Generalizing machine learning regression models using multi-site spectral libraries for mapping vegetation-impervious-soil fractions across multiple cities
Introduction
Optical satellite remote sensing has great potential for characterizing urban environments. Particularly the mapping of urban composition according to the vegetation-impervious-soil (VIS) framework (Ridd, 1995) has received considerable attention. This framework represents urban areas in a continuous ternary mixing diagram of vegetation, impervious, and soil cover fractions, and was proposed as a standardized mapping scheme to support urban ecosystem analysis, to monitor urban change processes, and for linking urban composition to urban morphology (Ridd, 1995). Numerous studies have exploited multispectral satellite data for mapping individual or all VIS components for different cities around the world (Phinn et al., 2002; Powell et al., 2007; Pu et al., 2008; Rashed et al., 2003). To match the quantitative nature of the VIS framework and to account for mixed pixels typical of urban environments, sub-pixel cover fraction mapping techniques based on linear spectral mixture analysis and its variants (Deng and Wu, 2013; Rashed et al., 2003; Small and Lu, 2006), or based on quantitative empirical modeling with regression algorithms or neural networks (Okujeni et al., 2015; Pu et al., 2008; Walton, 2008) have been widely adopted.
With the ongoing development in spaceborne imaging spectrometry, novel opportunities for a variety of environmental research fields arise. Several hyperspectral satellite missions are currently in preparation, including the Environmental Mapping and Analysis Program (EnMAP, Guanter et al., 2015). EnMAP will frequently collect high spectral resolution images over large geographic areas at a 30 m resolution, which will be passed through standardized processing chains to obtain consistent surface reflectance products. The availability of such imagery will open up new opportunities for global comparative analyses of urban composition and compositional changes. The hyperspectral information will most likely enhance the spectral separability of urban construction materials and vegetation types (Gamba and Dell'Acqua, 2006; Herold et al., 2003), which can lead to more accurate VIS maps. In addition, the spectral benefits will most likely enable the extension of VIS mapping into thematically more detailed impervious and vegetation sub-categories (Okujeni et al., 2015; Roberts et al., 2012; Wetherley et al., 2017). By offering the opportunity to derive more accurate and detailed descriptions of urban composition worldwide, spaceborne imaging spectrometry has considerable potential to introduce a new quality to urban remote sensing.
With regard to satellite imagery with large spatial and high temporal coverage, more generalized mapping and monitoring approaches that can be transferred throughout space and/or time are desired. Generalizing methods in remote sensing were originally introduced as “signature extension” (Botkin et al., 1984). Signature extension aims to move beyond image-by-image approaches by applying a model, which was trained with signatures from one image, to another image from a different geographic location (spatial generalization), a different acquisition time (temporal generalization), a different sensor (across-sensor generalization), or a combination thereof (Foody et al., 2003; Pax-Lenney et al., 2001; Woodcock et al., 2001). In the urban context, globally applicable models were mainly developed for mapping urban extent from MODIS data (Schneider et al., 2010) or different built-up cover types using Landsat data in combination with a digital surface model (Pesaresi et al., 2016). Several studies have explored the use of generalized approaches for mapping urban composition from Landsat data only. Amongst others, Small (2005) demonstrated the use of a global spectral mixture model to map high albedo substrate, vegetation, and dark surface fractions for 28 cities worldwide. Kaspersen et al. (2015) mapped impervious fractions for eight European cities using a regionally generalized regression model. Sexton et al. (2013) made use of a temporally generalized regression model to produce annual maps of impervious surface cover in the Washington-Baltimore metropolitan region between 1984 and 2010. Wang et al. (2014) examined the temporal generalization capability of neural networks, random forest classification, and regression trees for characterizing vegetation fraction dynamics in Zhongwei City between 1990 and 2010.
The availability of stable and comparable surface reflectance units between images is a crucial factor for successfully extending training signatures across scenes (Woodcock et al., 2001). Differences in acquisition conditions and dates, sensor characteristics, reflectance retrieval algorithms, etc., can lead to substantial radiometric inconsistencies between images, which can limit the model transfer across scenes (Olthof et al., 2005; Pax-Lenney et al., 2001). Studies therefore have focused on adjusting images by improved radiometric and atmospheric pre-processing (Olthof et al., 2005; Pax-Lenney et al., 2001), or on adapting the training signatures to individual images (Gray and Song, 2013).
The availability of comprehensive training information is another important factor influencing model generalization. Training signatures may not represent the full diversity and variability of cover types present in new regions or at different periods of time, which limits the model transferability across space and time. The use of multi-source training information representative for multiple sites or dates constitutes a suitable means to overcome these limitations. In the urban context, for example, the aforementioned studies by Kaspersen et al. (2015) and Sexton et al. (2013) demonstrated the use of specific multi-site and multi-annual training areas with impervious reference fractions calculated from high resolution land cover information for spatial and temporal regression model generalization. While this approach is straightforward and produces reliable results, the regression model training fully depends on the availability of accurately co-registered, high resolution reference data. In this regard, multi-source spectral libraries constitute an alternative solution that is independent from the availability of representative training areas and therefore marks a step forward towards more generalized mapping. For example, Michishita et al. (2012) demonstrated the use of a combined multi-annual library for mapping changes in urban composition for five time steps between 1987 and 2009. Similarly, Dudley et al. (2015) demonstrated that a multi-seasonal library can improve vegetation mapping and may support assessments regardless of the seasonality of the input image. All of these studies share the conclusion that multi-source training information provides a suitable means to enhance the spatial and temporal applicability and transferability of mapping models, and consequently their generalization capabilities.
