Balancing Land Surface’s Brightness-Shadowing and Spectral Reflectance to Enhance the Discrimination of Built-up Footprint from Surrounding Noise

Recent evolutions of the geospatial technologies are more accurate in mapping and monitoring land use land cover, LULC, in different environments and at different spatial scales. However, some urban applications keep facing issues such as misclassification and other noise in unplanned cities with disorganized built-up and mixed housing material, and surrounded by a composed biophysical environment. This paper reports the processing leading to a new spectral index, that balances the land surface brightness temperature and spectral reflectance to accurately extract the built-up. The namely Brightness Adjusted Built-up Index, BABI, is proposed as a weighted ratio of Landsat OLI-TIRS bands. The methodology is based on a multi-perceptron layers, MLP, regression between a classified image and individually classified red, SWIR1, SWIR2 and TIR bands reclassified “1 = built-up; 0 = Non-Built-up”, with an average r 2 =0.78. The same way, a linear regression of popular built-up spectral indices such as Normalized Difference Built-up Index, NDBI, and Urban Index, UI, or recently proposed Modified New Built-up Index, MNBI, and Normalized Difference Built-up and Surroundings Unmixing Index, NDBSUI, on one hand, by light-dark spectral indices such as, Normalized Difference Soil Index, NDSI, Bare Soil Index, BSI, and Shadow index on the other hand, stands for the natural environment noise assessment in and around the built-up, with an r 2 =0.75. The MLP r 2 standing for the built-up information, is rounded to 0.8 and according to their rank in the process, the weights allotted are 0.2, 0.4 and 0.8 in the numerator, and inversely 0.8, 0.6 and 0.2 in the denominator, to the red, SWIR1 and SWIR2 bands respectively. Whereas, the simple linear regression r 2 standing for the noise is used to weigh the brightness temperature, TB in the numerator and subtracted from the previous group. The value 0.001 multiplies the whole ratio to lower the decimals of the outputs for an easy interpretation. As results, on the floating images scaled [0-1], built-up values are ≥0.1 in Yaoundé (Cameroon) and ≥0.07 in Bangui (Central African Republic). The overall accuracies are 96% in Yaoundé and 98.5% in Bangui, with corresponding kappa coefficients of 0.94 and 0.97. These scores are better than those of the NDBI, UI, MNBI and NDBSUI. 2 Alfred Homere Ngandam Mfondoum et al.: Balancing Land Surface’s Brightness-Shadowing and Spectral Reflectance to Enhance the Discrimination of Built-up Footprint from Surrounding Noise


Background, Problem Statement and Study Area
Nowadays, the satellite imagery is a powerful and reliable tool to assess the global urban footprint [1]. One set of useful techniques include the image classification according to different algorithms [2][3][4][5]. These methods consider the shape, the size, the context as well as the spectral content, and are consequently important when the satellite image used has a very high resolution (VHR) [5]. Besides, the use of spectral indices has also been successful in mapping the built-up and urban impervious area with high accuracies. Pillar ones are the urban index, UI, [6] and the normalized difference built-up index, NDBI [7], that respectively enable the residential areas and the human settlements automatic mapping using simple ratios between two spectral channels. They were followed by several other spectral indices giving similar or higher accuracies depending on the test area [8][9][10][11][12][13][14][15][16][17][18][19].
However, these applications are enough challenging in the rapid and unplanned urbanization context of many developing countries. Amongst several reasons, one can mention the extent of slums built with recovery materials (plastics, sheet metal, etc.) inside cities and along asphalted or dusty roads, as well as suburbanization that blurs the limits of modern built-up and craft made housing. It has been noticed that the pixel combinations in areas with heterogenic objects [13,22,23] causes high rate of uncertainties and biases [9,[23][24][25]. Moreover, spectral signatures of impervious surface areas are similar to those of dry soils [10,11], whereas detecting surface water is a challenge in regard of its confusion with buildings' shadowing [24].
For illustration, some of these applications were tested in sub-Saharan Africa, specifically the urbanized areas of Yaoundé (Cameroon) and Bangui (Central African Republic) ( Figure 1). These cities have a common urban mixed structure, i.e., planned and unplanned build area. Their natural surroundings also have some similarities such as internal forest, gardens, savannahs or shrubs for vegetation, lakes, streams, or swamps for water bodies, rocky, dusty or sandy bare soils, and rough or mountainous terrain, which are spectrally noisy for the built-up extraction ( Figure 2). On the Landsat 8 subsets extracted for the study, vegetation and built-up are dominant in Yaoundé, while bare soils, rough terrain and water bodies are added to the two previous land cover classes in Bangui ( Figures 1&3).  On one hand, the combination of these conditions at different levels usually impact the discrimination of built-up from the other land cover features as noticed on the patterns of the NDBI [7] and the Normalized Difference Impervious Surface Index, NDISI [10] (Figure 3). Thus, although their original goals are the urban built-up mapping, the NDISI inverts the visual patterns of NDBI by highlighting dark impervious surfaces and water bodies.
On the other hand, the high values of land surface temperature, LST, are a mix of built-up and bare soils trends in the two sites. For the case of Bangui, several built-up hot spots even record medium to low LST values ( Figure 3). Fundamentally, the land surface temperature, LST, enables the mapping of urban heat islands (UHIs) [20,21]. However, it is highly influenced in its interactions with the climate, by the land features distribution [25][26][27][28][29].  (Table 1).  [30], and normalized difference soil index, NDSI [31].

