2.1.

Study Area

The Dianchi and Erhai Basins were selected as study areas. The Dianchi Basin is positioned at 24°28′13″ to 25°27′26″ N and 102°29′14″ to 103°00′51″ E, covering a total area of $2843.16{\mathrm{km}}^2$ and situated at elevations of 1652 to 2812 m [Fig. 1(d)]. It is located within the Yunnan-Guizhou Plateau, which is mainly characterized by Karst plateau landscapes and red mountain original geomorphology. Annual average temperature and rainfall levels reach roughly 16.5°C and 1031 mm, respectively. The Dianchi Basin covers the Wuhua, Guandu, Xishan, Chenggong, and Panlong districts of the city of Kunming, which form the city’s main areas of economic activity. Located southwest of Kunming, Dianchi Lake is the sixth-largest freshwater lake in China and the largest highland lake in Yunnan Province. The lake is an icon of the city of Kunming.

Fig. 1

Location map of the study areas: (a) Erhai Basin, (b) China’s Territory, (c) Yunnan Province, and (d) Dianchi Basin.

The Erhai Basin is positioned at 25°25′49″ to 26°25′55″ N and 99°49′56″ to 100°26′50″ E, covers a total area of $2608.73{\mathrm{km}}^2$, and is positioned at an elevation of 1847 to 4081 m [Fig. 1(a)]. The climate of the Erhai Basin is that of a typical plateau continental climate with distinct wet and dry seasons, with a rainy season running from May to October and a dry season running from November to April. Annual average temperature and rainfall levels reach 15.1°C and 1048 mm, respectively.³⁷

2.2.

Data Source

As our main data source, we used Landsat operational land imager (OLI) images of the study area downloaded from the official U.S. geological survey (USGS) website. In the interest of obtaining quality analysis results, remote sensing images used were cloud-free or included few clouds. Their acquisition dates, spectral bands, spatial resolutions, and radiation calibration parameters are shown in Table 1.

Table 1

Experimental data collection.

3.1.

Spectral Curves of Different Land Use Types

3.1.1.

Land use classification

Land use cover refers to the combination of natural foundations and surface elements covered by man-made structures, including vegetation, soil, lakes, wetlands, and various buildings with specific temporal and spatial attributes. In this study, we examine the geomorphic patterns of our study area and land uses are divided into eight categories: bright ISs, dark ISs, bare soil, arid land, forest, water, grass, and shaded surfaces. Here, the arid land class includes gravel land, bare rock, and stone desert land. The grass class includes urban green belts, lawns, and farmland with vegetation.

Support vector machines (SVMs), known as maximum-margin classifiers based on the structural risk minimization principle of statistical learning theory,^38,39 are nonparametric statistical learning methods that have recently been used in numerous applications of image processing.⁴⁰ Mustafa Ustuner and B. DIXON’s research^38,41 shows that SVMs can quickly accomplish high levels of classification accuracy with a small number of training datasets and are simple to apply. SVM was applied using environment for visualizing images (ENVI) software. Using ENVI version 5.1, we used a large number of training datasets for Landsat OLI images of a study area with eight categories of land use, and classification was performed using SVM classifiers.

To well obtain spectral information of different objects from images, we need to generate some spatial coverage samples⁴² that are uniformly distributed throughout the study area. Webster and Oliver⁴³ provided a rule of thumb that 150 to 225 points might often be satisfactory for a variogram computed of isotropic variables in a normal distribution. In the SVMs classification results, the surface was divided into eight categories, so it needed at least 1200 to 1800 points. In addition, considering that some categories had fewer points and the cost saving. Therefore, 2000 samples were generated in this study, and they uniformly distributed in the study areas.