With regard to the unprecedented opportunities of forthcoming spaceborne imaging spectrometers for assessing urban composition globally, the overarching goal of this study was to investigate how single regression models can be spatially generalized for VIS fraction mapping across multiple cities. We selected the combination of support vector regression (SVR) with synthetically mixed training data for fraction mapping (Okujeni et al., 2013). This approach proved to effectively handle urban cover types with high within-class variability, between-class similarity, and spectral mixing from airborne to spaceborne scales (Okujeni et al., 2015; Rosentreter et al., 2017). Moreover, this library-based approach is independent from the spatial context of the work with training areas and appears better suited for more generalized regression model training. Based on spectral libraries for the cities of Berlin (Germany), Brussels (Belgium), and Santa Barbara (U.S.), we created three separate models from the single libraries (henceforth referred to as “local models”), and one model from a combined multi-site library (henceforth referred to as “generalized model”). VIS mapping was subsequently conducted on simulated EnMAP data covering five cities. These included the three cities that were each represented in one local and the generalized model (henceforth referred to as “known sites”), and the two cities San Francisco Bay Area (U.S.) and Munich (Germany) that were not represented in the models (henceforth referred to as “unknown sites”). With this setup, we considered both spectrally more similar and dissimilar sites, known and unknown mapping constellations, as well as the challenges related to the use of different hyperspectral sensors underlying the EnMAP simulation. To demonstrate the good performance and improved transferability of a generalized regression model based on libraries from multiple cities for VIS fraction mapping, we defined two research questions:
- (1)
How does the performance of a generalized model compare to local models in mapping their respective sites?
- (2)
Is a generalized model more transferable than local models when transferred to unknown sites?
Section snippets
Study sites
The spatial extents of our five study sites correspond to the outline of the available hyperspectral images or a subset extracted thereof (Fig. 1). The Berlin site is located in northeastern Germany and covers a subset of the city's urban-rural gradient. The Brussels site is located in central Belgium and covers the city center and a cross-section through the city's urban-rural gradient. The Santa Barbara site is located in California and comprises the cities and surroundings of Santa Barbara
Development of local and generalized regression models
The schematic workflow for developing local and generalized regression models for fraction mapping is illustrated in Fig. 3. For regression model training, synthetically mixed data from spectral libraries are used (Okujeni et al., 2013) (Fig. 4). These are sets of pure library spectra that are structured according to the land cover categories of interest, their multiple artificial spectral mixtures, together with related mixing fractions per category. The synthetic spectra are then used to
Performances of the generalized and the local models in Berlin, Brussels, and Santa Barbara
The overall accuracy of the generalized model (BE + BR + SB) compared to the local models (BE, BR, and SB) in mapping their respective sites is illustrated in Fig. 5. The generalized model produced AV-MAEs of 8.5% for Berlin, 12.2% for Brussels, and 11.0% for Santa Barbara. Differences in AV-MAEs compared to the local model applications were small and within a range of ±0.7%. However, the transfer of the local models to the two other cities led to a considerable decrease in map accuracy, i.e.,
Application of the generalized model and the local models to known sites
We compared the performances of the generalized model and the local models when applied to the known sites Berlin, Brussels, and Santa Barbara. This comparison examined whether model generalization using a multi-site spectral library was possible without a relevant loss in mapping quality. Overall accuracies (Fig. 5), class-wise accuracies (Fig. 7), and fraction maps (Fig. 6) confirmed that the generalized model was well suited for accurate VIS mapping across the three cities. The performance
Conclusions
The overarching goal of this study was to examine how single regression models can be spatially generalized for VIS fraction mapping across multiple cities. With regard to the opportunity for global assessments of urban composition by means of forthcoming spaceborne imaging spectrometers, our analyses targeted the mapping of VIS fractions from simulated EnMAP data covering the study sites Berlin, Brussels, Santa Barbara, San Francisco Bay Area, and Munich. Based on our findings, we conclude
Acknowledgments
This research was funded by the Belgian Federal Science Policy (Belspo) as part of the UrbanEARS project (SR/00/307). The Berlin HyMap image acquisition and processing was funded by the Federal Ministry of Research and Education (BMBF, FKZ01LK0901A). The APEX image acquisition and processing was funded by Belspo (BELAIR SONIA 2015, SR/03/333). The AVIRIS images were supplied by the NASA Jet Propulsion Laboratory (JPL). Further image pre-processing and spectral library development for the Santa
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