Previous Experimentations
To address these issues, we recently experimented two new indices based on spectral bands arithmetic and they have been successfully applied in six different cities of Cameroon. The first one is the modified New Built-up Index, MNBI, to enhance the built-up extraction and analyse the spatiotemporal urban metabolism of Foumban (West-Cameroon) [32]. It uses the Landsat 8 images and enhances the NBI [8] results, by using the following algorithm: * 0 * 1 2 2 1 [32] Where, * and Surroundings Unmixing Index, NDBSUI, to automate the built-up extraction in five different biophysical environments [33]. Its detailed goal has been to extract the built-up features and interweave its spectral signal from surrounding noise. Therefore, still using the Landsat 8 image to, the algorithm was proposed as follows: On Landsat 8 satellite images of 2019, the outcomes view was better and the overall accuracies higher than comparative indices, i.e., OA=95.5% (KC=0.90) in the main study area of Yaoundé (humid forest). In the validation sites, they were the following: Yokadouma (humid forest) OA=98.9% (KC=0.88); Kumba (humid Mountainous forest) OA=97.5% (KC=0.94); Foumban (highlands savannah) OA=97.06% (KC=0.92); Ngaoundéré (high guinea savannah) OA=95.3% (KC=0.89); Garoua (sudano-sahelian shrubs) OA=74.86% (KC=0.42).
As a continuum, this research focuses on reducing the noise created by the land surface brightness and shadowing, while mapping built-up. The goal is to improve the accuracy of built-up extraction, while inhibiting the reflectance of natural features (vegetation, bare soil, water body) as well as buildings shadows, dark paved (asphalts) or unpaved (dusty/muddy) roads.

Satellite Images Acquisition
The satellite images of Landsat operational land imager and thermal infrared sensor, OLI-TIRS, were downloaded for the dry season (Table 2), from the website of United States Geological Survey (USGS). This phenological season is responsible of the highest level of soil bareness and rough terrain brightness/shadowiness around and in between the buildings, highlighting the issue of the land cover object confusions to be solved. Some visible and thermal infrared bands were used (Table 3). Both scenes were first pre-processed for atmospheric correction, conversion to radiance, and then to at-sensor reflectance for OLI bands using the LOW-COST model [37], and to brightness temperature for the thermal infrared band 10 following the steps proposed by references [38,39].

