determining the level of urbanisation and the quality of the environment and is rapidly increasing with the acceleration of urbanisation in developing countries. This paper proposes a novel remote sensing index based on the coastal band and normalised di ﬀ erence vegetation index for extracting impervious surface distribution from Landsat 8 multispectral remote sensing imagery. The index was validated using three images covering urban areas of China and was compared with ﬁve other typical index methods for the extraction of impervious surface distribution, namely, the normalised di ﬀ erence built-up index, index-based built-up index, normalised di ﬀ erence impervious surface index, normalised di ﬀ erence impervious index, and combinational built-up index. The results showed that the novel index provided higher accuracy and e ﬀ ectively distinguished impervious surfaces from bare soil, and the average values of the recall, precision, and F1 score for the three images were 95%, 91%, and 93%, respectively. The novel index provides better applicability in the extraction of urban impervious surface distribution from Landsat 8 multispectral remote sensing imagery.


Introduction
Impervious surfaces are artificial surfaces that water cannot infiltrate to reach the soil, such as parking lots, streets, and highways [1]. Changes in land use and land cover caused by the expansion of impervious surfaces are likely to influence the regional climate [2]. Jacobson et al. and Huszar et al. pointed out that the impervious surface area and land surface temperature are positively correlated, and the expansion of impervious surfaces will result in the increase of the land surface temperature which may cause uneven distribution of urban heat and trigger the urban heat island effect [3,4].
Accurate and fast extraction methods for impervious surface distribution are important which is helpful for detecting regional environmental changes in urban areas and achieving sustainable urban development. They can be divided into two categories, namely, field surveys and remote sensing [1]. Field surveys can provide more detailed information on impervious surface distribution but are time-consuming, laborious, and difficult to apply to the assessment of large areas. In contrast, widely-used remote sensing methods can extract impervious surface distribution quickly, and sources of commonly used remote sensing images include the QuickBird [5], WorldView-2 [6], and Landsat satellites [7], etc. When extracting impervious surface distribution in a large urban area, Landsat Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 15 rows × 480 columns with a pixel size of 30 m, and their (5,4,3) false colour composites are shown in Figure 1. Typical ground objects in these case images include vegetation, bare soil, water body, and impervious surfaces, and present more representative and complexely. In the (5,4,3) false colour composite image with a 2% linear stretch, the vegetation is red in summer such as Cases 1 and 2 and easily distinguished from impervious surfaces because of their different spectral features; bare soil is exposed in winter, such as in Case 3, and is easily confused with impervious surfaces because of their similar spectral features.

Proposed Method
According to the vegetation-impervious surface-soil (VIS) model [24], land cover consists mainly of vegetation (V), impervious surfaces (I) and bare soil (S), with the exception of water bodies. In remote sensing imagery, the largest difference in land cover is that between water bodies and land, and land can further be divided into impervious surfaces and permeable surfaces (vegetation and bare soil). Hence, the workflow can be divided into two steps, namely, masking water bodies and extracting impervious surfaces from land.
An impervious surface is an area without vegetation coverage and thus has a lower NDVI value [25]. Studies by Wang et al. and Mu et al. showed that impervious surfaces usually have higher values in the blue band [10,26]. Besides, Chen pointed out that the coastal band in Landsat 8 imagery can enhance information on impervious surfaces more significantly than the blue band, and the addition of the coastal band in the supervised classification of land use is beneficial for further distinguishing impervious surfaces from other ground objects [27].
In this study, a RISI was proposed for extracting impervious surface distribution on the basis of the coastal band and NDVI of a digital number (DN) image and is defined by Equation (1): where B1 and NDVI1 denote the coastal band and NDVI, respectively, after a 0-1 transformation. The workflow comprises the following four steps: (a) Water bodies are first masked; (b) The coastal band undergoes a 0-1 transformation to obtain B1; (c) The NDVI is calculated, and then a 0-1 transformation is performed to obtain NDVI1; and (d) The RISI is calculated and then segmented using a threshold determined by the Otsu method [28]. Typical ground objects in these case images include vegetation, bare soil, water body, and impervious surfaces, and present more representative and complexely. In the (5,4,3) false colour composite image with a 2% linear stretch, the vegetation is red in summer such as Cases 1 and 2 and easily distinguished from impervious surfaces because of their different spectral features; bare soil is exposed in winter, such as in Case 3, and is easily confused with impervious surfaces because of their similar spectral features.