Taking the Dianchi Basin as an example. Using the “sp” and “spcosa” packages^42,44 under R version 3.4.4, the study area was divided into 2000 strata through multiple iterations (partitioning a spatial object into compact strata by means of $k$-mean), and the mean squared shortest distance of the strata was measured as $247868.2{\mathrm{m}}^2$. Corresponding to strata, we generated 2000 sampling points from the center and used attributes of the SVMs classification image, and thus, the 2000 sampling points were set as the land use prediction points for the study area. After checking the original and high-resolution images, the overall classification accuracy level was measured at 89.90% with 202 of 2000 prediction points being error points classified under incorrect categories (Table 2). We corrected the classification used for error points and obtained 2000 classification points. These can be considered verification points (Fig. 2).

Table 2

The error matrix of SVM classification.

Count	Arid land	Bare soil	Bright IS	Dark IS	Forest	Grass	Shade	Water	User’s accuracy (%)
Arid land	314	2	7	7	9	3	1	0	91.55
Bare soil	7	91	11	2	4	3	0	0	77.12
Bright IS	2	5	236	15	0	1	0	0	91.12
Dark IS	9	9	3	132	3	4	1	0	81.99
Forest	23	1	0	5	507	4	1	0	93.72
Grass	11	5	8	10	6	236	0	1	85.20
Shade	1	0	0	0	3	0	57	2	90.48
Water	0	4	0	4	1	3	1	225	94.54
Producer’s accuracy (%)	85.56	77.78	89.06	75.43	95.12	92.91	93.44	98.68

Fig. 2

Land use classification of the Landsat-8 image acquired on March 14, 2017. The first column is the true color display, the second column denotes the SVMs classification results, and the last column represents the 2000 land-use classification points.

3.1.2.

Spectral curves of radiance and reflectance

Due to varying environmental conditions, the characteristics of radiated and reflected electromagnetic waves differ in wavelength. These are usually expressed as curves in a two-dimensional (2-D) geometric space. An abscissa denotes the wavelength (or band number), whereas an ordinate denotes the reflectance (or pixel value), which is called the spectral curve. Using the land-use classification data shown in Sec. 3.1.1, spectral curves of the radiance and surface reflectance were obtained from the images. Figure 3 shows the spectral curves for the Dianchi Basin.

Fig. 3

Spectral curves of the radiance and surface reflectance of the Dianchi Basin obtained from Landsat-OLI images. The image was acquired on March 14, 2017, when the solar elevation angle was 53.325 degrees and when the sun azimuth was 133.892 degrees.

Along the spectral curve shown in Fig. 3, the bright IS presents high values in each band, and waterbodies and shaded surfaces present relatively low values in each band. The spectral curve of the dark IS is similar to that of the bright IS, although the IS presents a correspondingly lower value.

3.2.

Enhanced Normalized Difference Impervious Surfaces index

From the pixel spectral curves analysis shown in Sec. 3.1.2, we found differences between ISs and natural surfaces in partial band variations. First, bright and dark ISs present stronger reflectivity levels in the blue and coastal bands, whereas the reflectance values for water, vegetation, bare soil, arid land, and shaded surfaces are clearly lower than those of IS. Second, reflectance values for vegetation, bare soil, arid land, and shaded surfaces measured from the SWIR-1 band to the SWIR-2 band are quite low, whereas ISs maintain higher reflectance values with less change. Third, due to the strong effects of water vapor on the coastal band, we selected the blue band as an IS enhancement factor. To amplify the difference between ISs and natural surfaces, we selected the ratio of the SWIR-1 band to the SWIR-2 band and the MNDWI as the inhibitors. Finally, to obtain an index value of $-1$ to 1, the inhibited factor was multiplied by $\alpha$. Thus, the ENDISI is written from Eq. (1):

3.3.

Automatic Threshold Selection Based on the Generalized Gaussian Model

The Kittler Illingworth (KI) threshold selection criterion assumes that observations are derived from a mixture of two normal distributions with respective means, variances, and proportions.^45,46 The criterion has been adapted to use GG distributions.⁴⁶ The optimization threshold $T$ can be calculated from the cost function $J(T)$ in the KI algorithm:

3.4.

Other Impervious Surface Indices

To assess the performance of the ENDISI, three other indices, the NDBI, MNDISI, and CBCI were employed to conduct a comparative analysis. The equations of these three indices are as follows:

4.1.