Spectral Measures
Based on 100 to 200 pixels sampled 40 at least at a time, spectral signatures of built-up, vegetation, bare soil and water body have been plotted and assessed. As shown in figure 5, SWIR1 and SWIR2 bands give the highest reflectance for built-up that stands in this study for the bright impervious surfaces. However, vegetation, soil and water reflectance are closer to the built-up in the SWIR1 (Vegetation= [16][17][18] Figure 5). The difference of reflectance between the built-up and other features is 6%, 3% and 6% for vegetation, soil and water in the SWIR2, versus 3%, 3% and 6% in the SWIR1 for the same order of appearance. The same way, the TIR band shows an increasing (in Yaoundé) or decreasing (in Bangui) trend of these features, emphasizing the questioning about its ability for built-up detection. As a reminder, reference [40] experienced that Landsat 8 images in-band and out-of-band measured spectral response for vegetation and soil, shows a lack of spectral uniformity between the radiance of the red, SWIR1 and SWIR2 bands. Indeed, the maximum and average radiance of soil is uniform, constant and continued in the red and SWIR1 bands, while it records the highest discontinuity in the SWIR2, then explaining the difference of reflectance previously mentioned.
In addition, recent studies noticed that the thermal infrared data is able to support the processing separating water bodies from impervious surfaces, yielding an identifiable temperature difference between them [41]. Whereas it was pointed out that bare soil has spectral response patterns highly similar to high-albedo (HA) impervious surfaces that is obtain by using TIR band [42,43]. Reflectance to Enhance the Discrimination of Built-up Footprint from Surrounding Noise

Built-up Information in Spectral Bands and the First Experimental Assumption
Two complementary regressions are performed to predict the informational rate of built-up features. The first one uses the Multi-Layer Perceptron, MLP. It is a class of feed forward artificial neural network, ANN, that is known as a connected network of processing units that are modelled on the most basic properties of the neurons in the human brain and has been satisfactorily used in several fields of research including remote sensing [44,45]. MLP utilizes a supervised learning technique called backpropagation for training [46]. Its multiple layers and non-linear activation distinguish MLP from a linear perceptron. In addition, it performs a non-parametric regression analysis between input variables and one dependent variable with the output containing one output neuron, i.e., the predicted memberships. For this later method, the values of the output predicted image is the activation level of the output layer node scaled to the original data range, which is expressed as follows: Where ? symbolizes the activation function, C and = are the weights and the biases. Using the K-means processing, an unsupervised classification was performed for the stacked image and for the individual bands red, SWIR1, SWIR2 and TIR. The results were converted in 2bits (binary), with 1 for the built-up and 0 for the other classes. Then, a MLP network ( Figure 6) logistic sigmoidal regression was implemented, inputting the classified individual bands as independent variables and the classified stacked image as dependent variable. Using an automatic training process, a total of 1000 pixels were defined for the learning, i.e., 500 for training and 500 for the testing, for a processing cycle of 1000 iterations (Figure 7). In Yaoundé, the . 1 of the model is 0.84 versus 0.73 for Bangui (Table 4). When assessing the sensitivity of the model, the constancy of the . 1 identifies the red band as ‵least influential′ with 0.84, and the SWIR2 as ‵most influential′ with 0.48 in Yaoundé, and in the same order, the values recorded in Bangui are 0.72 and 0.012 (Figure 7&Table 5).
The second set of regressions are the simple linear ones. Their trends confirm the presence of built-up features in each classified band, with the highest . 1 for the SWIR2, i.e., 0.84 in Yaoundé and 0.8 in Bangui, and the lowest ones for the TIR, i.e., respectively 0.75 and 0.47 in the same order. (Figure 8).    From the observations above, the first assumption is stated as follows: i) ratio of the predicted built-up information over the predicted noise might be able to extract at best the built-up features. The . 1 values resulting from the MLP model regression and the ordering of the variables resulting from the analysis of the sensitivity model are favourable to the respective decreasing weighing SWIR2, SWIR1, TIR and Red to influence the built-up extraction.
Then remains to determine the type and predict the level of noise, as well as its influence in the discrimination of built-up features. This infers their spectral and statistical relations.