Proposed Method
According to the vegetation-impervious surface-soil (VIS) model [24], land cover consists mainly of vegetation (V), impervious surfaces (I) and bare soil (S), with the exception of water bodies. In remote sensing imagery, the largest difference in land cover is that between water bodies and land, and land can further be divided into impervious surfaces and permeable surfaces (vegetation and bare soil). Hence, the workflow can be divided into two steps, namely, masking water bodies and extracting impervious surfaces from land.
An impervious surface is an area without vegetation coverage and thus has a lower NDVI value [25]. Studies by Wang et al. and Mu et al. showed that impervious surfaces usually have higher values in the blue band [10,26]. Besides, Chen pointed out that the coastal band in Landsat 8 imagery can enhance information on impervious surfaces more significantly than the blue band, and the addition of the coastal band in the supervised classification of land use is beneficial for further distinguishing impervious surfaces from other ground objects [27].
In this study, a RISI was proposed for extracting impervious surface distribution on the basis of the coastal band and NDVI of a digital number (DN) image and is defined by Equation (1): where B1 and NDVI1 denote the coastal band and NDVI, respectively, after a 0-1 transformation. The workflow comprises the following four steps: (a) Water bodies are first masked; (b) The coastal band undergoes a 0-1 transformation to obtain B1; (c) The NDVI is calculated, and then a 0-1 transformation is performed to obtain NDVI1; and (d) The RISI is calculated and then segmented using a threshold determined by the Otsu method [28].

Water Body Masking
Appl. Sci. 2019, 9, 2631 4 of 15 The water body index (WI) is calculated using Equation (2) [29]: where Green denotes the green band and SWIR1 denotes the shortwave-infrared band.
The value corresponding to the right valley of the WI histogram is manually fine-tuned as the segmentation threshold to mask water bodies.

0-1 Transformation of the Coastal Band
The coastal band undergoes a 0-1 transformation to obtain B1 according to Equation (3): where T0 and T1 denote the band before and after the 0-1 transformation according to Equation (3), respectively, and max and min are the maximum and minimum values of the band, respectively.

Calculation of the NDVI
The NDVI is calculated using Equation (4) [30]: where Red denotes the red band and NIR denotes the near-infrared band. Then, the NDVI undergoes a 0-1 transformation to obtain NDVI1 in an analogous way to Equation (3).

Calculation of the RISI
The RISI is calculated using Equation (1), and then its threshold is determined by the Otsu method and used to segment the image to obtain the impervious surface region.
The Otsu method is an adaptive threshold determination method and is widely used in image segmentation, which maximizes the class variance between objects and background [28].

Comparison of Methods
The NDBI, IBI, NDISI, NDII, and CBI methods were used for comparison. The segmentation thresholds of the NDBI and NDISI were both set to 0, which is the default threshold according to the authors who proposed these indices, whereas the thresholds of the other three indices were determined by the Otsu method here because the authors who proposed these indices determined the thresholds manually rather than setting a fixed threshold. In addition, in all the methods, water bodies were masked first so as to ensure the comparisons coincided.
(3) NDISI: Xu proposed the NDISI for extracting impervious surface distribution [9]: where TIR denotes the thermal band, which we replaced with the TIR1 band (10.6-11.19µm) in Landsat 8 imagery. MNDWI is calculated as follows [32]: (4) NDII: Wang et al. devised the NDII to extract impervious surface distribution [10]: where VIS represents one of the red, green and blue bands. Wang pointed out that the accuracy of extraction is highest when VIS represents the red band [10], and hence we also used the red band to calculate the NDII. (5) CBI: Sun et al. developed the CBI to extract impervious surface distribution [11]: where NDWI is calculated as follows [33]:

Method for Accuracy Assessment
Accuracy is determined in terms of precision, recall, and the F1 score. According to their actual and predicted values, pixels are divided into true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN), and then the precision (P), recall (R), and F1 score are calculated using Equations (13)- (15) [34]: where TP_N and FP_N are the total numbers of pixels in TP and FP, respectively.
where FN_N is the total number of pixels in FN.
The closer the F1 score is to 1, the higher the accuracy of the extraction of impervious surface distribution is.

Spectral Features of Impervious Surfaces, Bare Soil, and Vegetation
Typical samples of impervious surfaces, bare soil, and vegetation were selected from each case image after water bodies were masked, and the mean spectral values for each type of sample were calculated to obtain their spectral curves ( Figure 2). These show that impervious surfaces had similar spectral features to those of bare soil. The DN value of impervious surfaces in the coastal band was higher than those of vegetation and bare soil, and vegetation had the largest difference between the DN values in the red and near-infrared bands, followed by bare soil. In the TIR1 band, the DN value of impervious surfaces was the highest in Case 2, whereas in Cases 1 and 3 the DN value of bare soil was the highest.

Results of Extraction of Impervious Surface Distribution
The ground truth for impervious surface distribution was determined by visual interpretation in each case image and is shown in Figure 3: Impervious surface distribution extracted by the proposed method is shown in Table 1. We can see that water bodies were masked well by the WI. The RISI effectively distinguished impervious surfaces from bare soil and vegetation, especially the large amount of bare soil in Case 3.

Results of Extraction of Impervious Surface Distribution
The ground truth for impervious surface distribution was determined by visual interpretation in each case image and is shown in Figure 3:

Results of Extraction of Impervious Surface Distribution
The ground truth for impervious surface distribution was determined by visual interpretation in each case image and is shown in Figure 3: Impervious surface distribution extracted by the proposed method is shown in Table 1. We can see that water bodies were masked well by the WI. The RISI effectively distinguished impervious surfaces from bare soil and vegetation, especially the large amount of bare soil in Case 3. Impervious surface distribution extracted by the proposed method is shown in Table 1. We can see that water bodies were masked well by the WI. The RISI effectively distinguished impervious surfaces from bare soil and vegetation, especially the large amount of bare soil in Case 3.  The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.   The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.   The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.   The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.  The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.  The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.  The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.  The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.  The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.
The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 15 The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.   The impervious surface distribution extracted by six methods are shown in Figures 4-6. The segmentation thresholds of the NDBI and NDISI were both set to 0, and the thresholds of the other methods were determined by the Otsu method. In general, the impervious surfaces extracted by the five reference methods were still mixed with other ground objects even though water bodies were masked. In Case 3, bare soil were seriously mis-extracted.   Figure 4 shows that the NDBI resulted in serious omissions while the other four reference methods provided higher accuracy. Figure 5 shows that the NDBI lost a large amount of impervious surfaces and other reference methods also resulted in serious errors. Figure 6 shows that all five reference methods mis-extracted a large amount of bare soil, and the NDBI and IBI lost a large amount impervious surfaces.

Accuracy
The recalls and precisions of the six extractions are shown in Figure 7, and the F1 scores are shown in Figure 8. The NDBI, IBI, NDISI, NDII, and CBI gave high recalls and low precisions, especially in Case 3 which had a large amount of bare soil, where the F1 scores were all less than 65%. The extraction accuracy by the proposed method was higher than others in our three case images, and the average values of the recall, precision, and F1 score were 95%, 91%, and 93%, respectively.    Figure 4 shows that the NDBI resulted in serious omissions while the other four reference methods provided higher accuracy. Figure 5 shows that the NDBI lost a large amount of impervious surfaces and other reference methods also resulted in serious errors. Figure 6 shows that all five reference methods mis-extracted a large amount of bare soil, and the NDBI and IBI lost a large amount impervious surfaces.

