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Estimation of the Digital Surface Model (DSM) and building heights from single-view aerial imagery is a challenging inherently ill-posed problem that we address in this paper by resorting to machine learning. We propose an end-to-end trainable convolutional-deconvolutional deep neural network architecture that enables learning mapping from a single aerial imagery to a DSM for analysis of urban scenes. We perform multisensor fusion of aerial optical and aerial light detection and ranging (Lidar) data to prepare the training data for our pipeline. The dataset quality is key to successful estimation performance. Typically, a substantial amount of misregistration artifacts are present due to georeferencing/projection errors, sensor calibration inaccuracies, and scene changes between acquisitions. To overcome these issues, we propose a registration procedure to improve Lidar and optical data alignment that relies on Mutual Information, followed by Hough transform-based validation step to adjust misregistered image patches. We validate our building height estimation model on a high-resolution dataset captured over central Dublin, Ireland: Lidar point cloud of 2015 and optical aerial images from 2017. These data allow us to validate the proposed registration procedure and perform 3D model reconstruction from single-view aerial imagery. We also report state-of-the-art performance of our proposed architecture on several popular DSM estimation datasets.