Noise Prediction and the Second Experimental Assumption
Noise can be categorized as brighter and darker bodies, in and around the built-up. To assess its influence, the most accurate bare soil index, BSI [30] for Bangui and NDSI [31] for Yaoundé, and the shadow index [36] are each regressed by four urban/built-up, spectral indices, i.e., UI [6], NDBI [7], Reflectance to Enhance the Discrimination of Built-up Footprint from Surrounding Noise MNBI [32] and NDBSUI [33]. These regressions are positive with the BSI/NDSI and negative with the shadow index. The average correlation coefficient . 1 are 0.74 for both bright and dark noise on the two study sites (Table 6). It can be noticed that in Yaoundé, the bright noise (NDSI) is more effective with . 1 of 0.8 versus -0.68 for the dark noise (SI). While in Bangui, these . 1 record a slight difference, with respectively 0.75 (BSI) and -0.73 (SI).
The second assumption at this point is the following: ii) the average . 1 values resulting from the linear regression between NDSI/BSI and SI can be used to weigh T B , and then subtracted from the sum of weighted red, SWIR1 and SWIR2 bands. This should result in isolating surrounding noise, whilst enhancing the built-up detection and discrimination.

Summative Processing-the Brightness Adjusted Built-up Index, BABI
The outflow of preparatory processing above is an algorithm expressed as a ratio. The weights are affected differently at the numerator and the denominator. The average . 1 of the two sites resulting from the MLP model, i.e., 0.78 rounded to 0.8, is used to deduct a weight (w) for each visible band, exempting the TIR that is assumed still noisy. Therefore, to fill the gap in ranks and values caused by the previous assumption, for the numerator, the average . 1 is divided by 4 for red band (‵least influential variable′; w=0.18≈0.2), by 2 for the SWIR1 (w=0.39≈0.4), and by 1 for the SWIR2 (‵most influential variable′; w=0.78≈0.8). These weights are the estimated quantity of built-up information in the considered band.
The inverse and compensatory weights are used in the denominator, such as 0.8, 0.6 and 0.2 for red, SWIR1 and SWIR2 bands respectively. These weighs stand for the quantity of noise in each band.
Concerning the T B , its weights were given such as 0.74≈0.75 in the numerator and 1 in the denominator. The first weight is the predicted noise and the second weight stands for the entire information in the T B .
In this form, the difference of weights between numerator and denominator as well as the usual high values of the T B will induce high number of decimals that will be at the nearest thousandth. Therefore, an E value, 0.001, is introduced as a factor of the whole above operations to ease the results' interpretation.
From the above process, the Brightness Adjusted Built-up Index, BABI, is generated as a weighted ratio in the following formula:  For a background analysis, the Jenks natural breaks were used as automatic classifier. This method helps to reduce variance within groups and maximize variance between groups. Four natural breaks were applied on the raw floating results (Figure 10), and the thresholds for built-up features are ≥ 0.18 for Yaoundé and ≥ 0.074 for Bangui. Similar steps were used after the images were rescaled [0-1], thresholding the built-up extraction at ≥ 0.1 in Yaoundé and ≥ 0.075 in Bangui (Figures 9 &10). This distribution of values reduces the built-up features generalization with satisfactory visual appraisal when compared with classification and other spectral indices (Figure 9).

Built-up Extraction Efficiency
One important point is about the compensatory effects between sub-information and over-information. For instance, when using the class separability matrix detailed in table 7, the classification in both sites presents confusion between bare soils and built-up classes. Thus, the values of the separability between the built-up and the bare soils are not only the lowest, i.e., 47.9 in Yaoundé and 41.8 in Bangui, but they are also way below the best average separability, respectively sets at 60.8 and 57.9. Visually, while the classification of Yaoundé is over-informative in and around the built-up, the one of Bangui presents a low built-up detection compared to the RGB image and the BABI. Overall, on the two sites, the NDBSUI, MNBI, NDBI and UI are over-informative compared to the BABI ( Figure 9).  , rows 2 and 4), the BABI is efficient than compared spectral indices in reducing both high and low reflectance noise.  Further, the accuracy assessment was conducted between the unsupervised classification of all the indices compared with RGB classification image used as reference. The random sampling method proposed by [34] was used with 200 locations. The BABI is validated in Yaoundé with an overall accuracy (OA) of 96% and a kappa coefficient (KC) of 0.94, and in Bangui with respectively 98.5% and 0.97 (Table 8). On the two sites, the built-up class is spotted with 100% of OA and 1 of KC, and few water pixels were affected to vegetation class. These scores decrease in the order NDBSUI, MNBI, NDBI and UI in the two cities, due to the generalized built-up detection and the others classes confusion.