Accuracy
The recalls and precisions of the six extractions are shown in Figure 7, and the F1 scores are shown in Figure 8. The NDBI, IBI, NDISI, NDII, and CBI gave high recalls and low precisions, especially in Case 3 which had a large amount of bare soil, where the F1 scores were all less than 65%. The extraction accuracy by the proposed method was higher than others in our three case images, and the average values of the recall, precision, and F1 score were 95%, 91%, and 93%, respectively.  Figure 4 shows that the NDBI resulted in serious omissions while the other four reference methods provided higher accuracy. Figure 5 shows that the NDBI lost a large amount of impervious surfaces and other reference methods also resulted in serious errors. Figure 6 shows that all five reference methods mis-extracted a large amount of bare soil, and the NDBI and IBI lost a large amount impervious surfaces.

Accuracy
The recalls and precisions of the six extractions are shown in Figure 7, and the F1 scores are shown in Figure 8. The NDBI, IBI, NDISI, NDII, and CBI gave high recalls and low precisions, especially in Case 3 which had a large amount of bare soil, where the F1 scores were all less than 65%. The extraction accuracy by the proposed method was higher than others in our three case images, and the average values of the recall, precision, and F1 score were 95%, 91%, and 93%, respectively.    Figure 4 shows that the NDBI resulted in serious omissions while the other four reference methods provided higher accuracy. Figure 5 shows that the NDBI lost a large amount of impervious surfaces and other reference methods also resulted in serious errors. Figure 6 shows that all five reference methods mis-extracted a large amount of bare soil, and the NDBI and IBI lost a large amount impervious surfaces.

Accuracy
The recalls and precisions of the six extractions are shown in Figure 7, and the F1 scores are shown in Figure 8. The NDBI, IBI, NDISI, NDII, and CBI gave high recalls and low precisions, especially in Case 3 which had a large amount of bare soil, where the F1 scores were all less than 65%. The extraction accuracy by the proposed method was higher than others in our three case images, and the average values of the recall, precision, and F1 score were 95%, 91%, and 93%, respectively.

Discussion
With the economic growth of developing countries, the rapid urbanisation of rural land and its conversion to urban land directly lead to an increase in the area of impervious surfaces, which may lead to the urban heat island effect. Impervious surfaces are artificial surfaces that water cannot infiltrate to reach the soil, such as parking lots, streets, and highways. They often have a low specific heat capacity and heat up fast, which often leads to the higher temperature in urban areas than rural areas, the uneven distribution of heat, the abnormal hydrothermal cycle, and the harmful urban heat island effect [35]. It is important to build accurate and fast methods to extract impervious surface distribution which is helpful for detecting regional environmental changes in urban areas and achieving sustainable urban development.
The existing methods for the extraction of impervious surface distribution increased the difference between impervious surfaces and other ground objects and achieved high precisions in some cases [7][8][9][10][11]. However, differences between sensors, regions, and seasons often lead to inconsistencies in the spectral features of ground objects in images. Many methods have poor abilities to distinguish impervious surfaces from bare soil because of their spectral similarity [36], and it is also not easy to distinguish withered vegetation in winter from impervious surfaces. Figure 9 shows the differences between typical samples of impervious surfaces, bare soil, and vegetation in terms of the coastal band, blue band, green band, red band, ratio vegetation index (RVI) [37], NDVI, and difference vegetation index (DVI) [38], where all features underwent a 0-1 transformation. Of these three vegetation indices, the NDVI gave the greatest difference between impervious surfaces and other ground objects. Besides, the values for impervious surfaces in the coastal band were higher than those for vegetation and bare soil, and the contrast between impervious surfaces and bare soil gradually decreased in the coastal, blue, green, and red bands.