ENDISI Results

Using the ENDISI algorithm shown in Sec. 3.2, we obtained an ENDISI image of the Dianchi and Erhai Basins. Values range from $-0.95$ to 0.77 and $-0.98$ to 0.75, respectively. Due to 2% grayscale applied, image stretching can remove most outliers and show better results. We applied a 2% grayscale stretch to the ENDISI (2% and 98% of the ENDISI value). ENDISI values for the Dianchi and Erhai Basins range from $-0.57$ to 0.11 and $-0.57$ to 0.12, respectively, as shown in Figs. 4 and 5, respectively.

Fig. 4

ENDISI data for ISs of the Dianchi Basin. Three example subsets (a)–(c) are shown in the first and second columns of each line. The first column shows the true color display; the second column illustrates the ENDISI of the example subset; and the last column represents the ENDISI for the whole area.

Fig. 5

ENDISI data for ISs of the Erhai Basin. Three example subsets (a)–(c) are shown in the first and second columns of each line. The first column shows the true color display, the second column illustrates the ENDISI of the subset, and the last column represents the ENDISI for the whole area.

The ENDISI algorithm can suppress the effects of arid land, bare rock, and bare soil on IS extraction and can reveal information about ISs. The ENDISI results show that the values for waterbodies, shaded surfaces, and forest are very low, most of which fall below $-0.25$. Bright and dark ISA present higher ENDISI values in plateau basins, and they can be separated from bare soil and arid land areas. It is easy to observe the spatial distribution of ENDISI, with high ENDISI values concentrated in major urban areas and at airports, whereas the low ENDISI values mainly found throughout plateau lakes (Dianchi Lake and Erhai Lake) and along the borders of basins. We must add that as the reflectance of snow is very high, the numerous snowy surfaces located on the mountain summit positioned in the lower left corner of Fig. 5(III) present a high ENDISI value.

4.2.

Statistical Analysis

To further examine the ENDISI’s capacity to distinguish between land covers, we calculated the ENDISI values for the 2000 land use classification points corrected in Sec. 3.1.1. A statistical analysis of the ENDISI value distributions found for various land use categories was in turn conducted (Fig. 6).

Fig. 6

The distribution of ENDISI values for different land covers. (a) the ENDISI distribution for the Dianchi Basin and (b) the ENDISI distribution for the Erhai Basin.

The statistical results show that bright and dark ISs present high values, whereas waterbodies, shaded surfaces, forested land, and arid areas present lower values. Most bare soil areas present lower ENDISI values than ISs, and only a small portion of bare soil areas present ENDISI values that overlap with those of dark ISs. In addition, some farmland areas present ENDISI values that overlaps with those of IS areas. Local farmers have built many translucent artificial greenhouses on farmland, which has enhanced surface reflectance levels and thus affected ENDISI values.

4.3.

Automatic Threshold Selection

Threshold selection is central to ISA mapping, as it directly affects the accuracy of ISA mapping. Previous methods involve manually selecting a threshold through continuous debugging. This is not only time consuming but is also affected by human interference, often causing the thresholds of different images to vary. To address the above problems, we adopt an automatic threshold selection method that uses the minimum error threshold method as a constraint to enable automatic, rapid, and efficient selection over a relatively optimal threshold.

Figure 7 shows the automatic threshold selection process used for ENDISIs of the Dianchi [Fig. 7(a)] and Erhai Basins [Fig. 7(b)]. The KI threshold selection criterion based on the GG model proved to be effective in this experiment. Automatic thresholds applied in the ENDISI histogram of the Dianchi and Erhai Basins are measured at $-0.16$ and $-0.09$, respectively.

Fig. 7

Automatic threshold selection (T) applied to the ENDISI histogram of the Dianchi and Erhai Basins: (a) the automatic threshold is set to $-0.16$ for the Dianchi Basin and (b) the automatic threshold is set to $-0.09$ for the Erhai Basin.