Biophysical Noise Reduction Ability
According to the second specific goal, the BABI has been able to reduce surroundings brightness and shadowing. The histograms automatically produced for the maps floated [0-1] are monomodal for the BABI, i.e., only one population, assumed to be built-up, is highlighted. The same histograms are bimodal at different degrees for the compared indices, inferring the presence of information other than built-up ( Figure 11). In fact, the distribution of the pixels is mathematically assumed to be normal (Gaussian) and continuous [35]. A full one-peak bell-shaped curve identical to the observation densities (Figure 12), i.e., symmetrical, is considered satisfactory for regrouping similar pixels.
Based on a subset of 50,000 pixels described in ten classes, densities are concentrated between the first five classes, the standard error U 0 , V W 0.0001 and X 0.05 . The density distribution describes a full bell-shaped curve slightly right-skewed (positive skewness), with Y 0.268 and Z 0.065 in Yaoundé, for Y 0.283 and Z 0.04 in Bangui. The histogram limits the highest peaks in the tight bounds [0.2-0.4], which confirms the lower stretching of the image. This distribution fitting explains the noise reducing, a low confusion between LULC classes and consequently the neat separation of the built-up from surrounding features as pointed out by the accuracy assessment. Comparatively as shown in figure 13, the MNBI and NDBSUI trends are less stretched as for the BABI, their densities are concentrated with bell-shaped curves and their parameters (Y and Z) are low. While the densities of the UI and NDBI are widely stretched, with bell-shaped curves evolve around two to four distribution peaks, and their parameters are higher than BABI ones. These statements support higher trends of classes confusion in other indices, although the MNBI and NDBSUI results are close to the BABI one.

Discussions
To come up with the BABI, it was tested that urban land surface brightness mixes environmental and built-up information. Using another set of manipulations using the 8-bits recoded results of BABI and comparative indices, one can noticed that the built-up values are higher than those of the other land cover objects, although there are two cases of stretching ( Figure 14). In Yaoundé where the forest cover has considerably decreased, exposing rough hilly slopes and rocky soils, all the LULC objects are detected in the high values and close to each other in the stretching interval . Whereas in Bangui presenting an important forest coverage, less bare soil visibility, more shadowy rough high-altitude terrain and an important stream of the Ubangui river, LULC objects are detected in lower values in between the stretching interval .
On 500 pixels extracted in the highest urbanized area with mixed LULC classes BABI, NDSI/BSI, shadow index and NDISI, the trends confirm the separation between objects. Therefore, built-up can be detected in high or low values in comparison with other LULC spectral indices. As shown in figure 14, trends of BABI are closed to SI but higher than NDSI, while NDISI has the lower values in Yaoundé. For Bangui, trends of the BABI are the lowest, while BSI, SI and NDISI are higher. As the BABI better separates LULC object features, NDISI can be otherwise complementary in detecting dark built-up features (in Yaoundé) and natural impervious surfaces (in Bangui) than effective buildings, as it is closer to soil (NDSI/BSI) and shadow (SI) features.
As the high correlation coefficients were assumed to express the level of noise between and around the built-up area, these lower values are another set of proofs supporting the efficiency of BABI to discriminate built-up from surrounding features.

Conclusion
The main goal of this research has been to reduce the land surface brightness and shadow noise that is very challenging for the built-up extraction in unplanned cities with mixed housing materials. The Brightness Adjusted Built-up Index, BABI, gives an improved visual layout with low built-up generalization, confirmed by overall accuracies of 96% and 98.5% respectively in Yaoundé (Cameroon) and Bangui (Central African Republic), way higher than the four comparative spectral indices. Ongoing improvements consist in conducting the full process using a neural network. Further, the computation of BABI was tested in some urban subsets of Sentinel 2 satellite images with satisfactory results, but could not be completed for both whole areas of study because of clouds coverage. Presently, some tests are being conducted for other areas outside the tropics. One advantage of this method can be its potential integration in the population and housing census process of developing countries with low budget allocated. Thus, the BABI may represent an asset for an accurate mapping of human settlements and a better delineation of counting zones using freely accessible satellite images.