Discussion
With the economic growth of developing countries, the rapid urbanisation of rural land and its conversion to urban land directly lead to an increase in the area of impervious surfaces, which may lead to the urban heat island effect. Impervious surfaces are artificial surfaces that water cannot infiltrate to reach the soil, such as parking lots, streets, and highways. They often have a low specific heat capacity and heat up fast, which often leads to the higher temperature in urban areas than rural areas, the uneven distribution of heat, the abnormal hydrothermal cycle, and the harmful urban heat island effect [35]. It is important to build accurate and fast methods to extract impervious surface distribution which is helpful for detecting regional environmental changes in urban areas and achieving sustainable urban development.
The existing methods for the extraction of impervious surface distribution increased the difference between impervious surfaces and other ground objects and achieved high precisions in some cases [7][8][9][10][11]. However, differences between sensors, regions, and seasons often lead to inconsistencies in the spectral features of ground objects in images. Many methods have poor abilities to distinguish impervious surfaces from bare soil because of their spectral similarity [36], and it is also not easy to distinguish withered vegetation in winter from impervious surfaces. Figure 9 shows the differences between typical samples of impervious surfaces, bare soil, and vegetation in terms of the coastal band, blue band, green band, red band, ratio vegetation index (RVI) [37], NDVI, and difference vegetation index (DVI) [38], where all features underwent a 0-1 transformation. Of these three vegetation indices, the NDVI gave the greatest difference between impervious surfaces and other ground objects. Besides, the values for impervious surfaces in the coastal band were higher than those for vegetation and bare soil, and the contrast between impervious surfaces and bare soil gradually decreased in the coastal, blue, green, and red bands. Therefore, the ratio of the coastal band to the NDVI can maximise the information on impervious surfaces and increase the difference between impervious surfaces and other ground objects, and thus effectively distinguish impervious surfaces from bare soil, which is the main advantage of our method in comparison with the other five methods.

Extraction of Impervious Surface Distribution by Different Methods
The five methods used for comparison are applicable to different conditions and provide higher accuracy in other cases [7][8][9][10][11]. They exhibited differences in performance after water bodies were masked in our three cases, and the average F1 scores of extractions by six methods from the lowest to the highest value were in the following order: the NDBI, NDISI, IBI, NDII, CBI, and our proposed method. Therefore, the ratio of the coastal band to the NDVI can maximise the information on impervious surfaces and increase the difference between impervious surfaces and other ground objects, and thus effectively distinguish impervious surfaces from bare soil, which is the main advantage of our method in comparison with the other five methods.