4.4.

Accuracy Assessment

4.4.1.

Separation of ISs and PSs

We reclassified the 2000 classification points corrected in Sec. 3.1.1. The classification points are divided into IS and PS categories and are used as verification samples. The ISs contain bright ISs and dark ISs, and the PSs include natural surfaces such as bare soil, arid land, forested land, waterbodies, grassland, and shaded surfaces (as shown in Table 3). Figure 8 shows ENDISI histograms for IS and PS samples for the Dianchi [Fig. 8(a)] and Erhai Basins [Fig. 8(b)]. Visually, ISs and PSs present respective distributions and GG distributions of two different shape parameters. Although some overlapping ENDISI values between IS and PS are observed, the ENDISI separates ISs and PSs quite well.

Table 3

The accuracy and verification points of each class.

	Impervious surface		Pervious surface
	Bright IS	Dark IS	Arid land	Bare soil	Forest	Grass	Shade	Water
Producer’s accuracy (%)	89.06	75.43	85.56	77.78	95.12	92.91	93.44	98.68
User’s accuracy (%)	91.12	81.99	91.55	77.12	93.72	85.20	90.48	94.54
Verification points	265	175	367	117	533	254	61	228

Fig. 8

IS and PS histograms and SDI values of the ENDISI: (a) for the Dianchi Basin and (b) for the Erhai Basin.

The spectral discrimination index (SDI) can distinguish between two groups of data and can quantify a histogram’s separation with higher SDI values denoting more separable results.⁵⁰ For more detailed information on the SDI, please see Sun et al.¹⁶ and Pereira et al.⁵¹ From the verification samples, ENDISI SDI values were calculated via ISA extraction. ENDISI SDI values from the Dianchi and Erhai Basins were measured at 1.499 and 1.783, respectively.

4.4.2.

Overall accuracy

From our verification samples, an accuracy assessment was conducted using the error matrix approach.⁵² Here, the overall accuracy and overall kappa coefficient of the ENDISI were calculated for any given threshold ($\text{step}=0.01$). For the Dianchi Basin, the optimal threshold is $-0.16$ with 93.95% overall accuracy and 82.47% kappa coefficient. For the Erhai Basin, the optimal threshold is $-0.07$ with an overall accuracy level and kappa coefficient of 98.90% and 93.21%, respectively. At each given threshold, the overall accuracy and kappa coefficient values are shown in Fig. 9.

Fig. 9

Overall accuracy and kappa coefficient curves of the ENDISI: (a) for the Dianchi Basin and (b) for the Erhai Basin. Optimal (black line) and automated thresholds (red line) are marked in each histogram. For the Dianchi Basin, the automated threshold is equal to the optimal threshold ($-0.16$) with 93.95% overall accuracy and a kappa coefficient of 82.47%. For the Erhai Basin, the automated threshold is $-0.09$ and the overall accuracy level and kappa coefficient are valued at 98.50% and 91.02%, respectively.

4.5.

Comparative Analyses with Other Indices

Taking the Dianchi Basin as an example, NDBI (replacing ${\rho }_{\mathrm{SWIR}1}$ with ${\rho }_{\mathrm{SWIR}2}$ in the NDBI equation), MNDISI, and CBCI images were obtained using the equations shown in Sec. 3.4. Figure 10 shows the distribution of three indices for different land covers. Bare soil and arid land surfaces are the main interference sources of the three algorithms. Especially in MNDISI, the average values of bare soil and arid land surfaces are larger than bright IS and dark IS, which directly affect the mapping efficiency of MNDISI. Compared with MNDISI, NDBI, and CBCI can better resist the impact of vegetation information (forest and grass surfaces).

Fig. 10

The distribution of three indices for different land covers: (a) the NDBI distribution, (b) the MNDISI distribution, and (c) the CBCI distribution.

