In this paper, we establish a workflow for estimation of built-up density and height based on multispectral Sentinel-2 data. To do so, we render the estimation of built-up density and height as a supervised learning problem. Given the rational level of measurement of those two target variables, the regression estimation problem is regarded as finding the mapping between an incoming vector, i.e., ubiquitously available features computed from Sentinel-2 data, and an observable output (i.e., training set), which is derived over spatially limited areas in an automated manner. As such, training sets are automatically generated from a joint exploitation of TanDEM-X mission elevation data and Sentinel-2 imagery, and, as an alternative, from cadastral sources. The training sets are used to regress the target variables for spatial processing units which correspond to urban neighborhood scales. From a methodological point of view, we introduce a novel ensemble regression approach, i.e., multistrategy ensemble regression (MSER), based on advanced machine learning-based regression algorithms including Random Forest Regression, Support Vector Regression, Gaussian Process Regression, and Neural Network Regression. To establish a robust ensemble, those algorithms are learned with a modified version of the AdaBoost.RT algorithm. However, to reliably ensure diversity between single boosted regressors, we include a random feature subspace method in the procedure. In contrast to existing approaches, we selectively prune non-favorable regressors trained during the boosting procedure and calculate the final prediction by a weighted mean function on the residual models to ensure enhanced accuracy properties of predictions. Finally, outputs are concatenated into a single prediction with a decision fusion strategy. Experimental results are obtained from four test areas which cover the settlement areas of the four largest German cites, i.e., Berlin, Hamburg, Munich, and Cologne. The results unambiguously underline the beneficial properties of the MSER approach, since all best predictions were obtained with a boosted regressor in conjunction with a decision fusion strategy in a comparative setup. The mean absolute errors of corresponding models vary between 3 and 16% and 1–5.4 m with respect to built-up density and height, respectively, depending on the validation strategy, size of the spatial processing units, and test area. Also in a domain adaptation setup (i.e., when learning a model over a source domain and applying it over a geographically different target domain) numerous predictions show comparable accuracy levels as predictions obtained within a source domain. This further underlines the viability to transfer a model and, thus, enable a substitution of the training data in the target domains.

在本文中，我们建立了一个基于多光谱Sentinel-2数据估算堆积密度和高度的工作流。为此，我们将建筑密度和高度的估计作为有监督的学习问题。给定这两个目标变量的合理测量水平，回归估计问题被视为找到输入向量（即从Sentinel-2数据计算得出的普遍可用特征）与可观察到的输出（即训练集）之间的映射，它以自动化方式在空间有限的区域中得出。这样，可以从TanDEM-X任务高度数据和Sentinel-2图像的联合开发中自动生成训练集，或者从地籍来源中自动生成训练集。训练集用于回归与城市邻里尺度相对应的空间处理单元的目标变量。从方法论的角度出发，我们基于基于先进的机器学习的回归算法（包括随机森林回归，支持向量回归，高斯过程回归和神经网络回归）引入一种新颖的集合回归方法，即多策略集合回归（MSER）。 。为了建立鲁棒的集成，可以使用AdaBoost.RT算法的修改版来学习这些算法。但是，为了可靠地确保单个增强型回归变量之间的多样性，我们在程序中包括了随机特征子空间方法。与现有方法相反，我们选择性地修剪在增强过程中训练的不利回归变量，并通过对残差模型的加权平均函数计算最终预测，以确保增强的预测准确性。最后，使用决策融合策略将输出串联到单个预测中。从覆盖四个德国最大城市（柏林，汉堡，慕尼黑和科隆）居住区的四个测试区域获得了实验结果。该结果明确地强调了MSER方法的有益特性，因为在比较设置中，所有最佳预测都是使用增强型回归器结合决策融合策略获得的。相对于堆积密度和高度，相应模型的平均绝对误差在3％至16％和1–5.4 m之间变化，取决于验证策略，空间处理单元的大小和测试区域。同样在域适应设置中（即，当在源域上学习模型并在地理上不同的目标域上应用模型时），许多预测显示出与源域内获得的预测相当的准确性级别。这进一步强调了转移模型的可行性，因此可以替换目标域中的训练数据。