Extraction of Impervious Surface Distribution by Different Methods
The five methods used for comparison are applicable to different conditions and provide higher accuracy in other cases [7][8][9][10][11]. They exhibited differences in performance after water bodies were masked in our three cases, and the average F1 scores of extractions by six methods from the lowest to the highest value were in the following order: the NDBI, NDISI, IBI, NDII, CBI, and our proposed method.
The average F1 score of extractions by the NDBI after water bodies were masked was 32%. This index utilises the feature that the values for impervious surfaces in the SWIR1 band in Landsat 5 TM imagery are higher than those in the NIR band. However, the spectral features of impervious surfaces in Landsat 8 OLI imagery are different from those in Landsat 5 TM imagery because of the differences in the sensor, wavelength range, and quantisation bit. Figure 2 shows that the values for impervious surfaces in the SWIR1 band were comparable to those in the NIR band in Cases 1 and 3, whereas the values in the SWIR1 band were lower than those in the NIR band in Case 2. Conversely, the bare soil in Case 3 gave higher values in the SWIR1 band than in the NIR band, which resulted in more instances of error.
The average F1 score of extractions by the NDISI after water bodies were masked was 44%. The author who devised the NDISI pointed out that the values for impervious surfaces are higher than those of other ground objects in the thermal infrared band. This index led to instances of error in Cases 2 and 3, which were caused by the fact that the values for impervious surfaces in the Landsat 8 thermal infrared band were not always higher than those for other ground objects (Figure 2). Thermal radiation from impervious surfaces is more obvious in summer but may be lower than that from other ground objects in winter [39,40]. Therefore, the use of the NDISI for the extraction of impervious surface distribution in summer may provide high accuracy [9], but its accuracy may be low if it is employed in winter.
The average F1 score of extractions by the IBI after water bodies were masked was 47%. This index combines three indices, namely, the NDBI, MNDWI, and SAVI. In our cases, the NDBI values for impervious surfaces were not always higher than those for other ground objects such as the bare soil in Case 3 (Figure 10), which may have led to many instances of error.
The average F1 score of extractions by the NDII after water bodies were masked was 57%. Xu et al. pointed out that this index is unreliable because the values for impervious surfaces in the thermal infrared band are significantly lower than those in the visible light band [36]. Besides, this index requires that bare soil is masked in advance [10], which is difficult in practice.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 15 The average F1 score of extractions by the NDBI after water bodies were masked was 32%. This index utilises the feature that the values for impervious surfaces in the SWIR1 band in Landsat 5 TM imagery are higher than those in the NIR band. However, the spectral features of impervious surfaces in Landsat 8 OLI imagery are different from those in Landsat 5 TM imagery because of the differences in the sensor, wavelength range, and quantisation bit. Figure 2 shows that the values for impervious surfaces in the SWIR1 band were comparable to those in the NIR band in Cases 1 and 3, whereas the values in the SWIR1 band were lower than those in the NIR band in Case 2. Conversely, the bare soil in Case 3 gave higher values in the SWIR1 band than in the NIR band, which resulted in more instances of error.
The average F1 score of extractions by the NDISI after water bodies were masked was 44%. The author who devised the NDISI pointed out that the values for impervious surfaces are higher than those of other ground objects in the thermal infrared band. This index led to instances of error in Cases 2 and 3, which were caused by the fact that the values for impervious surfaces in the Landsat 8 thermal infrared band were not always higher than those for other ground objects (Figure 2). Thermal radiation from impervious surfaces is more obvious in summer but may be lower than that from other ground objects in winter [39,40]. Therefore, the use of the NDISI for the extraction of impervious surface distribution in summer may provide high accuracy [9], but its accuracy may be low if it is employed in winter.
The average F1 score of extractions by the IBI after water bodies were masked was 47%. This index combines three indices, namely, the NDBI, MNDWI, and SAVI. In our cases, the NDBI values for impervious surfaces were not always higher than those for other ground objects such as the bare soil in Case 3 ( Figure 10), which may have led to many instances of error. The average F1 score of extractions by the NDII after water bodies were masked was 57%. Xu et al. pointed out that this index is unreliable because the values for impervious surfaces in the thermal infrared band are significantly lower than those in the visible light band [36]. Besides, this index requires that bare soil is masked in advance [10], which is difficult in practice.
The average F1 score of extractions by the CBI after water bodies were masked was 65%. This index combines the PC1, NDWI, and SAVI, which represent high-albedo surfaces, low-albedo surfaces, and vegetation, respectively, but the ability to mask bare soil needs to be further enhanced [36].
The average F1 score of extractions by our proposed method was 93%. Our method not only identified impervious surfaces but also masked other ground objects such as bare soil and therefore provided higher accuracy than the other five methods.

Atmospheric Effect of the Proposed Method
The abovementioned impervious surface distributions were extracted on the basis of the DN values in the images.
When electromagnetic waves are transmitted across the atmosphere, they are scattered because of molecules and minute particles; the shorter the wavelength is, the stronger the scattering is, which causes radiation distortion in the coastal and blue bands of Landsat 8 images. Atmospheric correction The average F1 score of extractions by the CBI after water bodies were masked was 65%. This index combines the PC1, NDWI, and SAVI, which represent high-albedo surfaces, low-albedo surfaces, and vegetation, respectively, but the ability to mask bare soil needs to be further enhanced [36].
The average F1 score of extractions by our proposed method was 93%. Our method not only identified impervious surfaces but also masked other ground objects such as bare soil and therefore provided higher accuracy than the other five methods.