The SDI value indicates the separability between ISs and pervious surface. Among the four ISA extraction algorithms, ENDISI has the highest overall accuracy and SDI value (Table 4), reaching 93.95% and 1.499, respectively. Moreover, the relatively high SDI value (0.906) of the NDBI was also lower than that of the ENDISI, which was supported by the small overlaps of the histograms between the ISs and pervious surfaces [Fig. 11(a)]. Additionally, the histograms of MNDISI between the ISs and pervious surfaces displayed obvious overlaps [Fig. 11(b)], which was supported by a relatively low score of the SDI value (0.498). As shown in Fig. 10(c), some water bodies present CBCI values that overlap with those of IS areas, which was supported by a relatively low SDI value (0.705).

Table 4

The SDI value and overall accuracy of each index.

Fig. 11

IS and PS histograms of three indices: (a) the NDBI, (b) the MNDISI, and (c) the CBCI.

4.6.

ISA Mapping of ENDISI

Figures 12 and 13 show detailed ISA distributions for the Dianchi and Erhai Basins. To better observe the effects of IS extraction, we examine images of subregions and compare them with high-resolution images. The overall accuracy values derived from IS extraction applied to the study areas are $>93.9\%$, streets and houses are well separated from the background, and almost all bare soil and arid land areas are divided into PSs. In airports [Fig. 12(a)], residential areas [Fig. 13(c)], suburban areas [Figs. 12(b)], and rural areas [Figs. 12(c), 13(a), and 13(b)], building clusters, and streets are clearly defined. In dense urban areas [Fig. 13(c)], almost all pixels are classified as ISs with the exception of a few vegetation-covered areas. Additionally, there are some large areas of sand factories in Fig. 12(c), lots of sand and gravel have been accumulated on the ground. Because they are the main raw materials for ISs, the factory areas are also classified as ISs.

Fig. 12

ISA distributions for the Dianchi Basin. Three example subsets (a)–(c) are shown in the first and second columns of each line. The first column shows high-resolution images, the second column illustrates ISA distributions of the subset, and the last column represents ISA distributions for the whole area.

Fig. 13

ISA distributions for the Erhai Basin. Three example subsets (a)–(c) are shown in the first and second columns of each line. The first column shows the high-resolution images, the second column illustrates the ISA distributions of the subset, and the last column represents ISA distributions for the whole area.

4.7.

ENDISI for Landsa-TM/ETM Imagery

The ENDISI can be well applied to Landsat-TM or ETM images. With the automatic threshold extraction algorithm in Sec. 3.3, we can get the ISA distribution map quickly. Meanwhile, Figs. 14 and 15 were the consequences of ENDISI extraction with Landsat TM and ETM images as data sources, respectively.

Fig. 14

ENDISI data for ISs of the Landsat-TM image acquired on April 06, 2008 (in Dianchi basin). Three example subsets (a)–(c) are shown in each line. The first column shows the true color display, the second column denotes the ENDISI (with a 2% grayscale stretch) of the example subset, and the last column represents the ISA distributions of the subset.

Fig. 15

ENDISI data for ISs of the Landsat-ETM image acquired on June 14, 2001 (in Dianchi basin). Three example subsets (a)–(c) are shown in each line. The first column shows the true color display, the second column denotes the ENDISI (with a 2% grayscale stretch) of the example subset, and the last column represents the ISA distributions of the subset.

The experimental results illustrate that the ENDISI can well distinguish the bare soil and the arid land from the IS in the Landsat TM and ETM images, which overcomes the effect of the bare soil and arid land elegantly [Figs. 14(a) and 15(a)]. For one thing, in high ISA, the ENDISI can well differentiate buildings, airports, streets, and other man-made structures from natural surfaces [Figs. 14(b) and 15(b)]. For another, in low IS density areas, the ENDISI can extract the main roads and villages from the images [Figs. 14(c) and 15(c)]. However, owing to low spatial resolution and mixed pixel images, some narrow roads and mud roads in the study area were divided into pervious surfaces [Figs. 14(a) and 15(a)]. Generally speaking, the ENDISI can achieve good IS extraction effect on Landsat series images.