Atmospheric Effect of the Proposed Method
The abovementioned impervious surface distributions were extracted on the basis of the DN values in the images.
When electromagnetic waves are transmitted across the atmosphere, they are scattered because of molecules and minute particles; the shorter the wavelength is, the stronger the scattering is, which causes radiation distortion in the coastal and blue bands of Landsat 8 images. Atmospheric correction of images is usually required in order to obtain more realistic surface reflectivity, but this is often a cumbersome process.
As a comparison, the case images were corrected according to the FLAASH model in ENVI, and reflectance values that were less than 0 or greater than 100 were modified according to Equation (16): where f (x, y) and g(x, y) represent the images before and after modification, respectively. The impervious surface distributions extracted after atmospheric correction are shown in Figure 11. From a comparison with Table 1, impervious surfaces were less widely distributed, and the average recall, precision, and F1 score were 89%, 77%, and 83%, respectively, which represented decreases by 6%, 14%, and 10%, respectively. of images is usually required in order to obtain more realistic surface reflectivity, but this is often a cumbersome process. As a comparison, the case images were corrected according to the FLAASH model in ENVI, and reflectance values that were less than 0 or greater than 100 were modified according to Equation (16): ( , ) < 0 ( , ) 0 ≤ ( , ) ≤ 100 100 ( , ) > 100 (16) where ( , ) and ( , ) represent the images before and after modification, respectively.
The impervious surface distributions extracted after atmospheric correction are shown in Figure  11. From a comparison with Table 1, impervious surfaces were less widely distributed, and the average recall, precision, and F1 score were 89%, 77%, and 83%, respectively, which represented decreases by 6%, 14%, and 10%, respectively. Atmospheric correction did not provide additional information that could supplement the results based on the DN, but instead resulted in more mis-extraction and losing results.
Taking Case 3 as an example, Figure 12 shows the difference between the impervious surface distribution extracted before and after atmospheric correction, where (a) is a false colour composite of the (5, 4, 3) band and (b) is an RGB composite of the impervious surface distribution extracted before atmospheric correction, ground truth for the impervious surface distribution and the impervious surface distribution extracted after atmospheric correction. Here, the white areas were extracted in both instances, the green areas were lost in both instances, the purple areas were misextracted in both instances, the yellow areas were lost after atmospheric correction, and the blue areas were only mis-extracted after atmospheric correction. Atmospheric correction did not provide additional information that could supplement the results based on the DN, but instead resulted in more mis-extraction and losing results.
Taking Case 3 as an example, Figure 12 shows the difference between the impervious surface distribution extracted before and after atmospheric correction, where (a) is a false colour composite of the (5, 4, 3) band and (b) is an RGB composite of the impervious surface distribution extracted before atmospheric correction, ground truth for the impervious surface distribution and the impervious surface distribution extracted after atmospheric correction. Here, the white areas were extracted in both instances, the green areas were lost in both instances, the purple areas were mis-extracted in both instances, the yellow areas were lost after atmospheric correction, and the blue areas were only mis-extracted after atmospheric correction.
Actually, atmospheric correction using an atmospheric correction model is not always necessary and may decrease the accuracy of the extraction of remote sensing information [41]. With respect to our three case images, atmospheric correction did not help to improve the accuracy of the extraction of impervious surface distribution. of the (5,4,3) band and (b) is an RGB composite of the impervious surface distribution extracted before atmospheric correction, ground truth for the impervious surface distribution and the impervious surface distribution extracted after atmospheric correction. Here, the white areas were extracted in both instances, the green areas were lost in both instances, the purple areas were misextracted in both instances, the yellow areas were lost after atmospheric correction, and the blue areas were only mis-extracted after atmospheric correction.

Alternatives to the Coastal Band
There is no coastal band in other Landsat imagery, which may influence the applicability of the proposed method. Here, we compare and discuss the differences that occur if impervious surface distribution is extracted using the blue band instead of the coastal band.
The differences between the values for typical samples of impervious surfaces and other ground objects of the ratio of the coastal band to the NDVI (coastal band/NDVI) and the ratio of the blue band to the NDVI (blue band/NDVI) were calculated, as shown in Figure 13. We can see that if the blue band/NDVI is used, the difference between impervious surfaces and other ground objects decreases slightly. Actually, atmospheric correction using an atmospheric correction model is not always necessary and may decrease the accuracy of the extraction of remote sensing information [41]. With respect to our three case images, atmospheric correction did not help to improve the accuracy of the extraction of impervious surface distribution.

Alternatives to the Coastal Band
There is no coastal band in other Landsat imagery, which may influence the applicability of the proposed method. Here, we compare and discuss the differences that occur if impervious surface distribution is extracted using the blue band instead of the coastal band.
The differences between the values for typical samples of impervious surfaces and other ground objects of the ratio of the coastal band to the NDVI (coastal band/NDVI) and the ratio of the blue band to the NDVI (blue band/NDVI) were calculated, as shown in Figure 13. We can see that if the blue band/NDVI is used, the difference between impervious surfaces and other ground objects decreases slightly. The coastal band was replaced with the blue band, and the other parameters were the same as those used in the previous workflow to extract the impervious surface distribution from the above three case images. We also determined the accuracy and found that the average recall, precision, and F1 score were 93%, 87%, and 90%, respectively, which represented decreases by 2%, 4%, and 3%, respectively.
Therefore, it is feasible to use the blue band to extract impervious surface distribution from other Landsat remote sensing images without using the coastal band, albeit with a certain decrease in accuracy.
In contrast to validation using images for a single region and season [7][8][9][10], our study used three images obtained in summer and winter. The RISI exhibited higher accuracy and better applicability than the other methods used for comparison, and it avoids the additional feature selection and classifier selection processes used in classification methods.

Conclusions
This study proposed a novel index, namely, the RISI, for extracting impervious surface The coastal band was replaced with the blue band, and the other parameters were the same as those used in the previous workflow to extract the impervious surface distribution from the above three case images. We also determined the accuracy and found that the average recall, precision, and F1 score were 93%, 87%, and 90%, respectively, which represented decreases by 2%, 4%, and 3%, respectively. Therefore, it is feasible to use the blue band to extract impervious surface distribution from other Landsat remote sensing images without using the coastal band, albeit with a certain decrease in accuracy.
In contrast to validation using images for a single region and season [7][8][9][10], our study used three images obtained in summer and winter. The RISI exhibited higher accuracy and better applicability than the other methods used for comparison, and it avoids the additional feature selection and classifier selection processes used in classification methods.

Conclusions
This study proposed a novel index, namely, the RISI, for extracting impervious surface distribution from Landsat 8 imagery and validated it using three images covering urban areas of China in winter and summer. The results of the extraction were compared with those obtained using the NDBI, IBI, NDISI, NDII, and CBI. The main conclusions are as follows: (1) The RISI effectively distinguishes impervious surfaces from other ground objects, especially bare soil, and gives higher recalls, precisions, and F1 scores, of which the average values for the three case images were 95%, 91%, and 93%, respectively. The validation confirmed the robustness of the RISI.
(2) The use of the coastal band after a 0-1 transformation can further increase the difference between impervious surfaces and bare soil.
(3) The workflow has been shown to have good applicability in the extraction of impervious surface distribution from Landsat imagery.
It is still necessary to perform validation using more images with complex compositions and distributions of ground objects to refine the workflow so that it suits more situations.